Multicultural Curriculum Transformation in Science, Technology, Engineering, and Mathematics 9781498580526, 9781498580519

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Multicultural Curriculum Transformation in Science, Technology, Engineering, and Mathematics

FOUNDATIONS OF MULTICULTURAL EDUCATION Series Editor Christine Clark, University of Nevada, Las Vegas Advisory Board Amanda VandeHei, Nevada State College; Kenneth Fasching-Varner, Louisiana State University; Zaid Haddad, University of Texas, San Antonio The series focuses on explicating subject area- and grade level-specific multicultural curriculum transformation geared for PK-12 pre-service teacher education and inservice teacher professional development. It is geared towards PK-12 public school educators and administrators, as well as for teacher educators. However, the series is appropriate for all PK-12 teaching and learning contexts in which critical engagement of diversity is foundational in assuring educational equity and excellence for all students. There is a great need for contemporary, comprehensive, and teacher-friendly resources that provide concrete subject- and grade-specific examples for how to go about transforming mainstream, traditional, and/or Eurocentric curriculum. In particular, resources that “work” for PK-12 public school teachers, regardless of the specific standards and/or standardization culture of their schools, are needed. Because standards and related culture change frequently, it is also important that these resources are flexible enough to allow for pre- and in-service adaptation of them to their particular teaching contexts. As PK-12 public school student and parent populations around the country continue to become more and more diverse while both teacher candidate and veteran teacher diversity remains largely stagnant, resource rigor is more crucial than ever. Pre- and in-service teachers need specialized developmental support to be able to effectively adapt curriculum that is authentically multicultural, promotes teacher reflection, and, therefore, meaningfully addresses the key goal of PK-12 education—the education of our nation’s youth. The series invites PK-12 teachers and teacher educators to share their experiences and expertise in developing sociopolitically located multicultural curricular approaches for teaching in content- and grade-level specific manners. Titles in Series Foundations of Multicultural Curriculum Transformation in Science, Technology, Engineering, and Mathematics edited by Christine Clark, Amanda VandeHei, Kenneth Fasching-Varner, and Zaid M. Haddad

Multicultural Curriculum Transformation in Science, Technology, Engineering, and Mathematics Edited by Christine Clark, Amanda VandeHei, Kenneth J. Fasching-Varner, and Zaid M. Haddad

LEXINGTON BOOKS

Lanham • Boulder • New York • London

Published by Lexington Books A wholly owned subsidiary of The Rowman & Littlefield Publishing Group, Inc. 4501 Forbes Boulevard, Suite 200, Lanham, Maryland 20706 www.rowman.com Unit A, Whitacre Mews, 26-34 Stannary Street, London SE11 4AB Copyright © 2018 by The Rowman & Littlefield Publishing Group, Inc. All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without written permission from the publisher, except by a reviewer who may quote passages in a review. British Library Cataloguing in Publication Information Available Library of Congress Cataloging-in-Publication Data Available ISBN 978-1-4985-8051-9 (cloth : alk. paper) ISBN 978-1-4985-8052-6 (electronic) The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI/NISO Z39.48-1992. Printed in the United States of America

I know how strange it can sound to say that math literacy . . . is the key to the future of disenfranchised communities, but that’s what I think, and believe with all of my heart. Today . . . the most urgent social issue affecting poor people and people of color is economic access. In today’s world, economic access and full citizenship depend crucially on math and science literacy. . . . economic access, taking advantage of new technologies and economic opportunity, demands as much effort as political struggle required in the 1960s. . . . the absence of math literacy in urban and rural communities throughout this country is an issue as urgent as the lack of registered Black voters in Mississippi was in 1961. I believe we can get the same kind of consensus we had in the 1960s for the effort of repairing this [and] . . . that solving the problem requires exactly the kind of community organizing that changed the South [then] . . . —Robert Moses (2002, pp. 5–6)

Contents

Preface xi Acknowledgments xv Introduction xvii Christine Clark, Amanda VandeHei, Kenneth J. Fasching-Varner, and Zaid M. Haddad PART I  MATHEMATICS  1  Transforming Family “Math Night” with Latina/Latino Middle School Parents: Communicating about the Adoption of Common Core State Standards Yolanda De La Cruz

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 2  Using Iterative Visuals and Virtual Manipulatives to Support English Language Learners in Mathematics Education Sarah A. Roberts

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 3  Rethinking the Teaching and Learning of Latina/Latino Students to Promote a Multicultural Mathematics Education Javier Díez-Palomar and Carlos A. LópezLeiva

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 4  Students Who Speak English as a Second Language: Preparing Teachers for Changing Demographics—An Innovative and Collaborative Approach Bettibel Kreye and Gresilda A. Tilley-Lubbs vii

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Contents

PART II  SCIENCE  5  Teaching Biology in the Age of the Next Generation Science Standards: Methodology for Teaching in High Needs Schools Antoinette Linton  6  LGBT-Inclusion Across the Life Science Curriculum Mary Hoelscher  7  Earth Shaking Dragons and Orphan Tsunamis: Transforming Middle School Earth Science and STEM through Studying Ancient Science Inquiry and Multicultural Collaborations in Earthquakes, Tsunamis, and Disaster Preparedness Marna Hauk and Adam Masaki Joy  8  Classroom Meteorologists: Transforming Science Content in a Dual Language Second Grade Classroom Sandra Lucia Osorio

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PART III   MATHEMATICS AND SCIENCE  9  Rethinking Art in Mathematics and Science Jeff Sapp

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PART IV  ENGINEERING 10  Effective Engineering Models for Multicultural Curriculum Transformation in STEM: Engineering for All Laura Luna Twanelle Walker Majors, and Jennifer Meadows

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PART V  TECHNOLOGY 11  Multicultural Technology Education: The Need to Teach Digital Technologies to All Students Janessa Schilmoeller, Lori Griswold, and Neal Strudler

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PART VI  MATHEMATICS, SCIENCE, ENGINEERING, AND TECHNOLOGY 12  Coming Out of the Lab Closet: Queering STEM Education for Student Success and Well-Being Allison Mattheis, Jeremy B. Yoder, and Dixon Perey 13  Considering Women’s Ways of Knowing in STEM Tracy Arnold, Eshani Gandhi, Schetema Nealy, and Brian Trinh

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Coda 251 Christine Clark, Amanda VandeHei, Kenneth J. Fasching-Varner, and Zaid M. Haddad Resources 255 Index 265 About the Editors and Contributors

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RATIONALE This volume has been developed to respond to the great need for contemporary, comprehensive, and teacher-friendly resources that provide concrete subject- and grade-specific examples for how to go about transforming mainstream, traditional, and/or Eurocentric curriculum. More specifically, this volume contains resources that “work” for PK-12 public school teachers regardless of the specific standards and/or standardization culture of their schools are key, but because these standards and related culture change frequently, it is also important that these resources are flexible enough to allow for pre- and in-service adaptation of them to their particular teaching contexts. Resource flexibility is also crucial as PK-12 public school, student, and parent populations around the country continue to become more and more diverse, at the same time that both teacher candidate and veteran teacher diversity, as well as their preparation and on-going development in diversity, remains largely stagnant. Pre- and in-service teachers need specialized developmental support to be able to effectively adapt or, better, create anew, curriculum that is authentically multicultural, promotes teacher reflection, and, therefore, meaningfully addresses the key goal of PK-12 education—the education of our nation’s youth. It is toward these ends that this volume is dedicated.

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AUDIENCE This volume is primarily designed for in-service PK-12 teachers and administrators interested in multicultural curriculum transformation, whether or not that interest is intrinsically or extrinsically motivated (i.e., based on genuine concern for educational equity and excellence, or the result of policy mandates [sincere or contrived] and/or disciplinary interventions). Secondary audiences for this volume are teacher education faculty and their pre-service teacher education candidates. APPROACH This volume is designed to facilitate the growth and development of educators who embrace/want to embrace the efficacy of multicultural education for all students; it is also designed to “bring around” even long-standing doubters of and detractors to multicultural education as to the efficacy of this approach for bringing about educational equity and excellence for all students. This volume is also designed for teacher professional development providers and PK-12 district and school curriculum designers/reformers who choose to and/or are compelled to maintain fidelity to a standards-driven educational system while also providing a quality education to all students; two mandates that are often at odds with one another—this volume is designed to reduce if not resolve this dichotomy. Finally, this volume is designed for anyone interested in a better understanding of multicultural curriculum transformation—what it is, how and why it came about, the good it can and does do all students, how to undertake it in a meaningful and, ultimately, educationally successful way—perhaps especially those educational policy makers who have never spent a day in a PK-12 classroom. UNIQUENESS In general, the challenge with comparable resources to this volume is that they are dated, or so specific or so broad in myriad ways that they do not do enough on either end to help PK-12 teachers develop an internal schema for how to think about, understand, organize, and execute contemporary multicultural curriculum transformation in manners that work for their content areas, grade levels, and other teaching and learning context realities. Accordingly, this volume seeks to: 1) engage PK-12 teachers in the work of



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multicultural curriculum transformation by meeting them where they are and/ or in the context in which they teach; 2) interest and excite PK-12 teachers in multicultural curriculum transformation in order to push them to go beyond the superficial with it; and, 3) equip and inspire PK-12 teachers to continue the work of multicultural curriculum transformation on their own—to become multicultural educators in all aspects of their lives. ORGANIZATION, BENEFIT, AND USE This volume focuses on multicultural curriculum transformation in science, technology, engineering, and mathematics or STEM subject areas broadly, while also focusing on sub-content areas (e.g., earth science, digital technologies) in greater detail. The discussion of each subcontent area outlines critical considerations for multicultural curriculum transformation for the subcontent areas by grade level (early childhood and elementary school education, middle and/or junior high school education, and high school education) and then by organizing tool parameters: standards (both in a generalized fashion, and specific to Common Core State Standards, among other standards), educational context, relationships with and among students and their families, civic engagement, considerations pertaining to educational “ability” broadly considered (for example, for gifted and talented education, bilingual gifted and talented education, “regular” education, bilingual “regular” education, special education, bilingual special education), as well as relative to specific content and corresponding pedagogical considerations, including evaluation of student learning and teaching effectiveness. In this way, the volume provides a conceptual framework and concrete examples for how to go about multiculturally transforming curriculum in STEM curricula. The volume is designed to speak with PK-12 teachers as colleagues in the multicultural curriculum transformation work at focus in each subject area and at varied grade levels. Readers are exposed to “things to think about,” but also given curricular examples to work with or from in going about the actual, concrete work of curriculum change. It bridges the gaps between preparing PK-12 teachers to be able to 1) independently multiculturally adapt existing curriculum, and, 2) create new multicultural curriculum differentiated for their content areas and grade levels, while also, 3) providing ample examples of what such adapted and new differentiated curricula looks like. In so doing, this volume also bridges the gaps between the theory and practice of multicultural curriculum transformation in higher and PK-12 educational contexts.

Acknowledgments

There are several people we would like to thank for their help in pulling this volume together. Most important are our significant others. Your support of, and patience with us while we worked on this project is what ultimately made it all possible. The support of other immediate and extended family members, friends, and colleagues was also invaluable. The in-service teacher focus group participants provided us pivotal insight into how the volume was conceptualized overall, and, more specifically, the “theme and variation” organization of the content-specific chapters. Of course, the volume would not be what it is without the wonderful assistance of the volumes’ guest editors—Sandra Candel, Lauren Bell, Mónica J. Hernández-Johnson, and Cindy Bezard—as well as heart-felt contributions of the chapter authors, Yolanda De La Cruz, Javier Díez-Palomar, Eshani Gandhi, Lori Griswold, Marna Hauk, Mónica Hernández-Johnson, Mary Hoelscher, Bettibel Kreye, Antoinette Linton, Sandra Lucia Osorio, Laura Luna, Carlos LópezLeiva, Twanelle Majors, Adam Masaki Joy, Allison Mattheis, Jennifer Meadows, Schetema Nealy, Dixon Perey, Sarah Roberts, Jeff Sapp, Janessa Schilmoeller, Neal Strudler, Antoinette Linton Tilley-Lubbs, Brian Trinh, and Jeremy Yoder. We also appreciate the contributions of the cover blurb authors for the volume. Your collective willingness to lend your professional stature to this project has meant the world to us. Finally, we want to thank Lexington and its acquisitions and editorial staff for their commitment to this volume from its inception to its publication.

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Introduction Christine Clark, Amanda VandeHei, Kenneth J. Fasching-Varner, and Zaid M. Haddad

We, the editors of this volume, are teachers and teacher educators. We have been public PK-12 elementary, middle, and high school teachers in largely urban districts, ranging from medium sized to large, in the Southwest and the Northeast. We have taught in so-called regular and special education contexts, including in “behavioral schools.” We have taught in teacher preparation programs in mostly public higher education, again in the Southwest and Northeast, as well as in the Midwest and Southeast. We love being teachers, but, more so, we love teaching. We love interacting with our students and their families, and we love our reciprocal coengagement with students in the creative, inspiring crafts of teaching and learning. We also recognize that teaching, especially in the public arena, is, and has been for some time, in crisis. The inherently political nature of teaching and learning—the “real life” implications of who we are and who we are not as teachers (racially, ethnically, linguistically, socioeconomically, etc.), as well as what we teach, to whom, where, and how, remain fiercely contested as a function of our social order. The extent to which we, as teachers and teacher educators, are conscious of these implications and, once conscious, choose to act or not— through education and beyond—to change or reinforce the social order, has an impact on the teaching crisis in myriad ways. So many of us in teaching at all levels experience ever-growing tensions between increasing externally imposed job expectations and requirements (education policy), and actual teaching (pedagogy); between what we are told we must do to keep our jobs (educational administration), and what we know works in teaching (evidencebased praxis); between our own economic interest as teachers (private conxvii

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cerns), and the socioemotional interest of our students and their families (public concerns). This volume was developed as a resource for PK-12 teachers, teacher educators, and science, technology, engineering, and mathematics (STEM) educators to improve the quality of instruction (teaching), instructional experience (learning), and academic outcomes for all students, especially historically marginalized and minoritized students (HMMS) persistently underserved by public education in the United States (Walls, 2017). While most educators—as generalists or specialists in a field of study—know “traditional” or “Eurocentric” content and associated, largely didactic instructional strategies, few have ever had the opportunity to come to know their content and how to share it through “multicentric” or multicultural lenses. Multicultural curriculum transformation (MCT) can be understood as a process by which existing “traditional” or “Eurocentric” (imbued with uncontested dominant discourses) curricula are modified to equitably reflect “nontraditional” or “multicentric” curricular considerations related to the learning environment, relationships and relationship building related to the learning environment, content, pedagogy and evaluation in discipline-specific and grade level appropriate manners. MCT may also describe the on-going modification of already modified curricula. MCT can and should be differentiated from multicultural curriculum development (MCD), a process by which new curricula are created to equitably reflect the broad range of multicultural curricular considerations related, again, to environment, relationships, content, pedagogy and evaluation in discipline-specific and grade level appropriate manners. MCD also describes the on-going creation of multicultural curricula. Both MCT and MCD emerge from the field of multicultural education (MCE). MCE is an academic discipline, with roots in ethnic studies, that is generally situated within teacher education and/or curriculum and instruction. From a critically conscious or sociopolitically-located lens—with attention to dynamics of power in schools and society: 1.  MCE documents, across the curriculum at all levels of instruction, what has been taught, how it is has been taught, in what contexts, by whom, for whom, and toward what ends; 2.  MCE contests the accuracy and completeness of what has been taught, as well as the efficacy of how it has been taught, where, by whom, and its effectiveness for all students, but especially HMMS; and, 3.  MCE establishes processes through which education can be enacted to interrupt and remediate educational inequities, and ensure educational success for all students but especially HMMS, including through MCT and MCD.



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As the preceding paragraphs begin to reveal, MCT is a complex undertaking that is never-ending. For these reasons, it is challenging to teach—even to those who want to learn it—because doing so does not fit easily into existing educational frameworks (e.g., academic course structures, professional development sessions, accrediting body conference sessions, etc.). At the same time, students in the most pervasively underserved PK-12 schools need MCT-inspired and -adept teachers immediately. Recognizing the nature of the challenge and the urgency of need here, in developing this volume, we conducted two informal focus group discussions with in-service teachers in one of the largest metropolitan school districts on the country that is also persistently among the most low-performing, and that has one of the highest teacher-student demographic diversity gaps and an annual recurring teacher shortage of between 800–1200 teachers districtwide (Rebora 2016; Ryan, 2016; Takahashi, 2012). We, the coeditors of this volume, have been teachers in this district, and/or we have served as teacher educators for pre-service and veteran teachers in this district. In both of these roles, we situate ourselves both as part of the problem in teaching and teacher education—locally and nationally—as well as part of the solution, however imperfectly (Heim, 2016; LPI, 2017; Podolsky, Kini, Bishop, & DarlingHammond, 2016; Strauss, 2016; Sutcher, Darling-Hammond, & CarverThomas, 2016; U.S. DOE, 2016; Villegas, Strom, & Lucas, 2012). Three of us are white, one Asian, and the overwhelming majority of our PK-12 and higher education colleagues are white, though the overwhelming majority of our PK-12 students are from HMM communities. While these demographics alone do not explain the crisis in education, changing them is a part of the solution. Accordingly, we are all deeply committed to diversifying the teacher pipeline. At the same time, we are equitably committed to improving the preparedness of the existing, largely white, teacher workforce to teach all students, but, once again, especially HMMS. We know that the path to excellence in teaching is through diversity, not around it. The teachers in our focus groups were comprised of new teachers, midcareer teachers, and veteran teachers; teachers in the STEM fields at the high school level, as well as elementary and middle school generalists for whom STEM is one of many content areas they teach; high school teachers in other content specialties; and teachers who are pursuing advanced education in moving to teach in higher education contexts, both in teacher education and in STEM fields. These teachers were also racially and ethnically diverse, including black American, Latinx, and Asian/Pacific American teachers, and European/white American, as well as diverse along other identity dimensions (gender, sexual orientation, religion, and socioeconomic class background). We conducted these focus group discussions with these teachers to gain

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insight into how to best structure volume chapters to best appeal to, and meet the continuing educational needs of, PK-12 public school teachers, especially white teachers (WT) teaching high percentages of HMMS in poorly resourced schools. Data from the focus groups were culled into a “chapter organizing tools” format (discussed further below) for our volume chapter authors to use as “guidelines” in structuring their chapters as frameworks or templates for undertaking, and/or iterative of step-by-step processes in multicultural curriculum transformation to the extent possible, while, at the same time, maintaining their chapters’ uniqueness and creativity. CHAPTER ORGANIZING TOOLS The teachers in our informal focus groups indicated strong preferences for a high degree of “theme and variation” uniformity of organization across all of the chapters in the volume; their sense was that providing this would facilitate its ease of use as a “reference book.” Accordingly, we asked that the following chapter components or “organizing tools” inform and guide the authors’ chapter development, again, to the extent possible, while, at the same time, maintaining their chapters’ uniqueness and creativity. Basic Information Chapter authors were asked to integrate into the opening narrative of the chapter, the STEM content area(s) and grade level(s) at focus in the chapter, and for whom they imagined—as their reader audience—it would be most valuable and why. Chapter authors were also asked to make an explicit connection of the work being discussed in the chapter to MCT: how and why what the chapter describes, discusses, and analyzes is, in fact, an example of sociopolitically located multicultural education developed through a STEMfocused MCT process (as opposed to a more superficial form of multicultural education (e.g., a “heroes and holidays” approach) or simply education for a specific HMMS group (e.g., for students who speak English as a second language). In developing this section, chapter authors were asked to review three published works supporting MCT: 1) Nieto’s (n.d.) definition of multicultural education; 2) Bode’s (2006) synthesis of approaches to MCE; and, 3) Clark’s (2002) overview of MCT. Speak to Teachers Directly Chapter authors were asked not to assume that readers would not have prior knowledge about how to undertake such transformation, but also to not as-



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sume that they have no knowledge as to how to undertake such transformation. They were also asked to write their chapters as if their teacher colleagues were their readers and they were seeking to directly engage those colleagues in a conversation about the work of MCT (as opposed to imagining only that their readers were teacher educators engage in MCT work with pre- and in-service teachers). Further, they were asked to discuss MCT as a holistic approach to teaching and learning, rather than as a discrete component of it. Wherever possible, when appropriate to the chapter, specific suggestions for how to actualize this approach with greater efficacy over time was to be included, coupled with specific examples of how teachers have, with progressive success, executed these suggestions in their classroom practice. While the idea of building teacher prowess for MCT was to be foregrounded in the chapters to inspire teachers, discussion of challenges that could/have emerged was also to be included so that teachers can also learn from (and even be inspired by) failures cast as opportunities to build resiliency, muster resolve, and surface better alternatives/innovations. Story of Success Chapter authors were asked include, if possible near the outset of their chapter, a chapter-relevant story of successful MCT by a public PK-12 school STEM teacher and/or in a public PK-12 school STEM classroom/setting. Through this positive (not to be confused with perfect or superficial) “real world” teaching vignette, they were asked to illustrate how STEM-focused MCT is foundational to the core work of STEM teachers/teaching in the STEM fields, not “on top of” or “additive to” this work. Working Definitions Chapter authors were asked to identify any key terms, concepts, ideas, and so forth, that readers needed to understand to fully appreciate the wisdom of their chapters. Through these definitions they were asked to demonstrate their commitment to bridging the theory and practice of MCT in their content area(s) and grade level(s) by establishing common language/understandings that would encourage and facilitate this transformation (i.e., its actual implementation). Practice and Theory Chapter authors were asked to engage all of the organizing tools in discussion both the theory and practice of MCT, beginning with practice. More specifically, they were asked to think about actionable-step examples of

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STEM-focused MCT situated in content development, pedagogical engagement, and teaching and learning assessment cycles. They were also asked to think about critical consciousness—the key ethical dilemmas in STEMfocused MCT generally, as well as the specific “rubs” embedded in the content area(s) and at the grade level(s) at focus in their chapters. Chapter authors were asked to articulate these common conundrums, irreconcilable challenges, and most controversial concerns, as well as to discuss how they respond to them, and how they believe teachers should, ideally, respond to them in seeking to achieve critically conscious multicultural educational ends in STEM. Reflection Bridge In order to bridge practice and theory, chapter authors were asked to incorporate a brief reflection section (perhaps tied to their story of success) where they reflect on what can happen/has happened, what can work/has worked, what does not work/has not worked in their own/others’ experiences undertaking STEM-focused MCT. Chapter authors were also asked to provide their sense of “why” the things that work do, as well as to consider possible solutions for the things that do not work (but maybe could). Standards Chapter authors were asked not to speak exclusively to a particular standard, but to reference the roles of standards (e.g., No Child Left Behind [NLCB], Common Core State Standards [CCSS], subject area/professional practice) in their MCT work. This stipulation was included to prevent chapters from becoming (or seeming to become) out/dated given how frequently the standards environment and/or culture in PK-12 education changes (nationally, regionally, and locally), and to ensure that, regardless of the standards environment and/or culture (or lack thereof) in any classroom, school, district setting, the chapters would be regarded as relevant, apt, adaptable, and so forth. More specifically, chapters were to discuss how to work with “standards” regardless of which specific standards may be in play in any schooling context. Educational Context Chapters authors were asked to discuss the manners in which their STEMfocused MCT process was (in the example it provides), and could be (by readers in their own practice), adapted to specific teaching and learning settings (communities, schools, classrooms, students, etc.).



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Relationships with and among Students and Their Families Chapters authors were to discuss the approaches, strategies, and/or efforts undertaken to build relationships with students and students’ families as a part of their everyday MCT praxis (recursive thought, reflection, and action). Civic Engagement Chapters authors were asked to link their STEM-focused MCT work to the practice of citizenship in some way (e.g., the purpose of science is to improve the human condition). “Special” Populations Where relevant, chapters authors were to discuss STEM-focused, MCTinformed modifications and accommodations for gifted and talented education, bilingual gifted and talented education, “regular” education, bilingual “regular” education, special education, bilingual special education, among other clinical educational considerations, as well as critically conscious considerations about “dis/ability” (e.g., that it is a social construct that only “shows up” in schools when school communities are, like the larger society, inequitably organized). Content Linked to Pedagogy and Assessment Chapter authors were asked to describe how they impart their academic content through varied STEM-focused, MCT-informed student-centered pedagogical practices, as well as how they assess student learning, and the impact of teacher in/effectiveness (including in the selection and/or use of instructional materials) in student learning using through varied STEM-focused, MCT-informed forms of evaluations. Integrated Use of Technology Because the volume has only one chapter on technology to represent the “T” in the STEM content areas, all chapter authors were asked to discuss some manner in which educational technology is (in the example it provides), and can be (by readers in their own practice), integrated into the STEM-focused MCT process. Chapter authors were also asked to identify and critique the use of educational technology for technology’s sake (simply to be able to check the “technology integration” box on a curriculum plan), and to describe ways

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in which they and others can use it to genuinely enhance STEM-focused MCT work, and the quality of teaching and learning that ensue. Notes to Teachers Where relevant, chapter authors were asked to include “notes to teachers” sections that linked the STEM-focused MCT efforts at focus in the chapter to the unique experiences of teachers at different stages in their teaching careers seeking to undertake similar efforts (e.g., newly inducted, midcareer, and veteran). Resources The teachers in our informal focus groups expressed great interest in having access to STEM-focused MCT resources that go beyond the scope of what is possible to provide in a chapter or even a book format. Accordingly, chapter authors were asked to identify or reference (as was appropriate to their chapter content) resources that could include, but were not limited to videos (especially those that provide examples STEM-focused MCT “in action,” and/or that are designed to “narrate” processes of STEM-focused MCT, and so forth), PowerPoint presentations, document masters, case studies, photo exhibits, full-text articles, and links to other relevant sites. In some chapters these resources are included in the chapter narrative, in others they are in an appendix. Additional resources shared by chapter authors were integrated into the resources section of the volume. Evidence: Prove It Finally, our informal focus group teachers expressed a strong desire for this volume as a whole, and for each chapter in particular, to provide evidence of how MCT positively impacts teaching and learning in the STEM fields, specifically how it improves the motivation, performance, and overall academic success of students, especially HMMS, in these content areas. These teachers wanted this information for themselves (to be convinced that investing the effort to undertake MCT work was worth it), and for use with parents, colleagues, and their school leadership—to reduce resistance to, and cultivate buy in for, MCT initiatives. Accordingly, we asked chapter authors to (again, as was appropriate to the focus of their chapters) convey the value of MCT work, through empirical evidence (e.g., student performance numbers), as well as through anecdotal evidence (e.g., examples of teachers who have had good instructional results). We provided the following examples of how such evidence might be articulated in their chapters:



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• “Through multicultural curriculum transformation in the STEM content areas, I can prove that there is no need for a performance gap to exist in these classrooms.” • “In engaging in multicultural curriculum transformation, I will end up in a better place with my students; here’s how . . .” • “Multicultural curriculum transformation may seem overwhelming at first; that’s exactly how I felt about it when I first considered trying to undertake it, but this is what happened to me and my teaching practice as a result of persevering . . .” Food for Thought While Reading the Chapters There are thirteen discrete chapters presented in this volume, organized by their primary STEM disciplinary focus or foci as: 1) mathematics chapters; 2) science chapters; 3) math and science chapter; 4) engineering chapter; 5) technology chapter; and, 6) math, science, engineering, and technology chapters. We chose to lead with the mathematics and science sections (instead of going in S-T-E-M order) because, through the organic process of our call for chapters, these two content areas drew the most number of chapters, largely reflective of the past and continuing dominance of these two STEM fields in PK-12 education, despite the emerging influence of engineering and, especially, technology in PK-12 schooling, as well as in society at the global level. The four chapters in the Mathematics section include: Chapter 1: “Transforming the Family ‘Math Night’ with Latina/Latino Middle School Parents: Communicating about the Adoption of Common Core State Standards,” by Yolanda De La Cruz; Chapter 2: “Using Iterative Visual and Virtual Manipulatives to Support English Language Learners in Mathematics Education,” by Sarah A. Roberts; Chapter 3: “Rethinking the Teaching and Learning of Latina/Latino Students to Promote a Multicultural Mathematics Education,” by Javier Díez-Palomar and Carlos A. LópezLeiva; and, Chapter 4: “Students Who Speak English as a Second Language: Preparing Teachers for Changing Demographics—An Innovative, Collaborative Approach,” by Bettibel Kreye and Gresilda A. Tilley-Lubbs. These chapters attend to mathematics education at the elementary, middle, and secondary levels, focusing on the latter two levels. They focus on teaching mathematics to students who speak English as a second language, especially first language speakers of Spanish, and on engaging families in mathematics education. Finally, they stress the importance of pre-service teacher preparation to teach mathematics. The four chapters in the Science section include Chapter 5: “Teaching Biology in the Age of the Next Generation Science Standards: Methodology for Teaching in High-Needs Schools,” by Antoinette Linton; Chapter 6:

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“LGBT-Inclusion Across the Life Science Curriculum,” by Mary Hoelscher; Chapter 7: “Earth-Shaking Dragons and Orphan Tsunamis: Transforming Middle School Earth Science and STEM through Studying Ancient Science Inquiry and Multicultural Collaborations in Earthquakes, Tsunamis, and Disaster Preparedness,” by Marna Hauk and Adam Masaki Joy; and, Chapter 8: “Classroom Meteorologists: Transforming Science Content in a Dual Language Second Grade Classroom,” by Sandra Lucia Osorio. These chapters discuss science education at the elementary, middle, and secondary levels, with equitable attention across the levels. They focus on life sciences, earth science, and physical science broadly, as well as biology, geophysics, and weather/climatology in particular. They also focus on teaching science to students with diverse levels of English proficiency, to working class students and/or students in poorly resourced schools, to students who speak Spanish as a first language, and to Black American students. And, they emphasized using LGBT-inclusive examples, the importance of earning students’ trust and engendering student agency in the classroom, as well as overcoming fear in teaching from a multicultural perspective. One chapter each make up the Mathematics and Science, the Engineering, and the Technology sections. Respectively, these chapters are Chapter 9: “Rethinking Art in Mathematics and Science,” by Jeff Sapp; Chapter 10: “Effective Engineering Models for Multicultural Curriculum Transformation in STEM: Engineering for All,” by Laura Luna, Twanelle Walker Majors, and Jennifer Meadows; and Chapter 11: “Multicultural Technology Education: The Need to Teach Digital Technologies to All Students,” by Janessa Schilmoeller, Lori Griswold, and Neal Strudler. Chapter 11 was originally two separate chapters that were blended together to enable broader and comparative analysis. In sum, these chapters discuss mathematics, science, engineering, and technology education broadly at the elementary, middle, and secondary levels, with equitable attention across the levels, but not in all of the content areas (for example, the engineering chapter focuses more on elementary level education). They also discuss coding, computer science, computer They focus on gender, race, ethnicity (language, including students who speak English as a second language and monolingual English students’ predisposition for linguistic diversity in their classrooms), and the importance of using equity pedagogy and of creating empowering school cultures. They also discuss the importance of integrating the arts and history in the teaching of mathematics and science, and the use of primary source materials. Finally, two chapters are included in the Mathematics, Science, Engineering, and Technology section: Chapter 12: “Coming Out of the Lab Closet: Queering STEM Education for Student Success and Well-Being,” by Allison Mattheis, Jeremy Yoder, and Dixon Perey; and Chapter 13: “Considering



Introduction xxvii

Women’s Ways of Knowing in STEM,” by Tracy Arnold, Eshani Gandhi, Schetema Nealy, and Brian Trinh. These chapters discuss mathematics, science, engineering, and technology education as a whole, focusing on secondary education and postsecondary schooling and careers. They also focus on sex, gender, gender identity, and sexual orientation, and discuss the notion of “queering” STEM curricula to reveal gender- and sexuality-related biases, as well as race-related and other biases, in teaching in these content areas. At the same time that we used these content areas to structure the volume, our MCT orientation works against neatly packaging knowledge into discrete disciplinary categories; thus, these six disciplinary frameworks are not meant to lock the voice(s) in any of the chapters into a limited or limiting perspective, which is why we were happy to have received chapters that crossed these (and other) disciplinary lines in myriad ways, emphasizing the inherently interdisciplinary, perhaps nondisciplinary nature of knowledge building and of knowing. Accordingly, while the chapters in this volume focus on science, technology, engineering, and mathematics, true to MCT they also focus, in an integrated fashion, on race, ethnicity, language, national origin, gender, gender identity and expression, as well as the arts, social studies, and language arts. These additional foci derive, at least in part, from the identity diversity of our volume chapter authors, as well as the diversity of their individual, academic, and professional experiences. Like us, our volume chapter authors have also been PK-12 teachers and/or have served as teacher educators for pre-service and veteran teachers in various PK-12 educational settings across the country, as well as in myriad other educational roles, the majority of which have been in public educational contexts. Unlike us, our volume chapter authors are racially and ethnically diverse. All of us—editors and authors—are diverse along other dimensions of identity. We are all also highly disciplinarily diverse. This diversity has resulted in a volume that, in sum, “walks the talk” of MCT. However, as you read the ensuing volume chapters, we would still like you to keep in mind that they do not reflect “perfect” examples of MCT. We, as volume editors, our chapter authors, the additional educators at focus in the chapters, do not have perfect MCT consciousness. There is no perfect example or consciousness, precisely because curricular transformation work is predicated on consciousness transformation work—as people change, their practices change. As educators develop more critically conscious knowledge about how dynamics of power negatively impact students (especially HMMS), schools and school communities (especially underserved ones), and society as a whole, the manners in which they teach what they teach also becomes more critically conscious. With this in mind, we ask you to consider as you read whether, in what ways, and to what extent this volume and the chapters in it are as illustrative of transformative

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(along a developmental continuum) examples of educators doing MCT work. As you read, you decide if, in sum, we achieved the directives, while manifesting the dispositions, our focus group teachers requested. Finally, we ask you to read with both critical and self-critical consciousness as you imagine, and/or continue to reimagine, your own MCT work, remembering, as you do, that we are all works in progress. REFERENCES Bode, P. (2006). Multicultural education. Education.com. Retrieved from https://ltc. highline.edu/CR/Multicultural%20Education%20-%20Bode.docx Clark, C. (2002). Effective multicultural curriculum transformation across disciplines. Multicultural Perspectives, 4(3), 37–46. Heim, J. (2016, September 14). America has a teacher shortage, and a new study says it’s getting worse. The Washington Post. Retrieved from https://www.washingtonpost.com/local/education/america-has-a-teacher-shortage-and-a-new-study-saysits-getting-worse/2016/09/14/d5de1cee-79e8-11e6-beac-57a4a412e93a_story. html?utm_term=.8af499aa6049 Learning Policy Institute (LPI). (2017). Understanding teacher shortages: Notes and sources. Retrieved from https://learningpolicyinstitute.org/understanding-teachershortages-notes-sources Nieto, S. (n.d.). Commentary. Workshop 1: Engagement and dialogue. Teaching multicultural literature: A workshop for the middle grades. Annenberg Learner: Teacher Resources and Professional Development Across the Curriculum. Retrieved from http://www.learner.org/workshops/tml/workshop1/commentary3.html Podolsky, A., Kini, T., Bishop, J., & Darling-Hammond, L. (2016). Solving the teacher shortage: How to attract and retain excellent educators. Palo Alto, CA: Learning Policy Institute. Rebora, A. (2016). Faced with deep teacher shortages, Clark County, Nev., district looks for Answers. Education Week. Retrieved from http://www.edweek.org/ew/ articles/2016/01/27/faced-with-deep-teacher-shortages-clarkcounty.html Ryan, C. (2016). Nevada declares teacher shortage emergency to boost out-of-state hiring. Las Vegas Sun. Retrieved from http://lasvegassun.com/news/2016/feb/05/ nevada-declaresteacher-shortage-emergency-to-boos/ Strauss, V. (2016). The troubling shortage of Latino and black teachers—and what to do about it. The Washington Post. Retrieved from https://www.washingtonpost.com/news/answer-sheet/wp/2016/05/15/the-troubling-shortage-of-latino-andblack-teachers-and-what-to-do-about-it/?utm_term=.58fda71c502d Sutcher, L., Darling-Hammond, L., & Carver-Thomas, D. (2016). A coming crisis in teaching? Teacher supply, demand, and shortages in the U.S. Washington, DC: Learning Policy Institute.



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Takahashi, P. (2012). “Teacher diversity gap” cause for concern in CCSD schools. Las Vegas Sun. Retrieved from http://lasvegassun.com/news/2012/nov/25/districtlaggin/ U.S. Department of Education (DOE). (2016). The state of racial diversity in the educator workforce. Washington, D.C.: Office of Planning, Evaluation and Policy Development, Policy and Program Studies Service. Villegas, A. M., Strom, K., & Lucas, T. (2012). Closing the racial/ethnic gap between students of color and their teachers: An elusive goal. Equity & Excellence in Education, 45(2), 283–301. Walls, T. (2017). Race, resilience, and resistance: A culturally relevant qualitative examination of how black women school leaders advance racial equity and social justice in U.S. schools (Unpublished doctoral dissertation). University of Nevada, Las Vegas.

Part I

MATHEMATICS

Chapter One

Transforming Family “Math Night” with Latina/Latino Middle School Parents Communicating about the Adoption of Common Core State Standards Yolanda De La Cruz

INTRODUCTION Parent involvement is a crucial component of student success, yet it is particularly challenging to cultivate parental engagement in mathematics, where many parents may feel they cannot understand the material. These challenges are especially significant among parents of students learning English in highneed communities. With the adoption of the Common Core State Standards (CCSS) and increased emphasis on Standards of Mathematical Practices (SMP), both of which require varieties of deeper expertise in the content area, teachers must develop even greater capability to make math connections for students and their families. Students (and their families) now have to make sense of the math—to explain how they arrived at a mathematical solution—not “just do it.” Accordingly, teachers must be able to teach them how to make mathematical arguments from evidence and to critique the arguments others make. This chapter documents how a middle school “family math night” program was transformed to be standards compliant and successful in supporting parents to better help their children learn math while also learning English. This new family math night model evolved slowly through trial and error, or “field testing,” of various new math-learning activities with participating middle school families, including those with children new to English. Effectiveness of different aspects of the emerging model was assessed in a number of ways. First, parents and children were asked to try to answer math questions before and after each family math night; these questions were similar to questions 3

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Chapter One

asked during the family math night session, which took place between these pre- and post-tests. Second, a short-answer oral survey and an informal oral interview were undertaken with parents and children to ascertain their reactions to each family math night experience. Third, parents and children were asked questions designed to track the emergence of new math knowledge gained from participating in family math night sessions. Fourth, field notes were taken during each family math night. Fifth and finally, family math night teachers were interviewed. Collectively, these data sources led to the development of the new family math night model. More specifically, this chapter describes and discusses a step-by-step multicultural curriculum transformation undertaking by an educational team comprised of two middle school math teachers, a parent of a public school middle school math student, and a university professor. The team undertook this transformation process to create a new type of family math night model—a model that foregrounded “mathematical practices” that were not addressed in the pre-existing model. KEY DILEMMAS IN MATH EDUCATION It is well known that parent involvement is a crucial component of student success (Epstein, 2013; 2011; De La Cruz, 2008). The challenges of engaging parents in student learning are also well known, particularly in content areas like mathematics, where many parents may feel they will experience challenges in seeking to understand the material assigned to their children for homework. These feelings are particularly significant among parents of children learning English living in high-needs communities. De La Cruz (1999a) found that parents “can become the natural partners of teachers” if they are given access to the material their children are learning and guidance as to how to effectively assist their children to master it (p. 38). Models are needed that make mathematics interactions between teachers and families in the middle school setting more available; this is particularly the case in middle school settings where practical mathematical applications can significantly deter students’ waning interest in this subject area (Ball, Thames, & Phelps, 2008). One approach that has been successful in improving student understanding of mathematical practices is the use of family math nights. This approach provides the opportunity for students and their families to informally meet with teachers to discuss math content and go about learning it together in ways that are fun. This approach also builds parental confidence to facilitate



Transforming Family “Math Night” with Latina/Latino Middle School Parents 5

their children’s learning success in this content area and more broadly (De La Cruz 1999a, 1999b). The adoption of the CCSS requires middle school students to be able to explain how they made sense of a problem in order to solve it, not simply to solve it (ADE, 2012). This requires the development of more advanced critical thinking skills, requiring many teachers to change their mathematical instructional approaches. In turn, parents seeking to support their children’s math learning must also change. In the past, parents attended family math nights simply to improve their and their children’s basic understanding of math. With the adoption of the new standards, family math nights must now engage families in the more rigorous practices that lead to deeper mathematical understanding. Foundational for further study in mathematics (and science) are relationships between the CCSS and SMP that can be applied to everyday life (Irwin, 2001; Lappan, Fey, Fitzgerald, Friel, & Phillips, 2006; Kilpatrick, Swafford, & Findelle, 2001). For example, middle school students use ratios in geometry and in algebra when they study similar figures and slope of lines; high school students use these same ratios when they study sine, cosine, tangent, and other aspects of trigonometry. If these senses of quantity are understood and supported in the home (applied to “real world” proportions), students are more likely to succeed. Parents need to learn how to be supportive of their children’s math learning in this new way. The CCSS also expects students to be able to construct viable arguments and critique weaknesses in the reasoning of others. These more rigorous expectations of students also require more from parents seeking to promote their children’s success. This is especially the case because of the gateway role that middle school algebra, and that high school mathematics more generally, play in students’ overall academic success and the likelihood that they will attend college (Moses, 2002). Some teachers and many parents do not yet have the expertise necessary to support student math achievement in these more complex manners. In terms of math (and science) accomplishment, American students lag behind students from around the world. Among students in thirty-four developed nations, America’s fifteen-year-old students rank twenty-fifth in math and seventeenth in science (Fleischman, Hopstock, Pelczar, & Shelley, 2010, p. iv; Adjiage & Pluvinage, 2007; Ball, Thames, & Phelps, 2008). Middle school is when most students begin to lose interest in topics related to math (and science) (Ma & Ma, 2004; Moseley, 2005). Further, girls, historically underrepresented racial and ethnic minorities, students living in single-parent homes, and students living in poor socioeconomic conditions often begin

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Chapter One

school with lower interest in math (and science) even when they show aptitude for learning in this area (Espinosa, 2009). Two reasons cited for students’ waning interest in math (and science) careers during middle school are limited parental involvement in school and limited levels of math understanding within families (Ball, Lubienski, & Mewborn, 2001; Epstein, 2013; 2011). Involving parents in their children’s learning is recognized as necessary and important in several “status” reports on U.S. schools (De La Cruz, 1999b; Epstein, 2013; 2011). This recognition is consistent with social science research findings revealing that children have an advantage in school when their parents encourage and support schooling; this is especially the case for Latina/Latino families. It is important to note that: Latina/Latino students are supported at home in ways that typically result in very high academic achievement in majority student populations . . . [but teachers] have not built the relationships with Latina/Latino parents and, therefore, not built on the relationships between Latina/Latino parents and their children that are necessary to bring that very high academic achievement to fruition. (Clark, Flores, Rivera, Biesinger, & Morgan, 2012, p. 85)

Currently Latinas/Latinos comprise the largest ethnic minority group in the United States and are obviously transforming American culture and society in a variety of ways (Takaki, 1993). Of particular note, in seeking ways to improve their economic status in the United States, Latina/Latino families often view educational processes as a way of achieving this goal (De La Cruz, 2008). While family involvement is a powerful predictor of various adolescent outcomes—positive and negative—parent engagement in schools tends to decrease beginning in middle and into secondary school, in part due to adolescents’ increasing desire for autonomy, and in part due to changes in school structure and organization (HFRP, 2007). Preparing all students to become more successful in math assessed according to the CCSS will require more and deeper parental participation in schools, especially in middle school. In particular, parents need to understand a solely rote memorization approach to learning math as a thing of the past, and the focus on developing critical math literacy as the current and foreseeable trend. Little is known about how families are adapting to these aspects of the CCSS in mathematics, especially in the middle school grades and especially in families with limited English proficiency or in which only Spanish is spoken. This chapter provides insight into this adaptive process and how it can be guided towards student success in math learning.



Transforming Family “Math Night” with Latina/Latino Middle School Parents 7

CONCRETE EXAMPLE OF MULTICULTURAL CURRICULUM TRANSFORMATION IN MATH EDUCATION Our plan for multiculturally transforming the family math night program was undertaken to blend the “fun for everyone” aspect of the original program, with teaching and learning of deeper mathematical reasoning that supports development of critical math literacy. There were two primary steps in our transformation plan for the program: funding and curriculum. Funding Typically, public schools do not provide any type of funding for family math nights programs. While these programs do not require a huge investment of resources, they do require some for services (e.g., lamination of curricular aids), materials (e.g., assignments provide to parents in their take-home folders), incentives (e.g., small prizes to incentivize student engagement), and light refreshments (e.g., snacks to create a welcoming environment). Some city councils have money set aside for small grants for which teachers can apply. One of the teachers on our family math night educational team applied for and secured such a grant; it provided funding for two math nights. Our team then invited city council members to attend the opening family math night to enable them to see what their funding made possible, and for the program teachers, students, and parents to feel supported by their elected leaders. It is our hope that such opportunities for exchange will lead to additional funding down the road. Curriculum Overview Our family math night educational team began our curriculum rethinking process by compiling a list of all the learning activities we would want to include in an “ideal” family math night program. At the same time, because we know that many of the parents who have attended family math nights in the past have a fear of math, we also discussed not wanting to overwhelm the parents with too many activities. Accordingly, we felt that it was particularly important that the activities convey a sense of welcome and be engaging for the entire seventy-five-minute session allotted to each math night. While seventy-five minutes may seem like a lot of time to fill with parents, we found that it was never enough time, in part because families had various competing commitments. Therefore, it was imperative that we began each math night on time and used open-ended opening activities so that early arriving families did not have to wait for others before getting started, and so that later-arriving

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families could still participate fully. We also provided extension activities, related to the opening activity, to keep each family engaged until all the families completed at least the opening activity. Opening activities. We chose opening activities that reinforced math concepts that the children of the parents in attendance were learning in math class and that the entire family could work on together (see below for an example of such an activity). Jr. High Family Math Night 1.  Sign in 2.  Estimate how long it will take to burn a birthday candle 3.  Cut out all twelve pentaminoes 4.  Fit all twelve pieces of the pentominoes in 5” × 12” two-centimeter grid paper Other activities. All of our math night activities balanced teaching and learning of basic and deeper math. We engaged families in activities designed to demonstrate key skills and concepts; in particular we chose activities that introduced to parents and reinforced to children, concepts being taught in the children’s math courses. We stressed the importance of developing basic math skills, as well as deeper understanding of math concepts, and we made sure than families understood the emphases being placed on conceptual learning in the CCSS and SMP. We prioritized activities that made connections between key math concepts and “the real world” (see below for an example of such an activity). Why it is important to learn this (in the real world): • Probability is under to make predictions about the future based on results of the past. • Probability is used to help predict the weather, set insurance rates, and determine life expectancy. • Critical-thinking skills are used as people try to determine, with as much certainty as possible, what will happen. Activity enhancements. We awarded small prizes to families throughout each math night session to affirm successes with various math activities (e.g., guessing the correct number in an estimation portion of an activity). We also used a variety of media to make math night sessions as interactive as possible; further, using accessible online resources made it possible for families to revisit these resources from home or a community library. Closing. At the conclusion of each math night session, families were given a take-home folder with copies of all the activity materials used in the session.



Transforming Family “Math Night” with Latina/Latino Middle School Parents 9

Before leaving, each family filled out a brief survey called an “exit ticket.” The survey was designed to provide our educational team feedback on how effective families felt each session was so that we could undertake continuous improvement (from one night to the next); the “exit ticket” ritualized the end of each night in the same way the opening activity did the beginning. Curriculum Specifics As generalized in the preceding section, our family math night educational team built the new curriculum around activities designed to bridge skill and content learning in math in ways that would welcome and engage families, while reinforcing what the children have learned, are learning, or will learn in courses and would need to function effectively in life. More specifically, our educational team built this new curriculum around seven components. These components are the communication key, the checklist, the warm-up activity, the whole-group activity, the family activity, the family information packet, and the family exit survey. The communication key. The communication key is designed to help teachers be as successful as possible in communicating with families about and during family math night sessions. No matter how welcoming and engaging these sessions are, they have no value if families do not attend and/or if those in attendance cannot understand what is being shared. While communication details are often tedious or mundane, attention to these details is necessary to make each family math night session as successful as possible by ensuring that each is well attended, that all are regularly attended (families make a habit of attending), and that everyone who attends can fully participate. Not all families will have the same ability to communicate via different forms of communication, thus it is imperative to use multiple forms of communication and to repeat messaging multiple times (at the outset of the academic term, and then two weeks prior, one week prior, and the day prior to each session). Outside of the family math nights sessions, forms of communication that our educational team has found successful include speaking directly to parents (meeting them in the morning or afternoon when they drop off or pick up their children, speaking to parents via telephone [home and cell], email, text, or instant messenger, through web-based and print announcements and/or calendars posted on school websites and/or distributed through electronic and print media (e.g., a newsletter), and speaking to parents via various school communication interfaces (e.g., Marquee). Asking students and parents for suggestions as to what forms of communications are most effective can be particularly helpful, including communication in Spanish and/or in other first languages of family members.

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Chapter One

Of particular note in this regard, our educational team made use of Spanish interpreters during family math night sessions. Central to the communication key is the building of relationships between teachers and students, teachers and parents, schools and families, and within families. Time spent building relationships before a family math night program is established, while it is being established, during its implementation, and in the interim until the next program iteration occurs improves student attendance, homework completion, and learning outcomes in math as well as all other subject areas; it also improves parent involvement in schools and family civic engagement in schools and school communities (Clark, Flores, Rivera, Biesinger, & Morgan, 2012). The checklist. Like the communication key, the checklist is designed to help teachers remember all of the, again, often tedious or mundane, preparation details required to make each family math night session as successful as possible by ensuring that it is well-organized and -executed. Attention to these details is just as foundational to achieving the “ideal” family math night program outcomes as are the caliber of the math activities undertaken at each session: • Prior to start time: Set classroom temperature (as indicated), organize furniture (seminar style), prepare name tags, prepare sign-in sheets, prepare the information packets, prepare the estimation contest materials, set supplies on tables for warm-up activity, organize snacks, organize supplies for whole group and family activities, set up media to be used and test to ensure it works. • At start time: Sign in students by having them sign their names, and list the names of the adults with them, as well as the name of their math teacher on the sign-in sheet. Hand each family the family information packet, inclusive of the family exit survey. As needed (for newly attending families), briefly review the contents of the packet (including the instructions for completing the survey) with each family; indicate that additional review of packet materials will occur at the end of the session. • At start time: Aafter sign in, direct families to the “estimation contest” jar and have one member of the family fill out and submit the family’s estimate ticket proclaiming the number of items they believe the jar holds (items typically include marbles, dimes, or something else families might enjoy taking home at the end of the session if their estimate is the best). • At start time: After each family completes their estimation ticket, direct them to a table, review the open-ended, warm-up activity instructions with them and direct them to begin work on it; remind the family to go onto the extension activities associated with the warm-up activity if they finish the warm-up activity while other families are still working on it.



Transforming Family “Math Night” with Latina/Latino Middle School Parents 11

The warm-up activity. Warm-up activities are usually built around games with mathematical elements that families can play independently (without formal instruction) and immediately (upon arrival to the math night session). Such activities might include the use of tangrams, geoboards, geometrical shapes, and puzzles). As previously indicated, each warm-up activity must lend to extension activities (additional related challenges that families can engage in once the main activity challenge is completed). For example, after identifying geometrical shapes, families might write up a list of places in their homes and/or neighborhoods where they recall seeing these shapes. Each warm-up activity should also lend to family discussion so that they may uncover deeper mathematical concepts embedded in it. The key activity discussion question designed to reveal these concepts is this: What does the activity have to do with math? This question helps families begin to see relationships between, for example, a shape and a size. A specific warm-up activity using a geoboard might ask families to create a design and then find a quadrilateral in the design. An extension activity might ask families to create a rectangle and then, working in pairs, find the area and perimeter of it and then compare answers across pairs in seeking to identify the correct ones. This activity might conclude by asking the family to discuss how the activity has extended their math thinking (literacy). Warm-up activities, like all family math night activities, must also relate to math concepts that the children have studied, are studying, or will study in their current math courses. The whole-group activity. While warm-up activities often involve “the whole group,” they tend to be more collaborative (within families) and/or comparative (across families) in nature. In contrast, whole-group activities are usually designed to create a level of competition between families to encourage them to keep working on a harder math activity until at least one family solves it correctly so that all families can learn from their success (peer teaching) (see below for an example of such an activity). Fold into an Open Box Activity 1 1.  Each family will guess which of their pentominoes will form a network for a cube without a top. 2.  Fold the pentominoes to check their conjectures. 3.  On the laminated grid paper, draw each pentomino that folds in an open box. Whole-group activities require the family math night teacher to get all the families excited to compete against one other in a good-natured way. Wholegroup activities use this competition element to maintain the “fun” aspect, while also making more specific connections to CCSS, SMP, and “the real” application.

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Chapter One

The family activity. While warm-up and whole-group activities often involve “family” members working on an activity together, the members’ collaborative engagement is incidental. In family activities, coengagement of all members of a family is more intentional. The activity is begun during the family math night, but designed in such a way as to encourage specific continuing coengagement with the activity by the family as a whole after they return home. The materials included in the family information packet are intended to facilitate this continuing coengagement. Further, each family is given a set of the all the supplies used to undertake the activity during the math night session to take home with them. For example, our family math night educational team used an activity called “Hurkle” as a family activity (“Hurkle,” n.d.). Hurkle is designed to teach directionality by using a compass to read maps. Clearly, this is a “real world” skill. But Hurkle also embeds algebraic language (e.g., ordered pairs, negative and positive numbers, slope, quadrants) in teaching directionality. The family information packet. In addition to providing the parents who attend family math night sessions with copies of all the activity materials used in the sessions, the packet also includes information about their child’s school-based math curriculum, including any changes being made to it (e.g., CCSS and SMP). Also included in the packet are guidelines for parents to use to guide their children’s completion of their math homework, including types of questions to ask their children to encourage the children to explain their math reasoning in arriving at a particular solution. Additionally included are lists of links to various downloadable math applications (“apps”) for use with various handheld devices, iPods/notebooks, and/or on laptop/desktop computers, as well as links to excellent online math resources (including English and Spanish math tutorials, as well as other Spanish-language materials). A past parent participant in our family math night program was hired to translate all of the materials in the packet into Spanish. In sum, the materials in the family information packet are intended to put parents at ease by providing them accessible information and scaffolded strategies for building their own math skills and conceptual reasoning, at the same time supporting the development of the same in their children. The family exit survey. As previously noted, through implementation of this survey with family math night participants, our educational team was able to learn what parents gained from attending each math night session, and what adjustments (deletions, revisions, additions) needed to be made to subsequent ones. The survey also provided information as to how the entire family math night curriculum might need to be altered to accomplish its “ideal” goal. Usefulness was the word parents used most often in their survey comments to describe what they gained from attending the math night sessions; sessions



Transforming Family “Math Night” with Latina/Latino Middle School Parents 13

they attended in spite of busy life and work schedules. Parents also expressed in the surveys that they had felt “disconnected” from what their children were learning in school, especially in math, once their child reached middle school (in part because as children approach adolescence they communicate less with parents, and in part because the middle school model means children have several teachers instead of just one) (HFRP, 2007). Parents were particularly thankful that the family math night program helped them to “reconnect” to their child, their child’s current and possible future math teachers, and their child’s learning, especially in math. Surveys also revealed that parents felt they and their children gained increased knowledge of, and correct information about CCSS and SMP through participation in family math nights; in this regard, their learning far exceeded, in quality and accuracy, what they had “heard about” these standards in casual conversations or in television reports. Not surprisingly, parents were most concerned about how these standards might impact students considered to be “gifted and talented,” students in special education programs, and students learning English as a second language. Because the teachers on our educational team were required to attend district workshops about these standards, they were well-prepared to share what they learned with math night families. If, however, families posed questions about these standards that a teacher could not answer on the spot (i.e., before a math night session concluded), the teachers sought out and then provided the answer via one of the key communication avenues mentioned previously, and/or at the subsequent math night session. In sum, parents left math night sessions with an appreciation of the intended benefits of the standards for all students, and how differentiated instruction, including the use of exploratory strategies and hand-on activities, could support students, across academic proficiency levels, to build the skill and deepen the conceptual understanding in math that the standards prioritized. UNPACKING AND ERODING PARENTS’ MATH PHOBIA As discussed in brief previously, parents came to family math night session with significant math phobia, particularly regarding their inability to solve the middle school mathematical problems that their children were assigned for homework. Family math nights provided parents the opportunity to build their own math capacity, as well as to develop strategies for supporting their children’s math learning. Pre-math night session parent interviews revealed that many parents had resigned themselves to the belief that it is “okay” not to be good at math.

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Several parents remarked that they were never “good with math.” Accordingly, it was a generally accepted condition of existence (normalized) by many of the parents and, thus, made it “okay” for their children to not to like or to not be good at math, even to fear math. Family math night sessions worked hard to break down this belief. (It is important to note that there was a range of pre-existing math knowledge among the participants—parents and children—in the family math night sessions. Generally, the range was wider among the children than among the parents, evidence that some children were doing better in math than others, as well as better than their parents.) Post-session interviews documented a change in this belief, generally manifest as a less overall negative attitude toward math—feeling even just “a little less lost” after attending the first family math night session. The key factor in bringing about this change was parental experience of success in math learning through the varied and fun family math night activities, especially those that involved collaborative engagement with their children. And, remarkably, this belief change became evident after parents attended just one math night session. During a second math night session, a parent who had commented in the previous session that his failure to solve a math problem was okay because it was inevitable (“I was never good at math”), was overhead saying, “I love math now. This is so much fun.” In fact, all of the parents who attended the first family math night session returned for the second one. Parents particularly liked having each math night activity (a group of problems all related to a particular math skill or concept) explained while they and their children (as whole family groups), worked on an activity practice problem—in essence, they liked teaching while trying. Parents also liked having the visual support provide by multimedia and three-dimensional manipulative presentations; they felt that these presentations substantially improved their ability to develop skills and understand concepts. Bringing several families together created a sense of community that parents also felt contributed to their math learning success. Finally, parental buy-in, not only to attending family math night sessions but to learning math (skills and concepts), was amplified by the resources provided in the take-home information packet and the time spent during each session to review the resources and how they could be used at home to reinforce session learning. The ability to choose activities differentiated by content from among a menu of resources, and to repeat activities several times in seeking to develop mastery in a particular content area were noted as top reasons for the packets’ appeal. Of particular value were web-based resources that families could access from home (if they had Internet connection and at least a “smart” phone) or from neighborhood sites (e.g., community centers, public libraries, local



Transforming Family “Math Night” with Latina/Latino Middle School Parents 15

colleges (some sites, including some of the children’s schools, offered “iPod home loan” programs). Through this family math nights research, web-based resources were revealed as a key to linking parents with their children’s ongoing math learning on a regular basis. Regular (i.e., non-family math night) math teachers came to assign students the homework task of finding webbased resources to reinforce skills and concepts learned in class, especially those they might be struggling with, and then, sharing those resources with their parents. SUMMARY The multicultural curriculum transformation of the family math nights’ program documented herein brought parents, over a third of whom came from working class and predominantly Spanish-speaking households, and teachers together. In so doing, both the parents and their children built mathematical skills and conceptual knowledge, including that related to the CCSS and SMP. As a result, this program demonstrates the educational effectiveness of building supportive home–school relationships (Epstein, 2011, 2013). When teachers make strong efforts to establish these relationships, home-based funds of knowledge and out-of-school community cultural wealth are revealed to be richly present in the everyday experiences of almost all children that can be leveraged to support their learning in every subject matter, including mathematics (Moll, Amanti, Neff, & González, 1992; Yosso, 2005). But teachers must believe those funds and that wealth are present to begin with, and then invest the time and effort necessary for parents to develop enough trust in them to share of themselves in this way. A pivotal step in this investment process, teachers, like those on our family math night educational team, must express on-going appreciation and affirmation of the daily efforts parents make to raise their children; in our case this included making sure that parents knew how valuable their attendance at the family math nights’ sessions was. Parent involvement is a critical element in supporting all children’s success in school, and must be regarded as so by all teachers. Such involvement is even more critical in children’s success in math, precisely because so many parents feel challenged to understand the material, especially as their children approach middle school–level math curricula. With the adoption of the CCSS and SMP, these challenges are amplified (Donovan & Bransford, 2005). Adding a fourth dimension to these challenges is relationship building with working class parents and those who speak English as a second language. Our family math nights’ program provides one way that all of these challenges may be successfully reconciled, proving how essential and how possible it is

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for teachers to meaningfully involve all parents in their children’s mathematical education. REFERENCES Adjiage, R., & Pluvinage, F. (2007). An experiment in teaching ratio and proportion. Educational Studies in Mathematics, 65(2), 149–75. Arizona Department of Education (ADE). (2012). Arizona’s common core state standards. Retrieved from http://www.azed.gov/azcommoncore/mathstandards/68math/ Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problems of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook on the Research on Teaching (fourth edition, pp. 433–56). New York, NY: MacMillan. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of Teacher Education, 59(5), 389–407. Clark, C., Flores, R., Rivera, L., Biesinger, K., & Morgan, P. (2012). We make the road by walking: The family leadership initiative in Las Vegas. In A. Cohen and A. Honigsfeld (Eds.), Breaking the mold of education for culturally and linguistically diverse students: Innovative and successful practices for 21st century schools. (pp. 85–94). New York: Rowman & Littlefield. De La Cruz, Y. (2008). Who mentors Hispanic English language learners? Journal of Hispanic Higher Education, 7(59), 31–42. De La Cruz, Y. (1999a). A model of tutoring that helps students gain access to mathematical competence. In L. Ortiz-Franco, N. Hernandez, and Y. De La Cruz, (Eds.), Changing the faces of mathematics: Perspectives on Latinos. Reston, VA: National Council of Teachers of Mathematics (NCTM). De La Cruz, Y. (1999b). Promising research, programs and projects: Reversing the trend: Latino families in real partnerships with schools. Teaching Children Mathematics, 5(6), 296–300. Donovan, M. S., & Bransford, J. D. (Eds.). (2005). How students learn: Mathematics in the classroom. Washington, D.C.: National Academic Press (NAP). Epstein, J. (2013). Ready or not? Preparing future educators for school, family, and community partnerships. Teaching Education, 24(2), 115–18. Epstein, J. (2011). School, family, and community partnerships: Preparing educators and Improving Schools. Baltimore, MD: Westview Press. Espinosa, L. L. (2009). Pipelines and pathways: Women of color in STEM majors and the experiences that shape their persistence (Unpublished doctoral dissertation). University of California, Los Angeles. Fleischman, H., Hopstock, P., Pelczar, M., & Shelley, B. (2010). Highlights from PISA 2009: Performance of U.S. 15-year-old students in reading, mathematics, and science literacy in an international context. U. S. Department of Education, Institute of Education Sciences (IES), National Center for Education Statistics (NCES). Retrieved from: http://nces.ed.gov/pubs2011/2011004.pdf



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Harvard Family Research Project (HFRP). (2007). Family involvement in middle and high school students’ education. Cambridge, MA: Author. Hurkle (n. d.). Hurkle game. Retrieved from http://august10teacherinservice.wikispaces.com/file/view/Hurkle+Game+(Coordinate+Plane).pdf Irwin, K. (2001). Using everyday knowledge of decimals to enhance understanding. Journal for Research in Mathematics Education, 32(4), 399–420. Kilpatrick, J. Swafford, J., & Findelle, B. (Eds.) (2001). Adding it up: Helping children learn mathematics. Washington, DC: Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education, National Research Council (NRC)/National Academy Press (NAP). Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2006). Connected mathematics2: Comparing and scaling. Boston, MA: Pearson. Ma, X., & Ma, L. (2004). Modeling stability growth between mathematics and science achievement during middle and high school. Evaluation Review, 28(2), 1004–122. Moll, L., Amanti, C., Neff, D., & González, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132–41. Moseley, B. (2005). Students’ early mathematical representation knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies on Mathematics, 60(1), 37–69. Moses, R. (2002). Radical equations: Civil rights from Mississippi to the Algebra Project. Boston, MA: Beacon Press. Takaki, R. (1993). A different mirror. A history of a multicultural America. Boston, MA: Little, Brown, and Company. Yosso, T. (2005). Whose culture has capital? A critical race theory discussion of community cultural wealth. Race, Ethnicity and Education, 8(1), 69–91.

Chapter Two

Using Iterative Visuals and Virtual Manipulatives to Support English Language Learners in Mathematics Education Sarah A. Roberts

Understanding mathematical concepts is sometimes challenging for learners of all ages. While some students continue to effortlessly develop their mathematical understanding throughout their educational journey, others are turned off from mathematics at a young age. While there are numerous influences that affect this trajectory, we argue that students’ academic language, particularly in the area of mathematics, can have an impact on a student’s mathematical understanding as well as their attitude toward learning about mathematics. When designing mathematics curriculum, teachers often focus on either developing students’ conceptual understanding or their fluency with algorithms, while sometimes completely overlooking the need to develop other competencies, such as academic language. Particularly for the growing population of English language learners (ELLs) who make up over 11% of K–12 students in the United States, developing academic language is essential. Also crucial is the need for all students to be allowed greater access to, and support in, cognitively demanding, rigorous math courses (Lee & Buxton, 2013; Moschkovich, 2002). Given the many demands in math education, teachers must begin to consider new ways of redesigning curricula to build multiple competencies, rather than choosing one over another. Research has shown that when teachers provide students access to grade-appropriate instruction with purposeful scaffolding, students can learn both content and academic language (Understanding Language, 2013). Unfortunately, few teachers have had the necessary education and/or professional learning experiences to effectively marry multiple competencies in their classrooms. 19

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This chapter provides an example of multicultural curriculum transformation of middle school–mathematics curriculum, in an effort to redefine the conventional instructional model. Traditionally, students are taught complex math concepts in a very abstract way, more often than not forcing them to simply rely on memorization, when what they lack is actual comprehension. Given the challenges of choosing to focus on developing students’ content knowledge or developing their fluency with algorithms, one teacher discovered that she could effectively integrate both strategies by teaching students to create and apply a multidimensional model using not only written text but numerical and visual representations. Through class discussion and feedback surrounding a widely used algorithm, the teacher was able to gain the necessary insight regarding students’ successes and challenges in order to transform the curriculum to meet the students’ needs effectively. Mrs. Wicket, the middle school mathematics teacher responsible for the curriculum transformation, began by assigning her students a shared fraction multiplication problem set. Students were provided a worksheet with three columns: one column contained the text of the problem, while the second column encouraged the students to represent the words with numerical representation, and the third column called for a visual representation of the problem. Her students started by reading the problem aloud using the popcorn method, where reading was passed from person to person. After reading the passage, Mrs. Wicket asked students to code the text; a learning strategy to help students begin to make sense of a given text, in an effort to encourage deeper reflection and continued understanding. As students began to evaluate the problem, they found both familiar and unfamiliar terms and had the opportunity to share their interpretations with the class. In order to clarify any remaining confusion, Mrs. Wicket asked her students, “What words were there. . . ? Do we need to look anything up?” After explaining terms like brownies, suppose, and represent, Mrs. Wicket instructed her students to begin working with their assigned partners to create their own visual and numerical representations of the problem using the remaining two columns on the worksheet provided. One by one, students drew pictures of fractional brownie pans, using their pencils to draw lines that cut the brownies into new pieces. Once each pair had the opportunity to work through a few problems and subsequently share their methods with a few of the other groups, Mrs. Wicket had students use the National Library of Virtual Manipulatives (USU, 2017) website to work through the remaining problems. Students used the applet to create visual representations of the assigned problem set. Students were also encouraged to make comparisons between their drawings, numerical representations, and the virtual manipulatives, specifically to tease out any patterns and to look for the most efficient way for them to arrive at a solution.



Using Iterative Visuals and Virtual Manipulatives 21

Mrs. Wicket’s class concluded with the students coming back together to share individual solutions. She used this time of reflection to encourage students to be critical of their observations, and she pushed students to identify the most efficient method in solving this type of problem. Mrs. Wicket explained that she could have simply just shown the students the algorithm, but that method would not have been nearly as effective in facilitating the deeper understanding and comprehension gained through the transformed multidimensional model. Furthermore, Mrs. Wicket informed her students that because they were now familiar with and had used this new model, they could apply it, adapting it as necessary to future problems they might encounter throughout their lives, in mathematics classes, and beyond. This chapter seeks to thoroughly discuss Mrs. Wicket’s multidimensional model, following her multicultural curriculum transformation process from design to implementation. Multicultural curricular transformations affirm all students, including, English language learners (Clark, 2002), and focuses on how the modification of instruction can support students from diverse backgrounds to achieve academically (Banks, 1995; Clark, 2002; Suzuki, 1984). In this case, Mrs. Wicket’s model created multiple ways for English language learners to engage in meaningful ways, and it supported them in critically analyzing content (Suzuki, 1984) so that they were not simply memorizing an algorithm. Instead, students had access to a variety of pedagogical tools to support them in drawing on the resources they brought to class (Clark, 2002; Nieto, 2005). CONCRETE EXAMPLE OF MULTICULTURAL CURRICULUM TRANSFORMATION IN MATH EDUCATION Content Linked to Pedagogy and Assessment As described in the opening vignette, Mrs. Wicket’s lesson on fractions focused on her students’ development of their conceptual understanding to be able to multiply fractions through the use of visual and numerical representations, prior to the students learning the algorithm. The students used multiple learning tools and mathematical representations to learn about multiplying fractions, which included engaging in discussion, reading and coding text, exploring representational models, creating visual iteratives, using virtual manipulatives, and developing an algorithm. An obvious tool Mrs. Wicket used when transforming her mathematical curriculum was the inclusion of student dialogue. This lesson plan included time for structured and semistructured conversations. At times the students were conversing amongst themselves and during other parts of the lesson the

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teacher was a part of whole and small group discussions. Mrs. Wicket frequently stopped small groups that were working and had them explain their thinking to their partners, other groups, and the whole class. Students were expected to talk about their processes, challenges, and successes with their peers and teacher throughout each lesson. This type of student engagement and participation is not likely in classrooms where group work has not been modeled and discussed. Furthermore, Mrs. Wicket had to form a safe environment . . . that class was just really scared of math. So, I did this with a lot of lessons to get the kids . . . to have an opinion and their reason. And then they could talk to their group and try to figure it out, instead of just going, “I don’t know.” (X. W. Wicket, personal communication, February 19, 2010)

The second key pedagogical tool that Mrs. Wicket used in her multicultural curriculum transformation was to set-up the mathematical task that considered the content that needed to be addressed while also considering her student population. Because Mrs. Wicket knew the resources provided in the textbook were not going to address the needs of her learners and her teaching approach, she developed her own materials. The handout Mrs. Wicket created contained modified text from Bits and Pieces II (Lappan, Fey, Fitzgerald, Friel, & Philips, 2009) in one column and space for the visuals and numerical solutions in the other two columns: The first part was all the language; it was the language of the problem. And then the next two columns are the math that went with that problem. That breakdown alone shows what they needed to bridge between the language and the math, the construct. (X. W. Wicket, personal communication, April 27, 2010)

Mrs. Wicket explained, “A lot of it is just taking the text [from the textbook], and I’ve split it up into smaller chunks. So after each sentence, we can stop and say, ‘Did we understand that?’” (X. W. Wicket, personal communication, April 27, 2010). The class then coded the text, starting with the class reading of the text using the popcorn method. Mrs. Wicket described the class’s process for coding as the following: In coding the text in my sheltered class, it’s focusing on [the] meaning of the text, like comprehension, but also the words, the vocabulary that’s used. So, we start with the vocabulary and then we go to what does this mean? What does this problem look like? Where are they? What are they doing? The comprehension part. Not that in the advanced class that I never go over the vocabulary as many



Using Iterative Visuals and Virtual Manipulatives 23

times as I do in the sheltered, but in the sheltered class, it’s after almost every sentence. We say, “What words were there?” “Do we need to look anything up?” (X. W. Wicket, personal communication, April 27, 2010).

In the brownie pan fraction multiplication problem the students were working on during the class period, the class discussed the terms suppose, represent, brownies. Once the class was clear on the task and the associated key terms, they were ready to tackle the problems. Using Mrs. Wicket’s iterative visuals allowed the students to move through the multiplication of the fractions. First, students drew the original pan. Then they redrew the original pan but cut (with their “pencil knife”) so that they had fourths (for example). In this model, the students looked for the crossover in colors; the overlap. Finally, the students circled the piece that the person from the problem was going to buy. The iterative visuals supported students to think about an initial quantity and what resulted with multiplication. Mrs. Wicket shared that “with the sheltered kids, I wanted to really emphasize how much is there to start with and there can’t be any more than that. But, we can take away from that. So, that’s why I had them draw that three times” (X. W. Wicket, personal communication, April 27, 2010). This iterative process helped students understand not only the procedure of multiplying fractions with a visual model, but it also helped them to see and understand the context of the problems through the displayed visuals. (An example of one such visual is shown below with the accompanying mathematics task for Figures 2.1–2.5.) Mr. Williams walks up to a brownie station and sees half (½) of a pan of brownies. Represent one-half pan of brownies vertically on the brownie pan to the right. Mr. Williams does not want everything in the pan, so he buys one-third (⅓) of the brownies in the pan. Represent half of a pan of brownies vertically on the brownie pan to the right. Then, cut the brownies horizontally to represent the portion of the brownies that Mr. Williams buys; use red to color the part that Mr. Williams buys. Mr. Williams buys __________ of the pan of brownies. Aunt Serena walks up to the brownie station after Mr. Williams. In a different pan, there are three fourths (¾) of the brownies left over. Represent three-fourths (¾) of a pan vertically on the brownie pan to the right. Aunt Serena does not want everything in the pan, so she buys one-half (½) of the brownies in the pan. Represent three-fourths of a pan of brownies vertically in the brownie pan to the right. Then, cut the brownies horizontally to represent the part of the brownies that Aunt Serena buys; use red to color the part that Aunt Serena buys.

Figure 2.1.  Top: Initial brownie station representation. One-half of the first pan of brownies is shaded. Bottom: Brownie station representation of the available brownies cut into thirds; the one-half portion of shaded brownies is cut into thirds because Mr. Williams wants one-third of the remaining brownies.



Using Iterative Visuals and Virtual Manipulatives 25

Figure 2.2.  Top: Brownie station representation of the final solution. Mr. Williams will purchase one-sixth of the original pan of brownies because he bought one-third of the one-half of brownies that remained. Bottom: Brownie station representation of the second pan of brownies. Three-fourths of the brownies are shaded to represent the remaining amount.

Aunt Serena buys ______ of the pan of brownies Once the students worked through the word problems on their handout, they grabbed laptop computers to use “Fractions—Rectangle Multiplication” on the National Library of Virtual Manipulatives (USU, 2017; see Figure 2.4 for a screen shot of the virtual manipulative). A virtual manipulative is “an interactive, web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” (Moyer,

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Figure 2.3.   Top: Brownie Station Representation of the Available Brownies Cut into Halves; the three-fourths portion of shaded brownies is cut into halves because Aunt Serena wants one-half of the remaining brownies. Bottom: Brownie Station Representation of the Final Solution. Aunt Serena will purchase three-eighths of the original pan of brownies because she bought one-half of the three-fourths of brownies that remained.

Bolyard, & Spikell, 2002, p. 373). Virtual manipulatives allow for working through mathematical representations in a visual way and allow individuals to manipulate a computer visual to demonstrate and/or work through a mathematical concept. Mrs. Wicket’s use of the technology was two-fold. First, students used the applet to check their answers from their visual and numerical representations. Second, the students used the visuals in the virtual manipulative to identify and confirm patterns associated with multiplying and dividing fractions, which helped them understand most importantly, how and why the



Using Iterative Visuals and Virtual Manipulatives 27

Figure 2.4.   The Fractions–Rectangle Multiplication program.

algorithms work. The students identified patterns for multiplying fractions in more efficient ways than if they only used visual models. The final step in Mrs. Wicket’s multicultural curriculum transformation was to bring the class back together to identify patterns to develop a more efficient way to multiply fractions, an algorithm. Mrs. Wicket had students share the patterns they noticed in their numerical solutions, without the visuals. She described it like this: I take all the work that we did with all the pictures, condense it onto one page with the pictures taken away, just the numbers and have them find the algorithm themselves and then make the connection. So, if we’re saying the algorithm is to do . . . diamond method, numerator times denominator times numerator, does that work for every new problem? So, here’s a new problem. Draw it again. Get the answer with the drawing. Does the algorithm work? So usually do that order. They draw, put all the numbers together, find the algorithm, and then make sure it works for other problems. (X. W. Wicket, personal communication, April 27, 2010)

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Figure 2.5 illustrates some of the patterns that students noticed in their work. In this particular case, students noticed they could multiply across the numerators and across the denominators to find the same solution they found using their visual representations. After testing a couple of additional examples of their own choosing, the class agreed that this method worked. If students multiplied numerator-by-numerator and denominator-bydenominator, they should have gotten the same solution numerically and with the (iterative) visuals.

Figure 2.5.   A numerical representation of the brownie mathematics problem.



Using Iterative Visuals and Virtual Manipulatives 29

Assessment was an ongoing and important component of Mrs. Wicket’s fraction multiplication lesson with her sheltered mathematics class. There were multiple formative assessment opportunities throughout the lesson to see whether students were making sense of how to multiply fractions, how they were doing so, and what type of intervention they might need individually. For example, in the first part of the lesson, Mrs. Wicket checked in individually with students while they coded the text. She spoke with students to see which words were confusing and had other students explain the words to their peers. Mrs. Wicket also had students talk through their processes for drawing visuals and how they used visuals to get to a final visual and numerical solution. Finally, Mrs. Wicket used formative assessment within the whole class discussion when she brought the whole class together to have selected students share their reasoning for the patterns they noticed. During each part of the lesson, Mrs. Wicket had the opportunity to assess her students formatively and to make instructional decisions about whether she would provide additional support and instruction or to allow the students to move on to the next part of the lesson. Mrs. Wicket additionally found success in her summative assessments of students in her unit test. She remarked, “When I saw their test scores after this unit with the [textbook and visual representations], it just blew me away how much these kids can do if they have that support” (X. W. Wicket, personal communication, April 27, 2010). Mrs. Wicket found that with the right structures and supports in place, her students were very successful. She was hopeful about the long-term implications of her instruction: I wanted them to not just know the numbers-based part of multiplying the numbers; I wanted them to know why, so they didn’t just memorize what to do. But they knew why it happened that way, hopefully so that they remember it for the seventh grade. (X. W. Wicket, personal communication, April 27, 2010)

Teachers who might perform a curriculum transformation like this one would want to focus on using an instructional approach with a variety of learning opportunities (Clark, 2002) that would support students in developing a conceptual understanding of content that leads to understanding why more efficient strategies work. A key component of both Mrs. Wicket’s pedagogy and assessment was her use of talk with her English language learners and providing opportunities for English language learners to discuss the content in purposeful ways. Mrs. Wicket supported English language learners in talking through their thinking and allowed the students to use resources, like gestures, visuals, and colloquial language (Moschkovich, 2002), to make sense of and share their understanding of the content. This means that a teacher who would like to conduct a transformation like this one would

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need to be having constant conversations with her class as a whole as well as with individual students. Educational Context This multicultural curriculum transformation process took place in a sixth grade class situated in a metropolitan school in the western United States. The class was part of a sixth through eighth grade middle school consisting of approximately 1,500 students. During this time, approximately 55% of the student body received free or reduced-price lunch, and approximately 25% of the student body was classified as English language learners. The teacher, Mrs. Wicket, a fourth-year mathematics teacher, taught a sheltered mathematics course, for exclusively English language learners, made up of twelve students: eleven boys and one girl. The majority of the students spoke Spanish, but there were also students who were refugees from non-Spanish–speaking countries. All of her students had prior schooling/math experiences, and approximately 75% of the students did not speak English at home. The students within the course were also taking classes in English language acquisition. In any educational setting, it is important to remember that students and schools are individualized. In examining one’s own educational context, teachers should first examine student needs, especially in relation to their demonstrated competencies. Mrs. Wicket began by facilitating a class discussion, and she subsequently used student feedback to guide her next steps. Additionally, teachers may need to consider how Mrs. Wicket’s model might be modified based on available texts, accessibility to technology, any known issues with supplementing instruction with technology, as well as based on other factors such as class size or available time. To add, teachers might consider using different visuals or manipulatives in their classrooms, perhaps opting for a more tactile solution. Also, depending on the structure of their classrooms, some teachers may need to take a more hands-on approach, leading students through the varied portions of the model instead of grouping students together to work in pairs. Nevertheless, much of the work in this chapter is transferrable across contexts. In particular, a teacher’s model need not focus on fractions; many other content lessons could be used. Ultimately, teachers must consider their individual students, classrooms, and schools in order to decide what will be best for their students’ learning. Addressing Standards There are a number of different types of math standards that teachers might use to guide their instruction (e.g. CCSS-M, NCTM, state and local content



Using Iterative Visuals and Virtual Manipulatives 31

standards) and chosen content. Working with standards involves first identifying particular standards that an individual must address, which are often linked to a particular unit a teacher has organized. The classroom discussed in this chapter used standards related to the multiplication and division of fractions, particularly for sixth grade students. Once a teacher has identified standards, she should consider which curricular resources she plans to use to address the standards and why. A multicultural curricular transformation will include a varied instructional approach, with whole class, small groups, and one-on-one interactions and will employ a variety of learning activities (Clark, 2002). Mrs. Wicket’s school used the Connected Mathematics 2 text, Bits and Pieces II (Lappan et al., 2009), to link lessons with the state and district standards. Regardless of the standards one is using, students will likely be learning about the multiplication and division of fractions between fourth and seventh grade. Because Mrs. Wicket’s multidimensional model is highly adaptable, a teacher could use it with multiple content areas and standards. A teacher would first identify a starting quantity or expression, then include visual representations of the mathematical concept (e.g., one could include tables, graphs, drawings of manipulatives, etc.). Mrs. Wicket chose not to use this model with fraction division, so it is important to consider how a particular model links with the desired content standards. Ultimately, this model should serve as a foundational tool to give students access to multiple ways of examining a problem set, and eventually, through detailed instruction, students should be able to adapt the model for their own individual use. Relationships with and among Students and Their Families Mrs. Wicket worked very hard in her daily practice to develop and build relationships with her students, and her success was largely dependent upon those established relationships. Mrs. Wicket expected that all of her students would be collaborative members of the classroom, reading, writing, and speaking in class as they worked, regardless of language proficiency. Healthy relationships between students and their teachers are extremely vital to classroom success, especially with collaborative work. Mrs. Wicket helped to develop her students’ mathematical understanding and academic language in a discourse-rich community where all students were expected to actively participate. Through classroom engagement, students simultaneously developed both their language and mathematics skills. The multicultural curriculum transformation process for Mrs. Wicket relied heavily on her ability to use the already established relationships with her students to her advantage. The students depended on one another and

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pushed each other to grow within the classroom setting. When there was confusion, students would first go to each other with their questions to see if they could work through their challenges, with Mrs. Wicket serving as a guiding presence. Only after first attempting to solve a problem themselves did Mrs. Wicket’s students go to her to ask for greater clarification. Mrs. Wicket’s efforts to build, maintain, and extend these relationships were key in helping her to be successful in this process of multicultural curriculum transformation. Civic Engagement Mrs. Wicket’s class organization and instruction provided several opportunities for her students to practice citizenship in the classroom. More specifically, her students engaged in meaningful dialogue, worked collaboratively with one another, and supported each other’s learning. Mrs. Wicket created an inclusive and supportive community within her classroom where everyone had a voice and the expectation to participate because every student was a valued community member. Opportunities such as those in Mrs. Wicket’s class help to teach and prepare students to engage in the overall democratic society. Students’ engagement in such rich discourse allowed them to see each other as scholars. Students who develop a deep understanding of content learn how to analyze critically other knowledge and how to develop interpretations of that knowledge (Banks, 1995). To add, as students worked through their problem sets and learned to master content, Mrs. Wicket’s classroom further facilitated her students’ ability to affect the economic, political, and social systems within which they live and learn. For example, learning to work fluently with fractions provides a pathway to success in algebra. In succeeding in algebra, a student will have access to many more opportunities in today’s technological economy (Moses & Cobb, 2001). Moses and Cobb argue that there has been a shift in the economy that requires increased knowledge and use of technological skills. Mathematics, in particular algebra, provides access to this technological economy. Access to and success in mathematics supports students in being eligible to go to college and thereafter, having access to an economy that is highly dependent upon individuals who can do STEM work. Additional Considerations Because the context of this multicultural curriculum transformation was a sheltered mathematics course for English language learners, Mrs. Wicket designed the activities, tools, curricular materials, and instructional strategies in this lesson for her sheltered students to support their mathematics and



Using Iterative Visuals and Virtual Manipulatives 33

language development. For example, Mrs. Wicket provided specific supports for her English language learners such as modifying written text for sheltered students’ instructions, reading passages, and/or assignments. Mrs. Wicket noted: Since I know that they are going to need support with this aspect of reading, I put supports in place for that. . . . And, so, it might be good practices to have some sort of strategies in place. . . . I [might] modify the whole English text and break it down into chunks and do pictures and do a three column note style for that . . . each little check had the part for the numerical answer and the visual answer. . . . Just kind of that segmenting of the steps would be the biggest thing. (X. W. Wicket, personal communication, April 27, 2010)

To create these reading supports, Mrs. Wicket typed the text from Bits and Pieces II from the Connected Mathematics 2 Series (Lappan et al., 2009) onto consumable pages so students could write notes on the text, circle key terms, and make further connections. As part of this process, Mrs. Wicket decreased the amount of text and modified the text to repeat the key ideas. Additionally, the students’ problem worksheet was organized into three columns: written representation, numerical representation, and visual representation; students filled in the latter two. These reading supports are examples of additional considerations that Mrs. Wicket took into account to help her English language learners engage more fully in the text, the context, the language, and the mathematics. Teachers may choose to modify their curriculum in similar ways, with the use of visual mathematical representations, text modifications, consumable worksheets, and so forth. for all students. Mrs. Wicket’s model and other instructional supports provide an approach for engaging students in thinking through why they are making particular decisions and taking particular paths, and they aid students in explaining their thinking. Special education students often receive similar supports in their instruction. To engage students who may need an additional challenge or extension, teachers could consider providing more challenging number choices, having students prepare to explain to a younger child in their own words and using their own representations for how one goes about multiplying fractions, or requiring students to create their own problems to exchange with peers and to assess their peers’ understanding of the content. Integrated Use of Technology Technology in this multicultural curriculum transformation was a key aspect of the learning process for the involved students. The class worked with the

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National Library of Virtual Manipulatives (USU, 2017) to make sense of how to multiply fractions. The use of technology was tightly linked with the work in the text and extended the work that students had done in their own drawing of the fraction models (e.g., the brownie pan drawings that were part of their iterative visuals). Using technology provided students with a different but similar representation that allowed for more rapid manipulation of their representations. Students could move through multiple multiplication problems in the time that it would take to work on a single handwritten problem. This ability to use multiple representations in rapid succession helped students to continue to identify patterns in written problems (e.g., ½ x ¼) and visual representations. Such patterns helped students to begin to develop an algorithm. Mrs. Wicket felt that the virtual manipulatives really helped bring this lesson together. She remarked, I think [the students’ understanding] really set in after they were able to go on the laptops and use that [National Library of Virtual Manipulatives] and change the fractions and see what it did to the area that was the purple area in common, because the ticket out that we did before that I don’t really remember having great results on that. . . . But, after that laptop [experience with the virtual manipulatives] they were good. (X. W. Wicket, personal communication, April 27, 2010)

The technology allowed students to go beyond using only visual representations to solve problems and allowed them to develop a more efficient process as their knowledge and understanding developed. The use of technology also provided students with access to a technological tool that was previously unfamiliar to them, one that could be useful in their studies of other mathematical concepts. In this way, the technology could open up doors to students by providing them with access to a new tool that they could use with other fraction problems, such as adding fractions, comparing fractions, and/or finding equivalent fractions. Additionally, the National Library of Virtual Manipulatives includes manipulatives in the areas of algebra, geometry, measurements, data analysis, and probability, which students could use to develop their understanding in these other areas. Access to and awareness of technology is not always distributed equally, so making students aware of such a tool is important. Note to Teachers Instead of thinking about teachers as being discretely placed in categories of having a number of years of experience, I consider teachers coming to the



Using Iterative Visuals and Virtual Manipulatives 35

table with different types of experiences. For example, some teachers will have less experience using technology in their classrooms. For such teachers, this chapter provides an example of how a mathematics teacher could link the development of an algorithm with the use of visual representations and an available technology tool. Similarly, some teachers may not have thought about how to use visual representations with their students. The use of iterative visual models might be a place for starting to include more visuals in a classroom and to use such visuals to help students “see” what is happening with the mathematics in a task. Additionally, we know that few teachers have had learning experiences related to how to support English language learners in the classroom. This chapter provides one example of how teachers might support English language learners in learning content. For example, teachers could support their students in developing both content and academic language while using a context and text heavy textbook, which might seem counterintuitive. Teachers can use such a text as a resource by helping students code text, making sense of a problem’s context, using and developing visuals, and getting students to talk openly with their classmates and teacher about math. REFLECTION BRIDGE Mrs. Wicket’s work with her sixth grade sheltered students around multiplying fractions provides an opening into what we can do to provide access to challenging content in meaningful ways. Teachers have to modify their instruction in ways that facilitates the learning of students from diverse backgrounds (Banks, 1995). Mrs. Wicket used a variety of tools and strategies to engage her students, bringing together what she knew about her students and what she knew her students needed to conquer the content and language. The tools, as enacted, that Mrs. Wicket used in her classroom will not work the same in every classroom. Context matters and students matter. Teachers have to play with what works for their students until they find the right combination for their given classes at a given time. There are a lot of tools to use to support student learning in the context of a multicultural curriculum transformation. A teacher has to understand her students’ mathematical knowledge and language development in order to be able to make connections between multiple mathematical representations, algorithms, background language, language associated with the problem, and more. Ultimately, a teacher’s work with her English language learners goes beyond simply providing support with vocabulary. Mrs. Wicket’s multidimensional model worked because she knew her students, she considered

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what they needed, and she put a lot of coordinate supports into place simultaneously. Mrs. Wicket saw that her students brought resources and strengths (Nieto, 2005) to the mathematics classroom, and she found multiple ways to build on those strengths and resources. We know that all students deserve access to high-quality content and instruction, and there are multiple approaches, tools, and methods (Clark, 2002) for providing that access. CRITICAL CONSIDERATIONS IN STEM MULTICULTURAL CURRICULUM TRANSFORMATION: THE THEORY Over the past twenty years, the number of English language learners in U.S. schools has increased 152% (National Clearinghouse for English Language Acquisition, 2009), and over 11% of students in K-12 settings have been identified as English language learners (Lee & Buxton, 2013). English language learners face a double challenge of learning both social and academic language (Khisty & Chval, 2002). Further, educators have a responsibility to support the learning of all students, including English language learners, and to provide all students with access to high-quality curriculum and instruction (National Council of Teachers of Mathematics, 2000; Nieto, 2005). A multicultural curricular transformation allows for affirming all students and providing a more level playing field for all students (Clark, 2002). Moschkovich (2002) views mathematics education as situated in sociocultural contexts. She describes the practice as discursive and going beyond just simply learning vocabulary. Instead, teachers working with English language learners must use their students’ social, linguistic, and material resources; English language learners bring a variety of resources and funds of knowledge to mathematics classes that teachers can draw on to support English language learners’ inclusion in mathematics learning (Moll, Amanti, Neff, & Gonzalez, 1992). Such resources include home language, prior knowledge and experiences, gestures, objects, experiences with natural phenomena, codeswitching, and everyday experiences and practices (Duff, 2010; Esquinca, 2013; Goldenberg, 2008; Lee & Buxton, 2013; Moje, 2008; Moschkovich, 2002, 2007; Understanding Language, 2013). Drawing on English language learners’ resources allows teachers to “build on student interpretations and connect them to canonical mathematical discourse practices and important conceptual content” (Moschkovich, 2008, p. 578), supporting English language learners to become members of the mathematics community. Mrs. Wicket engaged with a multicultural curricular transformation in her teaching of multiplication of fractions; her goal in her instruction was making it accessible to all students (Nieto, 2005), especially her English language learners. Mrs. Wicket supported the inclusion of her English language learner



Using Iterative Visuals and Virtual Manipulatives 37

students in her mathematics classroom through her use of multiple tools and representations tailored to develop both their language and mathematics without stripping away the use of language or the complexity of the mathematics (Moschkovich, 2002). Mrs. Wicket also built on her students’ resources (Moschkovich, 2002; Nieto, 2005) in a number of ways. First, she helped students to make sense of the problem’s context through discussing students’ own experiences with brownies and fractions. Then she used the students’ shared experiences from the beginning of the year when they had used rectangular models to represent fractions. Finally, Mrs. Wicket used students’ experiences with technology and their excitement about using technology to engage students with fractional representations in another way. Throughout her lesson, Mrs. Wicket focused on student reasoning. She continually asked students to explain what they were doing and how it worked. Mrs. Wicket wanted her students to understand the concepts deeply and not to simply memorize an algorithm; she wanted her students to retain and be able to manipulate the content in the future (Clark, 2002). The big push at the end of the lesson was to take what the students had learned with their visual models and the virtual manipulatives to develop an understanding of the algorithm for multiplying fractions. This final step involved Mrs. Wicket helping her students to make connections between visuals, virtual manipulatives, and patterns to develop an algorithm for multiplying fractions. Mrs. Wicket maintained cognitive demand while also helping students to develop language, even with a language-heavy text. This chapter provides an example of a multicultural curricular transformation in a middle school mathematics classroom for English language learners. Mrs. Wicket approached her methods of instruction with an understanding of and sensitivity to her students (Suzuki, 1984), building on the strengths and resources they brought to class (Moschkovich, 2002; Nieto, 2005). The teacher used a variety of pedagogical tools, assessments, and learning activities (Clark, 2002) to support her English language learners in learning keystone content that could provide them access to future content and opportunities. REFERENCES Banks, J. A. (1995). Multicultural education and curriculum transformation. Journal of Negro Education, 64(4), 390–400. Clark, C. (2002). Effective multicultural curriculum transformation across disciplines. Multicultural Perspectives, 4(3), 37–46. Duff, P. A. (2010). Language socialization into academic discourse communities. Annual Review of Applied Linguistics, 30(1), 169–92.

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Esquinca, A. (2013). Transfronteriza pre-service teachers managing, resisting, and coping with the demands of mathematical discourse. International Journal of Qualitative Studies in Education, 26(3), 279–300. Goldenberg, C. (2008). Teaching English language learners: What the research does—and does not—say. American Educator, 32(2), 8–23. Khisty, L. L. & Chval, K. B. (2002). Pedagogic discourse and equity in mathematics: When teachers’ talk matters. Mathematics Education Research Journal, 14(3), 154–68. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Philips, E. D. (2009). Bits and pieces II: Using fraction operations. Boston, MA: Pearson. Lee, O., & Buxton, C. A. (2013). Teacher professional development to improve science and literacy achievement of English language learners. Theory Into Practice, 52(2), 110–17. Moje, E. B. (2008) Everyday funds of knowledge and school discourses. In MartinJones, M., de Mejia, A. M., & Hornberger, N. H. (Eds.), Encyclopedia of Language and Education (second edition, pp. 341–55). New York, NY: Springer Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and schools. Theory into Practice, 31(2), 132–41. Moses, R. P., & Cobb, C. E. (2001). Radical equations: Civil rights from Mississippi to the Algebra Project. Boston, MA: Beacon Press. Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2&3), 189–212. Moschkovich, J. (2007). Using two languages when learning mathematics. Educational Studies in Mathematics, 64(2), 121–44. Moschkovich, J. N. (2008). “I went by twos, he went by one:” Multiple interpretations of inscriptions as resources for mathematical discussions. The Journal of the Learning Sciences, 17(4), 551–87. Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372–77. National Clearinghouse for English Language Acquisition. (2009). How has the limited English proficient student population changed in recent years? Washington, DC: NCELA. Retrieved from http://www.ncela.us/files/rcd/BE021773/How_Has_ The_Limited_English.pdf National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM. Nieto, S. (2005). Public education in the twentieth century and beyond: High hopes, broken promises, and an uncertain future. Harvard Educational Review, 75(1), 43–64. Suzuki, B. H. (1984). Curriculum transformation for multicultural education. Education and Urban Society, 16(3), 294–322. Understanding Language District Engagement Subcommittee. (2013). Six key principles for ELL instruction. Retrieved from http://ell.stanford.edu/sites/default/files/ Key%20Principles%20for%20ELL%20Instruction%20wwit%20references_0.pdf Utah State University (USU). (2017). National library of virtual manipulatives. Retrieved from http://nlvm.usu.edu/en/nav/vlibrary.html

Chapter Three

Rethinking the Teaching and Learning of Latina/Latino Students to Promote a Multicultural Mathematics Education Javier Díez-Palomar and Carlos A. LópezLeiva

I say that reading is not just to walk on the words, and it is not flying over the words either. Reading is re-writing what we are reading. (Shor & Freire, 1987, p. 1)

INTRODUCTION In an informal and engaging environment, a group of bilingual Latina/Latino children are playing a probability game in Spanish with their mothers: Yay! I won! . . . I won, I won!

Raúl: ¡Yey! ¡Ya gané! . . . gané, gané! Madre1: Me quedaron tres. María: (whispers) Cheater! Raúl: (looking at María) I’m not a cheater! Orlando: A mí también. María: A mí me quedó uno. Raúl: ¡A mí me quedó cero! Madre2: (to Raúl) Hiciste trampa. Madre1: Porque acuérdate que aquí el que gana es como si perdiera. Tú estás jugando el mío, y yo el tuyo.

I had three left. [Tramposo!] [No soy tramposo!] Me too. I had one left. I had zero left! You cheated. Because remember that here who wins, it is as if he’d lost. You’re playing mine, and I am playing yours. 39

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Madre2: ¡Como ya llevas dos ganados, quedas descalificado!

Since you have won twice, you are disqualified. (CEMELA fieldwork)

Next, the group facilitator asks the children to make sense of recurrent number patterns and how they may be linked to the concept of probability: Facilitador: ¿Por qué tú crees que algunos salen más que otros? Orlando: (shrugging shoulders) ¡Yo no sé! Raúl: Con el dos no sale mucho . . . porque, porque casi no hay muchas posibilidades para hacer uno y uno, con el dos. . . . Y tampoco con el doce. Facilitador: ¿Y el siete, por qué sale tanto? Raúl: Porque hay más posibilidades . . . (pauses) . . . para sacarlo. Orlando: (chuckles when Raúl pauses) Facilitador: ¿Cómo qué? Raúl: Como: cinco-dos, cuatro-tres, y otros así. Facilitador: Ah! OK. Me convenciste!

Why do you think some come out more than others? I don’t know! The two does not come out often . . . cause . . . because . . . there aren’t many possibilities to make one and one, for the two . . . and neither for twelve. And, why does seven come out so often? Because there are more possibilities . . . . . . for it to come out. Like, how? Like . . . five-two, four-three, and so forth. Okay, you did convince me! (CEMELA fieldwork)

Together, this group of mothers with their children, with the help of a facilitator, uncovered the most likely combination, or probability pattern, when rolling two six-sided dice marked from one to six. They discovered through observation that the number, seven, was the most important number in the Counter’s Game. They argued: “If we all keep choosing the seven, we all are going to be tied” (CEMELA fieldwork). Because of our experiences working with Latina/Latino students and their parents in two, out-of-school STEM programs, we have gathered numerous success stories similar to the one mentioned above. We believe that these out-of-school settings provided us with a rare opportunity to observe parentchild interactions; interactions that most are very unlikely to observe in the traditional school environment (McDermott & Varenne, 1998). Further, we



Rethinking the Teaching and Learning of Latina 41

also present successful and challenging examples outside of the school arena that have allowed us to explore ways of supporting closer connection between students and mathematical cultures and languages. Through provocative questions and examples, we invite teachers to analyze and reflect on our experiences, translating the insight gained into possible future actions, attitudes, decisions, and principles to be applied in a classroom, especially in an attempt to promote more inclusive environments. Our examples come from our collected data and subsequent analysis of the two after-school programs/sites with Latina/Latino children and studies related to CEMELA (The Center for the Mathematics Education of Latinos/as). The included examples come from two elementary schools, one in Arizona, and the other in Illinois. Through examples from the school programs/sites, we introduce promising practices that support multi- or rather inter-cultural approaches to teaching and learning mathematics for diverse students, especially Latinas/Latinos. MULTICULTURAL EDUCATION Multicultural education has been defined in various ways (Sleeter & Bernal, 2004), but in this chapter we draw on Nieto’s (1999) and Clark’s (2002) work for further insight. According to Nieto, learning develops primarily from social relationships and the actions of individuals who are socially, culturally, and politically situated. She characterizes multicultural education with seven principles: antiracist, basic, important for all students, pervasive, education for social justice, and a process of critical pedagogy. This definition makes the assumption that learning is a social activity that cannot be separated from its situational context. As Bruner (1996) claimed, “learning and thinking are always situated in a cultural setting and always dependent upon the utilization of cultural resources” (p. 4). Further, teachers take part in the social, cultural, and political values of the communities they belong to; therefore, teaching is not a value-free activity. Nieto (1999) cites an “intriguing study” by Francisco Ríos (1994) about sixteen teachers who worked with students of color (p. 48). Only one of the sixteen teachers thought that her students wanted to learn; the remaining fifteen teachers wanted to control and discipline the students, rather than push them toward academic achievement. As a result, Nieto (1999) argues that learning is: (a) actively constructed; (b) that it emerges from and builds on experience; (c) it is influenced by cultural differences; (d) based on the context in which it occurs; and (e) is socially mediated and develops within a culture and community. According to

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her, a multicultural education should draw on students’ experiences through their family, community, cultural, linguistic, formal and other forms of knowledge, sometimes referred to as funds of knowledge (González, Moll & Amanti, 2013). However, multicultural education is not just a “holidays and heroes” approach, using the same label that Nieto mentioned in a personal interview divulged online. Multicultural education is more than just looking for food, music, and cultural traditions. We agree with Nieto that education should include diversity, but without reducing it to a folkloric approach. Rather than that, instrumental learning is crucial. According to Nieto: I also believe that multicultural education needs to be understood as basic education. It’s not a frill, it’s not a fad, it’s not an add-on, and it’s not something that is separate from the curriculum and the climate in the school. I see it as basic as reading, writing, arithmetic, and computer literacy. It’s basic for living in today’s world. And if we don’t teach all our children with a multicultural perspective, we’re not preparing them to live in the world. (Nieto, n.d.)

Multicultural education means incorporating students’ cultural experiences, within high quality academic curriculum basis. In a similar approach, Clark (2002) suggests the implementation of a multicultural curriculum across disciplines by applying certain parameters to support the transformation of a traditional curriculum into a multiculturally-transformed one, namely by: (a) including histories of oppression; (b) referring to students’ lives, cultures and countries of origin; (c) talking about the contributions that unrepresented people made to our body of shared knowledge; (d) including the underrepresented in the design and implementation of the curricula, (e) providing to the students a global picture (global inclusiveness) and the local representation of such picture (local responsiveness), (f) creating opportunities for faculty and students to share their own autobiographies, and (g) creating spaces for students to participate as authors of their own educational experience. Nieto (1999) and Clark (2002) hold a critical definition of multiculturalism and relate it to Freire’s (1990) paradigm which asserts that it is not enough to recall within the curricula the oppressed people’s voices, but we must open spaces for them to actively participate and “read and re-write the world” (Nieto, 1999, p. 3). Freire defines learning not as a repetition of ideas, which he refers to as banking education, where students serve as banks in which information is deposited and not generated, but as the creation and re-creation of those ideas. Educating students to become critical and socially responsible also means providing them with high quality curricula, asking them to excel in school and through which the students become critically reflective and



Rethinking the Teaching and Learning of Latina 43

socially engaged (Banks, 1993; Nieto & Bode, 2008; Sleeter & Grant, 2006). Hence learners must be active agents, and teachers can promote spaces that nurture their sense of agency towards social action, so that individual differences and cultural values support and become part of learning. Therefore in a transformative multicultural curricular approach, teachers must acquire tools and strategies to critically and successfully acknowledge and include students’ differences in their teaching to counteract mainstream values and practices. This curriculum encompasses three main intersecting goals: knowing, caring, and acting (Banks, 2013). For this reason, this chapter provides a set of three examples grounded on two after school experiences for teachers, to give them resources to incorporate multicultural experiences within the teaching of a STEM curriculum. Those examples highlight how knowing, caring, and acting intersect and may furnish teachers with concrete ways to bridge diversity, culture, social justice, and critical pedagogy, within a high quality curriculum. Lastly, these examples provide ideas to reflect on how families could get involved within the learning process in meaningful and responsible ways. CONCRETE EXAMPLES OF A TRANSFORMATIVE MULTICULTURAL CURRICULUM In this section, we present the three examples that help us reflect on and apply the prior framework. Additionally, these examples illustrate multicultural transformations in mathematics curriculum. The first two examples describe possible sources and processes that support the development and sustainability of a multicultural mathematics curriculum. The first one emerges from an after school experience, working with third, fourth, and fifth graders. The unit lesson on measurement and data was contextualized within the case of immigration. The second one comes from a “Math for parents” workshop, in which the third grade teacher facilitated the workshop and parents attended to it with their children. The excerpt describes a session on base-ten numbers and operations. The last example raises concerns about making external as well as internal arrangements in order to include parents and support the development of a multicultural approach in mathematics. These examples include facilitators (teachers), students, and parents working in mathematics (Clark, 2002). Through these situations, we examine the quality of educational contexts, practices, and relationships that support a multicultural curriculum in mathematics. Furthermore, table one aligns each of the examples with MCE basics, and the Common Core Standards.

Standards

Working Definitions

Explicit Connection to MCE/ MCT

Story of Success

Basics (Content/Grade)

MCT, social justice, education as a practice of freedom, banking education, agency, cultural background, funds of knowledge MP1: Make sense of problems and persevere in solving them MP2: Reason abstractly and quantitatively Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit

Measurement, unit conversion /3rd-4th grades Students understood unit conversion based on a lesson about “crossing borders” created by a group of students with the guidelines of the facilitator, from a student proposal Using students’ autobiographical information, students were also active designers of the lesson, as well as implementers

Vignette 1

Number and operations in base 2 (2NBT) Understand place value Use place value understanding and properties of operations to add and subtract

Types of parent involvement, dialogic learning, egalitarian dialogue, inclusion of all voices

Relationships: Involving parents’ within the learning process Drawing on parents’ cultural background (in terms of previous learning experiences)

Number and operations in base ten/2nd grade Student understood place-value algorithm for subtraction

Vignette 2

Table 3.1.   Key Elements to Develop Three Unit Lessons Connected to MCE/MCT

Division with whole numbers/3rd5th grades Mothers interested in their children’s math learning discover that students make better sense of the concept of division when the dividends and divisors these are named or contextualized Mathematics MCT encourages content and real-life events to be integrated to support greater student success. This teacher’s adaptation and acknowledgement of community’s funds of knowledge involves not only content, but also relationships with the community MCT/MCE, funds of knowledge, realistic mathematics education, mathematical task design/ adaptation, parent involvement MP1: Make sense of problems and persevere in solving them MP4: Model with mathematics MP2: Reason abstractly and quantitatively 3.OA, 2-4, and 6 Students interpret whole-number quotients of whole numbers;

Vignette 3

Civic Engagement/Citizenship

Relationships with/among students

Educational Context

Discussion among students themselves, and with the facilitators (adults who volunteer in the afterschool program) Students themselves investigate the situation One student presents the word (in a poster format) to the rest of the class General discussion Yes

Know relative sizes of measurement units within one system of units including km, m, cm, kg, g, oz, l, ml, hr, min, sec, etc. Using the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money Convert like measurement units within a given measurement system Represent and interpret data. After school program

Not requested for this task

Discussion among parents and children when solving the activities provided by the teacher Students and parents are in round tables Teacher navigates throughout the tables, participating in the discussions

Math for Parents Workshop (with children)

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction Add and subtract within 1000, using concrete models or drawings

Not requested for this task

Parents conversations with school teacher about classroom instruction, and exploration of student thinking at home and in an afterschool program Discussion between parents and a bilingual teacher about parents’ discovery of mathematical tasks adaptations that help their children become more successful at understanding division

   so that a whole dived number is understood as a number of objects that are equally partitioned into shares, or that a number of shares partitioned into equal shares equal one whole.

Integrated use of technology Notes to teachers

Additional Considerations (SPED, etc.) Content linked to pedagogy and assessment

Table 3.1.   (continued)

Not required for this task Teachers may meet with parents in order to agree with them the organizational aspects of the workshops (timeline, schedule, contents, etc.) Teachers may create a “natural and safe” environment for parents and children to work together and share different approaches to mathematics learning Recruitment should be a crucial aspect

Parents developed a pedagogical link to mathematics learning and teaching by assessing and paying attention to students’ ideas and strategies through clinical interviews with their children Teachers’ MCT pedagogical approaches need to acknowledge, support, promote, and learn from parents’ participation in their children’s education Not requested for this task Teachers are imposed constraints by school curriculum and regulations. It is important that these constraints not limit the connections of teaching with the students and their community MCT is based on a genuine connection between these two. The development of dialogic relationship with the community is part of this connection; not only regarding the content but also personal relationships Instructional activities (set up previously by the teacher) Instructional materials (structured and teacher-guided activities, using the student’s textbook)

Problem-solving dialogue Multi-faceted and multimediabased instruction (using maps, scales, rulers, etc.) Instructional material (maps, rulers, blank paper, pencils, chart paper for poster presentation) Instructional activities (open-ended activities)

Not required for this task Teachers may encourage students’ interactions, peers’ support, being also attentive with respectful attitudes towards diversity Teachers might be attentive to reframe children’ discussions to make sure not to lose the mathematics focus

Not requested for this task

Vignette 3

Not requested for this task

Vignette 2

Yes

Vignette 1



Rethinking the Teaching and Learning of Latina 47

CROSSING BORDERS: HOW TO RE-THINK THE CURRICULUM BASED ON A CRITICAL APPROACH This first scenario emerges from an activity conducted in an after school program developed at an urban school in south Tucson, Arizona. Latinas/Latinos populate this particular region where Spanish is widely spoken. To add, many Mexicans owned or ran the shops in the area and it was also commonplace to find puestos de burritos y tamales on the street corners. Labeled as English language learners (ELLs), over 80% of students at the public school were of Latina/Latino descent, with the remainder of students identifying as white, Native American, and African American. Due to the wide variety of languages and cultures, teachers often experienced a cultural clash within the classroom; an issue that was aggravated by Arizona’s ban on bilingual education. In the after school program, the children worked with measurements, specifically dealing with the topic of unit conversion. Tasked with conversions between the U.S. system and the metric system, one group of students, with the help of their facilitator, decided to investigate the number of immigrants in the US and the distances that the immigrants had traveled. The students began by searching the U.S. Census database so that they could create unique tables and graphs to chart the percentage of Latinas/Latinos within the U.S., as well as in Arizona. Next, they decided to focus their research on the unit topic of migration, surely a familiar topic to many, at least for most within and around the community. Many of the students had experienced immigrating with their families to the U.S., and if they had not, many of their relatives had. Not to mention, many had family members living on the other side of the Mexican border. Everyone knew someone who had crossed the Sonora Desert, hid from the migra, or the police, and survived the dangers of the hot and arid desert. The coyotes were also well-known characters in the community, with popular shared stories making up part of the community’s social imagery. For the children, the subject of migration soon evolved into exploring the needs and challenges that immigrants faced during their journey to the U.S. Eventually, Miriam, one of the students, introduced a new topic that had caught her attention the previous night. She mentioned a story on the news about a car accident that involved immigrants, which moved the conversation to a discussion about crossing the border, specifically between Northern Mexico and the United States. Through a series of discussions, the children used their math skills to begin to pose problems that were of major importance to them and the surrounding community. Together, they took up agentive roles in their own learning (Clark, 2002; Freire, 1990).

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Note for teachers: Use students’ cultural backgrounds to challenge the core STEM curriculum. Design your own lessons and make your own exercises through a dialogue with students to pose new (and meaningful) problems.

The excerpts below highlight a portion of their discussion, which focused on topics of identity and belonging, and in turn pushed students to use the skills they were developing in math to try to understand the issues with their community. Furthermore, this vignette serves as an example of the integration of mathematics curriculum with the students’ meaningful experiences and knowledge, their facilitator’s support, and keen social justice perspectives. After one student posed the topic described below, her group of peers openly and critically discussed the topic of immigration: Miriam: Miss, I need to tell something, I saw on the news. Marleen: Yeah. Miriam: You know the coyotes? Marleen: (nods) Mhm. Diana: Okay, yeah, keep going. Miriam: You know the bottom of the cars of the [Diana: Trunks] Hay personas / There are persons in and they had an accident. Tuvieron un . . . , se chocaron/ They had a . . . , they crashed. [Marleen: ¿Chocó?/ Did it crash?]. Albert: So they died? Diana: Wasn’t he in a trunk? Some of them. Miriam: También una persona, pero eso es en otro. /Also a person, but it is in another one Marleen: Yo vi algo que decía cuántas personas mueren tratando de cruzar la frontera y muchos mueren en accidente de carro y todo eso y es otra cosa que se puede buscar los números de esto./ I read something that said how many people die trying to cross the border and many die in car accidents and all of that and this is something that we can find statistics of. Diana: Traíamos un camper y la policía lo paró como tres veces cuando íbamos, veníamos por acá porque pensaban que éramos un coyote. Y ahí mi mamá me dijo, yo iba dormida. /We had a camper and the police stopped us like three times when we went, and also when we came back because they thought that we were a coyote. And my mom told me and I was asleep. Marleen: Sí ahí puedes poner como cuentos y así, si quieres puedes poner cosas sobre los viajes de los inmigrantes, puedes poner cuentos tuyos y de los que encuentras en las noticias en tu póster./ Yes, there you can tell stories like this,



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so you can tell stories about the trips of immigrants, and you can tell your own as well as those that you read on the news on your poster. (CEMELA fieldwork)

The group continued discussing the accident seen on the news and relating it back to their personal experiences. However, in an effort to encourage the group to use their developing skills, Marleen, the facilitator, proposed that the children used math to look at the issue of immigration more critically. The connection to math was not immediately clear for the group, but Marleen was crucial in framing the group’s perspective. On a map, students located the different places where their relatives lived or that the news mentioned. They selected the starting and ending points of immigration and figured out the distances. The discussion continued: Mary Jo: Where’s México then? Jocelyn: It’s right there, this line, that’s the border. This big line that goes across. Mary Jo: So you can go from Tucson, you can go down there. You walk all the way her [México]. And then you take that way. Jocelyn: This is México right here. It’s going to take a long time to go. Mary Jo: Yeah, so right here to here. Like right here to right here is a mile. Jocelyn: I think it’s more than a mile. Mary Jo: Eight miles? Jocelyn: There’s a scale on the map somewhere, let’s look. Jocelyn: Let’s measure this, how long is this? Okay, first of all what are these numbers here, what do those represent? Mary Jo: Inches, one inch. Jocelyn: Then what are these numbers? Mary Jo: Millimeters. Jocelyn: What’s millimeters? Mary Jo: Millimeters are more than, no. Jocelyn: Do you see the mm? Where’s the mm? Mary Jo: Oh, these are millimeters, these are inches. Jocelyn: Each one of these little marks, that’s one millimeter. So one of these is like a one two, three, those are centimeters. And each one of these big numbers

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are inches. Okay, so what’s that? Three inches, okay, equals, what’s the scale on the map. Okay. Mary Jo: One hundred and twenty. (CEMELA fieldwork)

Finally, the group decided to explore the journey for an immigrant who crosses the border coming from Nogales in Sonora, México to Tucson in Arizona, United States. Both of these places had special significance to them. So, they opened a map on the floor to estimate the distance between Tucson and Nogales; and they used a ruler to measure distances on the map. Jenny: To go from Nogales to Tucson? Oh let’s see how far does it say it is on the map? Can we find the key that tells us how far things are? Over here, does this tell you some information? Let’s see, is it on this side? Oh there’s a key down here that might give you some information about distances. Yeah. Josep: So, you understand what it means, this, sí/yes? (Points to scale on the map)

Figure 3.1.   Mapped Location of Nogales on Small Map of US/Mexico Border.



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(Jazmin shakes her head) Jazmin: Porque no dice para hasta Tucson, como para aquí, o para acá./ Because it does not say all the way to Tucson, like up to here or over there. Josep: (gets the ruler) ¿Cuántos son?/ How many are there? Jazmin: One inch. Josep: Un inch ¿y cuántos milímetros son? ¿Estás midiendo hasta la frontera o hasta aquí?/ An inch, and how many millimeters is that? You’re measuring all the way to the border or up to here? Jazmin: Hasta Nogales./ All the way to Nogales. Josep: Hasta Nogales, diecisiete. Diecisiete qué?/ To Nogales, seventeen. Seventeen what? Jazmin: Milímetros./ Millimeters. Josep: ¿Milímetros o inches o millas? Diecisiete kilómetros? ¿Sabes que está aquí? / Millimeters, inches, miles? Seventeen kilometers? Do you know what’s here? (points to scale on the map) Jazmin: Hasta aquí. Hasta el número dos. / So up to here, up to number two. One inch equals . . . Josep: One inch equals what? ¿Aproximadamente cuánto?/ Approximately, how much? Jazmin: A kilometer or punto dos of a mile./ One kilometer or point two of a mile. Josep: ¿Y ahora tenemos que interpretar esto para saber cuánto mide en realidad, no?/ And now we have to convert it to know how much it measures in reality, right? Jazmin: (nods) Mhm

The debate continued for about thirty minutes, and the group moved fluently between converting the measurements from the map to actual distance. They also talked about the different metric systems in México and the U.S. At one point, someone asked what if someone crosses the border by foot, all the way from Nogales. This probing question refocused the discussion from distance traveled to the immediate needs required by immigrants, such as drinking water, to walk and survive the journey from Nogales to Tucson. Together, the children talked about real people who had died in the desert on a similar journey. As the conversation progressed, the calculations they made became more and more meaningful as they related to the journey, estimating a total walk of twenty hours.

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Mary Jo: Twenty hours. Jocelyn: So it’s almost one full day, to walk. If you walked, just kept walking the whole time. Never took a break. Mary Jo: You would get there at ten at night probably. Mary Jo: You would get there at ten at night probably. [ . . . ] Mary Jo: How much water would a person need? Jocelyn: So how much water would someone need to take with them? Now let’s, um. Mary Jo: Hold on, you would need like sixty bottles of water. Jocelyn: Well let’s look at the information here, what does it tell us about how much? Mary Jo: One needs water, ten glasses per day. Ten glasses. So you would need ten bottles. Jocelyn: Ten, you need ten glasses, how much is a glass, what does it say? Mary Jo: Eight, sixteen ounces. Jocelyn: Eight, sixteen ounce portions so you need eight glasses that are sixteen ounces each. Mary Jo: And ten, sixteen, seventeen, eighteen, nineteen ounces. I don’t know, Miss. Jocelyn: It’s just saying that you need eight, sixteen ounce glasses. And one pound is sixtee ounces, so let’s figure out how many pounds of water someone would need to take with them. (CEMELA fieldwork) Reflecting questions for teachers: What are other topics that could similarly support mathematics learning and teaching?

As a result of a critical discussion, mathematics became a central tool to understanding the journey of an immigrant. Mixed with real life experiences, math helped the children to begin to grasp the severity of the journey to the U.S. from Mexico. This scenario describes a way to transform a mathematics curriculum through a multicultural approach, specifically to connect the mathematical content with real situations, in which students used mathematics in meaningful ways. Clark (2002), suggests nine parameters to transform a “traditional didactic pedagogy” into a multicultural one: “problem-posing dialogue, multifaceted and multimedia-based instruction, assessment of student needs, organizational tools, instructional materials, use of instructional materials, instructional approach, instructional strategies, and learning activities” (p. 40). A multicultural



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curriculum transformation must push students towards in-depth learning, helping them to develop a critical awareness of diversity, social justice, responsible citizenship, etc. According to Freire (1990), a meaningful educational action should focus on the individuals’ critical consciousness, rather than on the mechanic procedures of memorizing list of facts and data. Only this way, will teachers be able to transform education in the practice of “freedom.” The example of border crossing shows a group of students having and building a strong sense of identity by drawing on their cultural roots, not as an anecdotic activity, but by using their cultural background to illustrate and make meaning to important and crucial mathematical concepts. When Miriam poses the case of an immigrant crossing the border, then she (and her peers) created a whole lesson around measurement contextualized in the case of real situations. Miriam and Marleen discuss the case of crossing the border under the bottom of the trucks. Then Diana recalls her family being stopped several times by the police because they were looking for coyotes. This use of autobiographical grounded situations, crucial element in the multicultural curriculum transformation (MCT) approach (Clark, 2002), illustrates and helps students and teachers make meaning of the lesson. The episode narrated by the students, as well as the lesson built on that story, incorporates crucial standards such “making sense of problems and persevere in solving them” (MP1) or “reasoning abstractly and quantitatively” (Common Core State Standards Initiative, 2010). Students made conjectures (“how much water would someone need to take with them?” in order to cross the border), monitored and evaluated their responses (“you need ten glasses, how much is a glass?”), contextualized mathematical concepts (measurement, unit conversion, etc.), and then decontextualized them by going back again to the situation with a clearer view of its meaning (discussing about what a kilometer and a mile mean, or what 17 mm on the map meant in the real world). Further, the determination of the amount of water needed for a person to go over the border from Nogales to Tucson, provides some hints for teachers to observe a particular case of putting a mathematical concept such as volume into a very contextualized and cultural situation, which is also related to social justice issues; in which some people were forced to leave their country and faced and overcame really difficult situations by the fact of not being “European,” “white,” “US citizen,” and so forth. Borderlands then are always conflictive areas due to a complex set of factors (Portes & Rumbaut, 2011). The discussion on immigrants led the group to explore some reasons why immigrants take such risks. The children brought up issues of social justice revolving around immigration. Given the power to ask their own questions, the children in this scenario positively engaged in using mathematics to topics personally meaningful.

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Doing Subtraction: Interactions between a Father and His Daughter In this scenario, we look at intergenerational differences within a family, stemming not from a difference in age, but in education. As Clark (2002), suggests, “Multicultural curriculum transformation also encourages faculty to look at the nature of the relationships between and among students and themselves both inside and outside the classroom” (p. 43). This means that we, as teachers, need to look for ways to include students’ friends, family, and other members of the community because learning is related to these kinds of student relationships. To illustrate this statement, we draw on the interactions between a father and his daughter, within a particular educational context: a workshop for parents and children, facilitated by a teacher. Sergio (the father) and Berta (the daughter) take part in this vignette. Sergio, born in Mexico, migrated to the United States as an adult with his wife and son. His daughter, Berta, was born in the United States, never experienced Mexican schooling, which is pedagogically different from the United States’. For Sergio, his memories of schooling in Mexico are clearly connected to his cultural background. For him, learning meant the acquisition of propositional knowledge; mathematics was a set of algorithms and procedures that he had to learn by heart. This vignette begins when Sergio and his wife attended a parent mathematics workshop with Berta. The goal of the workshop was to provide parents with several strategies to assist their children at home. Berta’s teacher began by introducing subtraction strategies based on the “mathematics reform” (Thames & Ball, 2010; Whitacre & Wessenberg, 2016) to demonstrate several strategies for parents. Using a Freddie the Frog hundreds chart and a number line, the teacher showed parents how to subtract two numbers. She moved a counter over the number line, starting from the minuend; she skipped—with the counter—the amount indicated by the subtrahend. The result, or difference, was the point or number where the counter landed on the number line. After several demonstrations, the teacher invited parents and children to solve several tasks together. Sergio, Berta, and Marisa (Berta’s mom) began to work together, but Berta struggled with some problems, so she asked her dad for help. Sergio willingly responded, but soon a conflict emerged due to a difference in strategy used to solve the problm. Sergio focused on place-value based subtraction algorithm. He asked Berta to notice the relative value of a number so that the position of a number matters; hence, number three, for example, could mean either “three” or “thirty” depending on its place within a number. This method, the one Sergio learned in Mexico as a child, was confusing to Berta as it was very different from what the U.S. teacher taught her. Despite the willingness from both to work together, this different strategy soon became a sore subject.

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Berta: Dad, I need help. Sergio (father): Look m’hija. It’s very easy; look, just pay attention. You put . . . Berta: But I have to do it! (raising her voice) Sergio: I know, I know. I’m not going to do it for you. Look, if you have seventy, eighty, ninety, one hundred, how much, how much is it? Ten, twenty, thirty. But since you already have three, it wouldn’t be thirty. It would be, how much? If you have thirty. Berta: One thousand! Sergio: No. You have three here . . . Berta: Ninety! Sergio: No, just a moment. Berta: Eighty! Seventy! Sergio: Wait, wait. If you have seventy-three here, seventy-three to eighty, it’s seven. From eighty to ninety, it’s ten. From here to there, another ten. How much would it be? Seven, ten, and ten, how much? Berta: Twenty-seven! (yelling) Sergio: That’s it! Let’s see . . . so, erase, erase. And do it well. Berta: (at the same time and yelling) Dad, dad but I have to do it this way! Sergio: And how did they teach you? Berta: Like this, I have to do it like this; like one, one, and how much, and then this plus zero, six zeros . . . (CEMELA fieldwork) Reflecting questions for teachers: How does this situation contribute to Berta’s mathematical identity? What image might Berta think this conflicting strategy provides to the teacher? What would the teacher see if Berta turned in her homework as is? What takeaways does this vignette provide to us to teach mathematics?

Berta was anxious, and although her dad helped her solve the task, she felt that her father could not help her solve the problem the way the teacher expected. Berta knew the approach her teacher had modeled was different than her father’s approach to solving the problem, and for this reason Berta was hesitant to accept her father’s suggestions. Similar to his daughter, Sergio felt inadequate to support Berta properly since his method conflicted with the teacher’s. Learning from this experience, teachers need to keep in mind that multicultural curriculum, particularly in the area of mathematics, should not

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limit ways of thinking, but instead multicultural curriculum transformation should support an expanding and inclusive way of doing and understanding. Valdes (1996) pointed out that parent involvement might not be enough to transform the curriculum into a more inclusive, multicultural approach. She argues that while many teachers and parents may disagree among themselves, still there is a clear plethora of evidence proving the effectiveness of family and community involvement (Díez-Palomar, 2015). Drawing on our experience, it is also clear that not all types of family involvement may be effective, producing better achievers. It depends on how parents and other community members are included within the school contexts. As Clark (2002) recommends in her model of multicultural curriculum transformation, it is crucial to look carefully to the type of relationships between and among students themselves and with other educators. Educational research suggests the inclusion of parents’, teachers’, and students’ voices through egalitarian dialogues in educational contexts may prevent conflict while increasing students’ opportunities to learn (Flecha, 2000, 2015). Accordingly, it is crucial to include their voices without losing the goal of increasing the quality and excellence of the curriculum. For example, parents may support teachers managing the classroom, but the teacher is the “expert” deciding the lesson and how to perform it. Parents may also look over their children making sure that they complete homework at home; or they may “contribute” to teachers’ evaluation providing teachers with significant information about children after participating within classroom activities, for example. There are many different ways for parents to demonstrate involvement. The example reported in this vignette illustrates a possible situation in which teachers could include parents’ voices within their regular teaching practices, which is a transformative feature of a multicultural curriculum (Clark, 2002; Nieto, 2000). The confrontation of different approaches to the same concept may open doors to a number of possibilities for learning, which is supported from a multicultural perspective. Sergio’s subtraction challenged Berta to think beyond the teacher’s method to subtract. Berta, however, did not experience that situation neutrally. She experienced a conflicting interaction with her dad because she could not recognize her dad’s strategy as a legitimate way to solve a subtraction. Nevertheless, such challenge helped Berta to move further and learn deeply the notion of subtraction. In fact, in the next sequence of tasks, which we have not described here, Marisa was at the blackboard solving a two-digit subtraction, using the place value algorithm. Berta was looking at her mom solving the subtraction very slowly—which showed lack of competence [on purpose]—and she jumped in and without hesitation she “taught” her mom how to efficiently perform that calculation. This is a clear example of success of confronting a student with two alternatives to solve the same type of problem, incorporating the interaction with family members, their previous knowledge, and using them to transform the normative curriculum.



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This example shows how interactions between parents and schools reflect structural relationships of these individual in the wider society (Valdes, 1996). However, as Nieto (2000) notices, “Parent involvement still represents a potential avenue for bringing community values, lifestyles, and realities into the school” (p. 116). Berta’s interactions with her father and her mother were crucial to consolidate their learning about place value when solving the subtraction. She argued heavily with her dad (‘Dad, dad, but I have to do it this way!’), however, while arguing she was also exposed to a different subtraction algorithm solution, different from Freddy the Frog one, closer to the place value one. She was able somehow to integrate the teacher’s way to solve subtraction, with their father’s approach, making sense to “understanding place value” (Common Core State Standards Initiative, 2010). This is just one example of how teachers may incorporate parents and other community members to transform the curriculum from a multicultural point of view, looking both for inclusion of their voices and for inclusive contexts, in the regular classroom. Sharing Teaching Insights: Interactions between Mothers and a Teacher At an after-school program in Illinois, a group of mothers developed a series of interviews to be used with their children in order to help understand how they solved mathematics problems. The mothers began by creating and subsequently, solving several mathematics problems amongst themselves. Then they selected some of these problems to use when interviewing their children. After interacting and working with their children, the results were so encouraging that they decided to share them with the mathematics teachers. The mothers were incredibly excited to share what that had learned, as never before they were positioned as holders of knowledge (González, Andrade, Civil, & Moll, 2001). The mothers were empowered by their newfound knowledge. They never saw themselves having the expertise to suggest possible activities and pedagogical approaches to the mathematics teachers so that their children’s educational experience could be more meaningful. This is especially important in multicultural curriculum transformation since minoritized groups families’ knowledge is often not deemed as a legitimate general cultural capital, but one that belongs to an isolated context, outside of school. When it was time to meet with the math teachers, only one teacher came to the meeting. It is not surprising that the teacher who came to the meeting and listened to the parents was perceived by the group of mothers as one of the most open and welcoming teachers at the school. This teacher was also

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bilingual, so as the meeting evolved into an informal conversation, everyone conversed in Spanish. In essence, the major meeting points shared included this: Franca: What we’ve seen helpful to the child is to find connections to the real world, because math is everywhere in our lives. Alicia: Yes, because when you [the teacher] told me my son was struggling with division, what I saw helped him understand it at home was when we thought about real-life situations. Like twenty oranges and divide them among three kids and so forth, like giving names to the numbers. Division is problematic to children cause though at times they get the correct answers, when you ask them, they did not know why they had done what they did. But, by giving names to the numbers, then they understood and knew how to explain what they were doing in mathematics.

Even though the group of mothers had discovered that connections to the real world or naming the numbers helped their children understand mathematics better and shared these findings with the somewhat open-minded teacher, their ideas were met with resistance. To these and other interventions from the mothers, the teacher responded with constraining situations such as planning and being required to follow the school curriculum. The teacher spent most of the time trying to make the mothers understand the limitations of his work. Very little of the teacher’s responses addressed the mothers’ suggestions. A year later, three of the mothers met with a member of this research team (coauthor of this paper) and watched the videotaped interaction with the teacher, and the mothers recalled their experiences and reflected on it as follows: Alicia: All we learned, we learned from the children because we tried not to close to our way, but open up the way kids think. And we learned that everyday has value and interests kids. We saw that naming to the numbers helps them in mathematics. Marta: Yes, kids are creative. But the teachers don’t seem to respond as well when one teaches them as when they teach you. It is as if they felt they were being defied. Dora: It seems that barriers between their positions and ours are strong. At school all seems that way. Though all are together, the teachers are here, the principal is there, and the parents are somewhere else. Alicia: I think in the after school, it’s different because the program was like a family where there was no difference among groups. It was a place where children had the opportunity to express themselves as they are.



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Marta: And that built more trust for us and for the children, it promoted more communication and to more communication, more trust. Reflecting questions for teachers: What could support better communication between the mothers and the teacher? How could the teacher and the mothers improve their work together? What is the group of mothers teaching us?

The group of mothers recognized that the different barriers created by the school system were the source of separation between what their children needed and what they actually receive in terms of education. The mothers also felt that as parents at school, their voices had no power. They, however, envisioned that a communicative and dialogic process, a more equalizing process between school and parents would help to build stronger relations, a community where they have the ability to express themselves as needed. Though the school provided language translation and at times the use of Spanish to support the mothers’ participation at the school, this fact did not guarantee that their voices counted, so the school could hear them back. The mothers wanted an opportunity for an open dialogue and contribute to their children’s education. This situation presents a challenge to bilingual schools to see that using other languages besides English and even having teachers and families from similar ethnic backgrounds at school does not guarantee explicit attention to families. The genuine quality of social interactions matters. This vignette teaches us about mathematics MCT at several levels. Mathematically, the mothers’ discovery of “naming the numbers” is corroborated through a realistic mathematics education approach (Freudenthal, 1968), which supports that connections between everyday and mathematics best support children’s mathematical understanding. As teachers We need challenge ourselves to recognize our tendencies to treat mathematics as if it is valuable in and of itself; rather, we need to be cognizant that is people who make mathematics valuable and that across cultures and communities mathematics holds different meanings, values, and procedures. (LópezLeiva & Willey, 2013, p. 3)

Thus, in order to provide a MCT in mathematics, not only do teachers need to bridge school and community knowledge, but to do so they need to be lifelong learners and learn about the students they teach, so teachers can affirm students’ experiences and others’ through their teaching (Nieto, 2000). This approach includes a mobilization of students’ funds of knowledge into the classroom; the mobilization, however, includes not only the content, but also the social relationships that support the knowledge exchange process (Moll,

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1992; Moll, Amanti, Neff, & González, 1992). While this exchange is student centered, it also encompasses their parents. REFLECTION BRIDGE Similar to Clark (2002) and Lee (2009), we understand MCE not as a multicultural folkloric view (Sleeter & McLaren, 2009), but as both a transdisciplinary approach “that cuts across all subject areas, and addresses the histories and experiences of people who have been left out of the curriculum” (Au, 2009, p. 10); and as a transformative approach that acknowledges the multiple identities within and across individuals that need to intersect with each other through a permanent dialogue. In direct relation to a STEM MCE/ MCT approach, we have discussed three examples in which we addressed: (1) designing a lesson with students rather than to them, which Clark (2002) denominates: problem-posing dialogue; (2) including family members’ voices within the learning process, which has been also noticed by Nieto (2000) and others (Clark, 2002) as a crucial point of the multicultural curriculum transformation; and similarly, (3) improving the communication between teachers and parents. We presented data that depict how the establishment of a dialogue between students and teachers within MCT approach is not an easy task. For this purpose, Clark (2002) provides some practical strategies that include (a) thinking about and making explicit oppressive situations, (b) drawing on the biographies of students from different cultural origins, and (c) having students illustrate and/or create activities for the class, and so forth. Another important point in MCT is to include family members’ contributions into the teaching process (Nieto, 2000). This process is difficult as well. Building on Clark’s (2002) argument and our set of examples, we suggest activities to address the topics in STEM. First, communication with families and students are the foundation to this approach. We need to provide an environment in which students and their families feel comfortable to share their ideas, who they are, and what they know. Teachers can pose problems, or even better, they can engage on an inquiry process with their students about a topic that relates to students and would be flexible enough to rechannel through the school content as well (Moll, 1992). For example, one vignette showed how issues of immigration were not only relevant to the students but also relevant to promote meaningful mathematical concepts. This example presents a way in which students can critically learn about culture and political oppression of immigrant people as well as the mathematics embedded in these lives and cultures (Clark, 2002; Freire, 1990). The introductory vignette



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described how children were learning together with their mothers about probability. While the latter does not explicitly targets issues of oppression, the functional structure of mathematics learning has already been rechanneled to promote new relations in how to learn mathematics. These examples show that teachers can address equity issues at different levels. In Sergio and Berta’s vignette, we elaborated on how mathematical differences across cultures may open a space for dialogue and mutual learning. For example, after a discussion with her father, Berta guided her mom by using the place value algorithm and subtracting. Different mathematical approaches to solve a problem can provide a curricular transformation as we acknowledge other mathematics as legitimate mathematical content (Clark, 2002). The parent workshop addressed created this space to learn about other standard algorithms. Such knowledge should be accessible not only to parents, but also to students and teachers. Teachers can invite parents to talk with them and learn from one another. There are a number of examples to improve relations and communication with parents from a MCT perspective (Díez-Palomar, 2015) and allows parents to be viewed as an asset and leaders. Doing this creates spaces where parents can take on different roles in the school setting (LópezLeiva & Torres, 2013). Some schools currently hold Math Family Nights, in which parents, teachers, and children meet to do mathematics. Although this is an important and related activity, this takes place only a couple times in a school year. Some parents may have more flexible schedules that might allow them to be part of the school mathematics during school day. While MCT/MCE approaches build on students’ community, students need to expand their awareness, knowledge, and respect for other cultures (Banks, 2010). For example in mathematics education, Avicena’s biography could be used to teach some numerical rules, such as adding series of odd numbers organized in square arrays. It may also guide students in thinking about how Arabs in Al-Andalus created a multicultural science incorporating elements from ancient Greece that preserved and sometimes improved classic works such as the Almagest, or transmitted the hindu numerals to Europe as documents such as the Codex Conciliorum Albeldense (also known as the Codex Vigilanus, the first document using hindu-arabic numerals). In this process, incorporating students’ concerns, talking with them, and being open minded to build on their questions and comments, may lead teachers to create and design powerful lessons such as the Crossing Borders. A safe environment again is crucial for students to contribute to the lesson, so then teachers can build on students’ comments to create and mathematize problematic situations with them (Freudenthal, 1968; Gutstein, 2003, 2006). Furthermore, students can expand and research on other ways of doing mathematics and solving standard algorithms across cultures, other number systems, or math-

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ematical games through multimedia and online resources (Clark, 2002). Even parents who cannot come to the schools directly could join the class via online conferences and share with students the mathematics activities they do at work. CRITICAL CONSIDERATIONS IN STEM MULTICULTURAL CURRICULUM TRANSFORMATION: THE THEORY Generally in multicultural education, language has been identified as a crucial aspect that is closely connected to the learning of culturally diverse students, such as in the examples of Latina/Latino students presented earlier. Khisty (1995) states that to understand the educational ecology of a mathematics classroom, we should analyze not only the curriculum, but also what is said and how it said. Khisty’s claims are supported by previous research (Cazden, 1986; Tharpe & Gallimore, 1988). According to these research findings, the differences between English and Spanish may ascribe some difficulties for speakers moving across languages in mathematics (Castañeda, 1983; Cuevas, 1984). The examples provided in this chapter describe how children and other participants used fluently both languages, not only to talk but also to speak mathematically such as the naming of units of measurements (miles, millimeters, milímetros, kilómetros, etc.), but also with the understanding of two measurement systems (English and metric systems) utilized in two different countries. Thus, this situation shows children comfortably and enthusiastically engaged in a mathematically, linguistically, and politically complex meaning making process. We can see that the use of more than one language supported the learning process (Cummins, 2000). The Crossing Borders example also shows the inclusion of themes relevant to students’ lives that go beyond a “folkloric” curriculum, but one that is meaningful to students and that promotes a relational engagement (Domínguez, LópezLeiva, & Khisty, 2014; Sleeter & McLaren, 2009). Moreover, this example also shows how modeling with mathematics is a tool that supports mathematical as well as critical reasoning (Gutstein, 2003, 2006). In the case of Sergio and Berta, we see that the root of their differences was based on a simple difference of strategy. A multicultural mathematics curriculum needs to be inclusive of multiple ways of doing mathematics, or a transcultural mathematics approach (Lee, 2009). Mathematics procedures as well as our national and linguistics identities are social constructions that may either include or exclude others, depending on how dialogue from multiple perspectives is supported (Mead, 1934). In fact, Sen (2006) argues that bor-



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ders of countries, as well as identities and subjects fields, are not clear; and that in the end, it is us, the people (teachers, students, and researchers) who decide where to place the borders. This idea is presented in the introductory example, the Counters Game, in which the possible boundaries between participants’ roles (facilitator, mothers, and students), as well as content (probability) blurred in a dialogic learning process and communication (Flecha, 2000). This communication included their feelings, reasoning, descriptions of patterns, and experiences that supported their understanding of probability. Together they built a zone of mathematical practice (González et al., 2001). Finally, the meeting between the mothers and the teacher points to the issue that an approach that considers a multicultural mathematics curriculum needs to address issues larger than the content, the language, and the teaching strategies that promote student participation and learning in mathematics interculturally. An intercultural curriculum in mathematics inherently entails a productive context and dispositions to coconstruct an environment of dialogic participation, communication, and learning. Academic success and failure are the result of social organization (Moll & Díaz, 1987). In fact, Racionero, Ortega, García, and Flecha (2012) have demonstrated how the support that schools receive often mirrors the resource distribution of the society at large. As a result, uneven distribution of opportunities and resources may be seen as the norm; what is expected. In a multicultural mathematics curricular approach, these assumptions must be challenged. Here, Raúl and Orlando; Mary Jo, Jazmin, Miriam, and Josep; Berta and Sergio; and Alicia, Franca, Dora, and Marta have helped us see new approaches and perspectives of a multicultural mathematics curriculum. From this investigation, what do you find useful to apply in your classrooms? How ideas in a book like this, may help us maximize and improve the opportunities that we provide to children and their parents such as the ones that spoke through this chapter? What stories will children in our classrooms tell in the future? CODA We would like to thank CEMELA (Center for Mathematics Education of Latinos/as) for allowing us to conduct this study as a part of their overall research agenda. CEMELA was funded by the National Science Foundation under grant ESI-0424983. We would also like also to thank the Ramon y Cajal Program for its support during the development of this chapter.

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REFERENCES Au, W. (2009). Rethinking multicultural education: Teaching for racial and cultural justice. Milwaukee, WI: A Rethinking Schools Publication. Banks, J. A. (1993). Multicultural education: Historical development, dimensions, and practices. Review of Research in Education, 19, 3–49. Banks, J. A. (2010). Multicultural education: Characteristics and goals. In J.A. Banks, and C.M. Banks (Eds.), Multicultural education: Issues and perspectives (seventh edition, pp. 189–207). Boston, MA: Allyn & Bacon. Banks, J. A. (2013). An introduction to multicultural education (fifth edition). Boston, MA: Pearson. Bruner, J. (1996). The culture of education. Cambridge, MA: Harvard University Press. Castañeda, A. (1983). Mathematics and young bilingual children. In T. H. E. Escobedo (Ed.), Early childhood bilingual education: A Hispanic perspective (pp. 139–47). New York, NY: Teachers College Press. Cazden, C. (1986). Classroom discourse. In M.C. Wittrock (Ed.). Handbook of research on teaching (third edition, pp. 432–63). New York, NY: McMillan. Clark, C. (2002). Effective multicultural curriculum transformation across disciplines. Multicultural Perspectives, 4(3), 37–46. Common Core State Standards Initiative. (2010). Common Core State Standards (CCSS) for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. Cuevas, G. (1984). Mathematics learning in English as a second language. Journal for Research in Mathematics Education, 15(2), 134–44. Cummins, J. (2000). Language, power and pedagogy: Bilingual children in the crossfire. Clevedon, UK: Multilingual Matters Ltd. Díez-Palomar, J. (2015). Family math: Doing mathematics to increase the democratic participation in the learning process (pp. 397–412). In U. Gellert, J. Gimenez, C. Hahn, & S. Kafoussi (Eds.), Educational paths to pathematics. Dordrecht, UK: Springer. Domínguez, H., LópezLeiva, C. A., & Khisty, L. L. (2014). Relational engagement: Proportional reasoning with bilingual Latino/a students. Educational Studies in Mathematics, 85(1), 143–60. Flecha, R. (2000). Sharing words. Theory and practice of dialogic learning. Lanham, MD: Rowman & Littlefield. Flecha, R, & Gómez, J. (1995). Racismo: No, gracias. Ni moderno ni postmoderno. Barcelona SP: El Roure Editorial. Flecha, R. (2015). Successful educational actions for inclusion and social cohesion in Europe. Dordrecht, UK: Springer. Freire, P. (1990). Education for critical consciousness. South Hadley, MA: Bergin & Garvey. Freudenthal, H. (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1(1), 3–8.



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González, N., Andrade, R., Civil, M., & Moll, L. C. (2001). Bridging funds of distributed knowledge: Creating zones of practices in mathematics. Journal of Education for Students Placed at Risk, 6(1 & 2), 115–32. González, N., Moll, L. C., & Amanti, C. (2013). Funds of knowledge: Theorizing practices in households, communities, and classrooms. New York, NY: Routledge. Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 37–73. Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. New York, NY: Taylor & Francis. Khisty, L. L. (1995). Making inequality: Issues of language and meanings in mathematics teaching with Hispanic students (pp. 279–97). In W. G. Secada, E. Fennema, & L. Byrd (Eds.). New directions for equity in mathematics education. Boston, MA: Cambridge University Press. Lee, E. (2009). Taking multicultural, anti-racist education seriously: An interview with Enid Lee. In Wayne Au (Ed.), Rethinking multicultural education. Teaching for racial and cultural justice (pp. 9–16). Milwaukee, WI: A Rethinking Schools Publication. LópezLeiva, C. A., & Torres, Z. (2013). Working with families in bilingual mathematics: Supporting a leadership space for Latina mothers. Journal of Research in Mathematics Education, 2(3), 293–315. LópezLeiva, C.A., & Willey, C. J. (2013). Diversity and communal work in mathematics education. Noticias de TODOS, 9(1), 1–3. McDermott, R., & Varenne, H. (1998). Adam, Adam, Adam, and Adam: The cultural construction of a learning disability. In H. Varenne & R. McDermott (Eds.), Successful failure: The schools that America builds (pp. 25–44). Boulder, CO: Westview Press. Mead, G.H. (1934). Mind, self and society. From the standpoint of a social behaviorist. Chicago, IL: The University of Chicago Press. Moll, L. (1992). Literacy research in community and classrooms: A sociocultural approach. In R. Beach, J. L. Green, M. L. Kamil, & T. Shanahan (Eds.), Multidisciplinary perspectives on literacy research (pp. 211–44). Urbana, IL: National Council of Teachers of English. Moll, L., & Díaz, S. (1987). Change as the goal of educational research. Anthropology and Education Quarterly, 18, 300–11. Moll, L. C., Amanti, C., Neff, D., & González, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory into Practice, 31(2), 132–41. Nieto, S. (n.d.). Teaching multicultural literature. Retrieved from: http://www. learner.org/workshops/tml/workshop1/commentary3.html Nieto, S. (1999). The light in their eyes. Creating multicultural learning communities. New York, NY: Teachers College Press. Nieto, S. (2000). Affirming diversity: The sociopolitical context of multicultural education. New York, NY: Longman. Nieto, S., & Bode, P. (2008). Affirming diversity: The sociopolitical context of multicultural education (fifth edition). Boston, MA: Allyn & Bacon.

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Portes, A., & Rumbaut, R. (2011). Legados, la historia de la segunda generación immigrante. Barcelona SP: Hipatia Press. Racionero, S., Ortega, S., Garcia, R., & Flecha, R. (2012). Aprendiendo contigo. Barcelona SP: Hipatia Press. Sen, A. (2006). Identity and violence: The illusion of destiny. New York, NY: Norton & Company, Ltd. Shor, I., & Freire, P. (1987). A pedagogy for liberation: Dialogues on transforming education. New York, NY: Bergin & Garvey. Sleeter, C. E., & Bernal, D. D. (2004). Critical pedagogy, critical race theory, and antiracist education: Implications for multicultural education. In J. A. Banks & C. A. McGee Banks (Eds.), Handbook of research on multicultural education (second edition, pp. 240–58). San Francisco, CA: Jossey-Bass. Sleeter, C. E., & Grant, C. (2006). Making choices for multicultural education: Five approaches to race, class, and gender (fifth edition). Hoboken, NJ: Wiley. Sleeter, C., & McLaren, P. (2009). Origins of multiculturalism. In W. Au (Ed.), Rethinking multicultural education. Teaching for racial and cultural justice (pp. 17–20). Milwaukee, WI: A Rethinking Schools Publication. Thames, M. H., & Ball, D. L. (2010). What mathematical knowledge does teaching require? Knowing mathematics in and for teaching. Teaching Children Mathematics, 17(4), 220–25. Tharpe, R. & Gallimore, R. (1988). Rousing minds to life. Boston, MA: Cambridge University Press. Valdes, G. (1996). Con respeto. Bridging the distance between culturally diverse families and schools. New York, NY: Teachers College Press. Whitacre, I., & Wessenberg, D. (2016). Strategies are not algorithms. National Council of Teachers of Mathematics (NCTM). Retrieved from http://www.nctm. org/Publications/Teaching-Children-Mathematics/Blog/Strategies-Are-Not-Algorithms/

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Students Who Speak English as a Second Language Preparing Teachers for Changing Demographics—An Innovative and Collaborative Approach Bettibel Kreye and Gresilda A. Tilley-Lubbs

INTRODUCTION Anyone who has ever spent time in a public school classroom can remember the numerous in-service programs that teachers are required to attend. Depending on the amount of years spent in the classroom, you may have folders on any number of topics, from information on working with special education students to blood borne pathogen handling procedures and everything in between. Each in-service program was designed with the intention of fixing a specific problem at the forefront of government minds at the local, state, or federal level. However, after attending the workshops and taking precise notes on new strategies, you filed away your notes in their respective places and went on addressing the needs of your students the best way you knew how. In the chaos of daily teaching life, the pertinent information gained from those countless in-service programs was all too often forgotten or found impractical due to the limited amount of information offered. Anna’s Epiphany Anna, a dedicated teacher, not unlike us, experienced a similar situation. As a mathematics teacher enrolled in a master’s program to earn her licensure as a K-8 mathematics specialist, she was required to attend numerous in-service programs and class seminars; a number of them focused on developing strategies for working with English language learners (ELLs). As a young, conscientious math teacher, Anna was devoted to trying her best to meet the 67

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needs of all her students. After learning several new teaching strategies, she developed a statistics lesson for her eighth grade class in which groups of students were required to collect and analyze data about the probability of finding certain colors of Skittles in the bunch given randomly to each group. The lesson focused on using the Skittles as manipulatives, useful for helping students concretize the abstract concept of probability, and it also required that students work in groups so they could share strategies for solving the given problem. Upon assigning the statistics activity in her class, Anna’s students seemed engaged. She even noticed four students sitting in the back of her classroom animatedly discussing the problem using limited English, the only language they shared. When one of the boys raised his hand to ask a question, Anna expected to be asked how to solve the problem, but to her surprise, she heard, “Teacher, what is orange?” The possibility of her ELLs not understanding the language used in the problem had not even occurred to her. In that moment of eureka, Anna realized that for her ELLs, the difficulties they experienced in learning English did not necessarily lie in understanding mathematical concepts as had been suggested by her training, but in establishing a shared vocabulary, particularly in the case of colors. Up until that point, Anna thought the strategies provided in the in-service programs were sufficient, but in reality, she discovered that teaching mathematics to English language learners required much more. Anna would have to continually adapt her lessons, using regular assessments and other strategies, to bridge the linguistic gaps, or the gaps between the content knowledge students are expected to perform and the necessary language skills that enable them to do so (Kreye & Tilley-Lubbs, 2014). A Collaborative Start The multicultural curriculum transformation project that frames this chapter began when Betti Kreye, the program leader for secondary mathematics education, shared Anna’s story with her colleague, Kris Tilley-Lubbs, the program leader for English as a second language (ESL) education. She expressed her desire to implement new instruction that would better prepare math pre-service teachers to teach ELLs, and she responded with a similar desire, especially given concerns expressed to her by several ESL pre-service teachers regarding their apprehensions about teaching math content. Kris also shared a story about an ESL pre-service teacher who nearly dropped out of the program when she learned she would be expected to teach a geometry class for ELLs during her student teaching placement. Together, our shared concerns about teacher education for pre-service math and ESL teachers



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served as a catalyst for developing a collaborative project between our two fields. Subsequently, we combined our efforts to determine the most effective way to provide pre-service teachers not only with the knowledge and skills needed to effectively teach content, but also with the necessary knowledge and skills to teach appropriate academic language to ELLs so they could access the content required for success in school. That conversation provided the impetus for multicultural curriculum transformation that has resulted in mutual benefits for all pre-service teachers involved in our programs, whether for mathematics pre-service teachers learning to teach academic language for mathematics to ELLs, or for ESL pre-service teachers developing appropriate knowledge to work with their students in push-in or pull-out situations for mathematics classrooms. In addition, both groups of pre-service teachers develop a disposition that indicates they will seek out similar collaborations as they enter the profession, providing further evidence that they find value in learning collaboratively from/with their peers. Relying on our nearly fifty combined years in the K-12 classroom, we used our collective experiences in public schools to guide our process, noting the necessity for working closely with in-service teachers whose goals for ELLs matched ours. We wanted our pre-service teachers to have relevant experiences, requiring them to work in actual classrooms under today’s standards of accountability; as much as possible, pre-service teachers were provided opportunities to work under the guidance and mentorship of in-service teachers. Over the course of four years, we have worked collaboratively to bring our respective pre-service teachers together in a project that focuses on preparing math and ESL education pre-service teachers to work collaboratively so that ELLs can successfully access core content curriculum. Through experiential education within the context of a public middle school, pre-service teachers have the opportunity to develop theoretical knowledge and successive praxis surrounding inclusive education. By fostering collaboration across disciplines, ELLs, among others, are provided greater access to an equitable education. In an after-school program, our pre-service teachers put the multicultural curriculum theory they study in their combined class, Diversity and Multicultural Education in Teaching ELLs, into practice. They have the opportunity to move their thinking about multiculturalism from a focus on the “a ‘holidays and heroes’ approach to diversity or a ‘tourist’ approach to diversity” (Nieto, 2005). As they work with students from over forty countries, who speak over thirty languages, in addition to other students identified as “at-risk,” they learn to work with students whose races, ethnicities, genders, languages, socioeconomic statuses, abilities, religions, and other cultural backgrounds cause them to perform their lives in ways that may be different from the lives our pre-service teachers have known.

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We infuse multicultural education throughout our curriculum for the course we co-teach. Our multicultural transformation is designed to “cultivate an educated, skilled, and principled [pre-service teacher]” (Clark, 2002, p. 40). In our co-taught class, we use Affirming Diversity: The Sociopolitical Context of Multicultural Education (Nieto & Bode, 2011), which provides the basis for our curriculum. Through readings, discussions, numerous and varied instructional strategies, service-learning experiences, reflections, and research experiences in the middle school, pre-service teachers develop knowledge and dispositions to create classrooms that incorporate access and equity in a safe and secure environment for all students. We encourage pre-service teachers to explore and understand different cultural perspectives from outside their own beliefs. We emphasize that we are not trying to get them to change their own beliefs, but rather to focus on creating a multicultural classroom with a “human relations approach,” one that assumes that one of the major purposes of schools is to help students learn to live together in harmony, with the goal of establishing a classroom environment that promotes respect among all students regardless of race, class, gender, or disability, and that fosters positive interactions among diverse students and helps them to develop a class identity to reduce stereotyping and to promote pride among students who might feel marginalized (Grant & Sleeter, 2013). Further, we have the goal of creating a curriculum based on the multicultural education social justice approach, which deals more directly with oppression and social structural inequalities in order to prepare future teachers to take action to make society better serve the interests of all their students, particularly the marginalized. We purposefully lead our pre-service teachers in ways that allow them to learn “to analyze structural inequalities in their own life circumstances” (Grant & Sleeter, 2013, p. 51) so they can engage in social action and build bridges among various oppressed groups (Grant & Sleeter, 2013). Multicultural education presents “a philosophy, an approach, and actions that embody treating all people with fairness, respect, dignity, and generosity” (Nieto & Bode, 2011, p. 12). We provide a space for pre-service teachers to examine school policies and practices so they can enter the profession with appropriate knowledge, skills, and dispositions to foster equitable education for all students. This approach provides ample opportunities for pre-service teachers to develop the necessary skills to push against prevailing deficit notions regarding marginalized students (Nieto & Bode, 2011). We incorporate service learning as a “method/pedagogy that joins three concepts: community action [work in the after-school program] and academic knowledge, with deep reflection on the intersection of the two” (Tilley-Lubbs, 2009, p. 60). The service-learning experience provides ample opportunities for the pre-service teachers to put theory into practice. Perhaps even more important, they have the opportunity to experience diversity and multicultur-



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alism in a real-life setting. The students who attend the afterschool program represent every aspect of diversity, and in the informal setting of the program, they tend to perform life in ways that are often based on their backgrounds. Our pre-service teachers learn that they are not the expert fixers who have all the knowledge. Rather they learn that teaching and learning are reciprocal, and they can learn from the teachers and students at the after-school program. For example, they learn games from Africa that they incorporate into their teaching to make it culturally responsive, or they learn the value of seeking out folktales from Latin America to capture the imaginations of their Spanishspeaking students. They learn about different ways of counting and about the different foods they can use in their math or ESL lessons, once again moving them away from a superficial glance to an authentic lived experience that enriches their own teaching. In terms of academic knowledge, we “vary [our] instructional strategies” by having the pre-service teachers “engage in whole class discussions . . . , small group work, partner work, individual work, one-on-one work with the professor[s], [and] peer teaching and learning,” (Clark, 2002, p. 42). In addition, we used YouTube clips of classroom teaching and of student testimonials about being marginalized in schools. We also used Ted Talks presented by speakers who identified as oppressed. We had guest speakers, both in person and via Skype, once again speaking on topics of being teachers in schools. Some of the teachers identified as being from marginalized groups, such as African American or lesbian. Other teachers who visited our class spoke about teaching in Title I schools where poverty is a way of life for their students. We invited a colleague who specializes in rural education to come to our class to provide insight about the Appalachian students in our area and how their ways of knowing may be vastly different from the ways of knowing of our pre-service teachers. In the final course evaluations, these guest speakers were cited as one of the greatest strengths of the course. In this chapter, we work from the premise that our collaborative interdisciplinary work with pre-service teachers can and should be applied to PK-12 classrooms. We frame the entire multicultural curriculum on fostering understanding of the role power and privilege play in schools, whether in reference to the invisible or the visible curriculum. They become aware of the “sociopolitical nature of education” (Clark, 2002), and their role in transforming their own curricula as teachers of diverse students. KEY DILEMMAS IN ELL EDUCATION As demographics shift globally, the likelihood that most public school teachers will encounter ELLs in their classroom increases each year. According to

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the Census, approximately 4.7 million ELLs were enrolled in public schools across the United States in 2010. Furthermore, approximately 22% of all students, aged five to nineteen, live in homes where English is not spoken, and in 2003, about 42% of public school teachers taught at least one English language learner (United States Census, 2010; Turner, Dominguez, Maldonado, & Empson, 2013). With the ever-increasing emphasis on accountability and high stakes testing, the growing statistics indicate that mathematics teachers are facing or will soon be faced with the pressing need for preparing ELLs for success in STEM courses. Due to No Child Left Behind (NCLB), high stakes testing carries unprecedented weight in its impact on school systems, ranging from “school funding, grade-level promotion, and graduation” (Coltrane, 2002, para. 4). This is particularly true for ELLs who face standardized tests that, even if they match their content knowledge, are inaccessible in terms of language proficiency (Coltrane, 2002). For this reason, it is imperative that STEM teachers become familiar with strategies that provide the means for ELLs to access the content material in English. Demographics of ELLs ELLs come from a variety of cultural, socioeconomic, religious, and ethnic backgrounds and they exhibit a wide range of language abilities, whether in oral or written language. ELLs may be foreign- or native-born, but both groups often have limited exposure to English prior to entering school, particularly when their parents speak limited or no English. To add, ELLs may have attended schools in other countries where a language other than English is the primary language of instruction, and although their transcripts demonstrate evidence of grade level completion, they may have learned completely different content from what is taught in the United States. Alternatively, ELLs who enter the United States as refugees may have never attended school. Also, students who immigrated with their parents to the United States. may have missed months of school as their family sought to resettle in a new place. At varying levels, ELLs may struggle with both content and language, while at the same time learning to cope with adjusting to a new life in a new culture. To make the situation even more complex, the gap between language proficiency and content level expectations widens as content difficulty increases. As Coltrane (2002) says, we need to be aware that due to the gap between performance and content knowledge, student results may reflect “English language proficiency and may not accurately assess the content knowledge or skills” (para. 6). An examination of mathematics standards reveals that the complexity of tasks increases throughout the grade levels, moving from identifying and extending to proving and creating. A similar



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examination of language proficiency levels shows that students don’t reach adequate language proficiency to accomplish higher level tasks until after intensive language study over a period of time. Thus, the more advanced the content, the wider the gap will tend to be between students’ ability to access the content, to say nothing of their linguistic ability to demonstrate acquisition of content knowledge. Additional linguistic concerns include generational status, literacy level in the mother tongue, and previous schooling level (Varghese & Stritikus, 2013). Nieto and Bode (2011) support that Multicultural education is a process because it concerns intangibles such as expectations of student achievement, learning environment, students’ learning preferences, and other cultural variables that are absolutely essential for schools to understand if they are to become successful with all students. (p. 53)

In other words, through multicultural curriculum transformation, teachers can acquire necessary knowledge, skills, and dispositions to work effectively with all learners, including ELLs. CONCRETE EXAMPLE OF MULTICULTURAL CURRICULUM Transformation in Math and ESL Education Over the months following our initial conversation, we engaged in numerous discussions and brainstormed several ways our students could effectively work across their respective disciplines. We were both committed to developing meaningful experiences that would help our pre-service teachers to internalize more inclusive values and the need to provide an equitable education for all students, such that they would automatically consider the needs of all their students. Our pre-service teachers needed to discover new ways to adapt their instructional strategies (i.e., lesson and unit planning, assessments, classroom discussion, and curricula design) to fit the needs of any ELL student in their classrooms. As we designed the curriculum, we analyzed the areas where we had observed issues as our pre-service teachers designed their lesson and unit plans, especially when we asked them to keep in mind teaching ELLs in math classes or teaching content in their ESL classes. We had observed that most of our pre-service teachers represent a fairly homogeneous group, primarily representative of the dominant culture, white, middle-class, privileged families, with few exceptions. Due to those observations and our discussions, we decided to center our curriculum in multicultural education, including activities to help the pre-service teachers to develop an understanding of

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their own culture in contrast to the cultures of the students they would teach. As we analyzed the standards and proficiency levels for ESL, compared to the mathematics content standards, the need became evident for designing activities that would force the pre-service teachers to compare and contrast the linguistic proficiency necessary to complete the tasks required by the content standards. Through experiential education within the context of a public middle school, pre-service teachers have the opportunity to internalize theoretical knowledge and to develop praxis based on that theory. To provide them with the opportunity to create practice from their knowledge, we first decided to have them participate in service-learning in an afterschool program designed for ELLs, and then to require them to collaborate with peers in designing and implementing lesson plans. The final step involved having them assess the effectiveness of their teaching strategies. Each step of the process built on the former step and anticipated the following step. In the following sections, we have included quotes from students who participated in the course in fall 2014. At that time, the course was known as Topics in Diversity and Multicultural Education. The quotes are identified by source, and all represent work completed for that course. Each quote is identified as coming from reflections on assigned readings, reflections on observations in classrooms, reflections on lesson plans after implementation, final papers, the final roundtable discussion that occurred during the last class in December 2014, and the final master’s exam, which was comprised of an e-portfolio presentation. The students are referred to by pseudonyms. Session One Exploring identity and culture. For the first combined session, we divided the pre-service teachers into mixed groups (i.e., from both subject areas) in which members used guided activities to help them identify and articulate their individual cultural perspectives regarding topics such as race/ethnicity, religion, gender, sexual orientation, language, and socioeconomic status, as well as any inherent privilege associated with their dominant identities. The groups were also instructed to discuss personal educational experiences from kindergarten to graduate school. With very few exceptions, pre-service teachers largely identified themselves as white, of European descent, from middle- to upperclass professional backgrounds, English-speaking, Christian, conservative, and gifted. In the final share-out of session one, we led a discussion about how individual cultural perspectives and educational experiences influence teaching methods, which can affect one’s teaching perspective and expectations of students. In this session, we heard students express transformed ideas about



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themselves and their students as cultural beings. In the culture activities at the beginning of the semester, their attitudes had resonated with Convertino, Levinson, and González’ claim that “White/Anglo pre-service teachers consistently claim that they have no ‘culture’ and are therefore genuinely concerned about how they will teach ‘culturally diverse’ students in their classroom” (2013, p. 26). In the final paper for the course, Erin remarked, “[This semester] . . . really helped me to appreciate how complex and multidimensional an individual’s culture can be . . . yet, teachers need to know the individual cultures of all their students to successfully teach to the needs of every learner in their classroom.” We doubt that most of our pre-service teachers would have understood the importance and complexity of the various perspectives within their classrooms without participating in these activities. Discrepancies between standards and language proficiency. We also instructed pre-service teachers to identify and analyze possible discrepancies between grade-level specific math standards and language proficiency levels as defined by the World-Class Instructional Design and Assessment (WIDA, 2014) Can-Dos or descriptors of the various levels of English language proficiency. Within each group, the math pre-service teachers explained the content knowledge requirements for their discipline, and the ESL pre-service teachers explained the linguistic gaps that may exist for ELLs at varying levels of English language proficiency. Working together, groups closely examined the verbs used to define math standards (e.g., interpret or analyze a graph) and the linguistic ability required to understand the verbs to be able to meet a given standard. This activity helped many pre-service teachers realize students’ English language proficiency might only allow them to complete simple tasks, such as matching pictures with single word explanations, regardless of prior content knowledge. Our group sharing process also shed light on the marked difference between having mathematical content knowledge and ability, and being able to express that ability confidently using academic English. Coming to the realization that content assessment needs to incorporate an understanding of each student’s individual culture and language proficiency, Holly stated in a reflection, “[W]hen the students cannot answer the good questions due to their limited English proficiency, the task of teaching becomes extremely difficult.” Reflecting on the lesson plan he and his group taught at the afterschool program, Josh remarked, “I don’t think the misunderstanding was coming from the content, because everyone was able to draw them, but only a few had the appropriate language to say why it’s a rectangle and not a square.” By the end of the first session, pre-service teachers started to become more aware of the difference between understanding a math concept and being able to articulate that understanding.

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Classroom observation assignment. At the end of the first session, we gave each pre-service teacher an assignment to complete an individual observation in one math and one ESL classroom at a local middle school known for its large ELL student population. We asked them to focus on instructional strategies, classroom design, student-to-student and student-to-teacher interactions, student engagement, and language(s) of communication. We also gave preservice teachers an observation protocol guide to make their own notes and draw a sketch of the classroom set-up. Session Two Observed differences in instruction. For the second combined class, we asked pre-service teachers to discuss their classroom observations within their collaborative groups. Additionally, groups were asked to compare and contrast their experiences, specifically focusing on gaps that might occur based on a student’s level of language proficiency and the content material being presented. After sharing with their groups, we led a class discussion about the observations; many pre-service teachers mentioned that the ESL classroom seemed much more active and engaged than the math classroom, which consisted primarily of a teacher-centered lecture. In most of the observed contentfocused classrooms, the pre-service teachers reported seeing evidence of ESL learning and teaching strategies, such as word walls, vocabulary instruction, and student partners, but many did not see evidence that classroom teachers were using those tools effectively. Alternatively, the pre-service teachers reported seeing the same ESL tools and strategies from the math classrooms being used in the ESL classrooms; however, they reported enhanced instruction for ELLs. As Carrie commented in her reflection on her observations in middle school math and ESL classes, “[T]he observations . . . at the middle school struck a chord with me in understanding the true benefits behind ELL strategies I had only read about in books.” Overall, pre-service teachers reported that ESL teachers seemed more aware of their students’ needs and abilities than teachers in the math classrooms. Lynn said about her observations, “[T]he ESL class was very small and organized, and it really got me to see how the students learn.” However, they noticed a disparity in class size; the typical ESL classroom had 6–10 students while the math classes had 25–30. Many asserted that it seemed more difficult to work in classrooms with a larger numbers of students. Integrated lesson plans. Using the findings from their observations and the subsequent discussion, we instructed pre-service teachers to work in groups to design lesson plans that would fulfill the mathematical content standards while also addressing the possibility for varying English language profi-



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ciency among students. Our pre-service teachers worked together within a framework we call the Cycle of Instructional Planning and Support (CIPS) to understand ELLs and their specific educational needs: 1) understanding prior knowledge, 2) requirements demanded by content standards, 3) language proficiency as defined by WIDA (World-Class Instructional Design and Assessment), the gaps that exist between the content standards and middle and high school students’ language proficiency, 4) appropriate strategies for teaching the content to ELL, and 5) reflection on the lesson after it is taught. Pre-service teachers began by using the CIPS competencies to figure out how best to assess students’ baseline math content knowledge, as well as their task-based language skills. In the lesson plans, the pre-service teachers needed to include both language and math standards-based objectives. As Beth, a math pre-service teacher, wrote, “We all came from different backgrounds. We were strong in the mathematical content and she was strong in the ELL content so . . . combining our minds and ideas only made our lesson plan stronger.” As Carrie, an ESL pre-service teacher, commented during her final exam for her master’s degree, [I] learned the passion of math teachers for teaching math, not just test-taking tricks. . . . the goal of getting to real math that students need, not to look for a quick calculator fix, but to make the math accessible to all WIDA levels through different strategies. (Carrie, personal communication, n.d.)

Many of the math pre-service teachers saw the added value of collaboration as evidenced by their lesson plans; the ESL pre-service teachers pushed them to think about language in ways that previously would never have occurred to them. Collaborative teaching experience. After two weeks of work, each group submitted their lesson plans to us, which we reviewed together, side-by-side, for content integration. We learned a lot throughout this process as well as each lesson plan required significant discussion between us to fully clarify the content outside of our individual disciplines. After receiving our suggestions, the pre-service teachers used their revised lesson plans to teach a collaborative group lesson for ELLs at an after school program. After a time of reflection, Holly, a pre-service teacher in ESL, stated, “[R]eading about how to plan effective ESL lessons or about what strategies work best to educate ELLs is wonderful, but you never fully understand the benefits of these practices until you see them for yourself.” Additionally, Sophie, another math pre-service teacher, noted, “[G]etting to implement our lesson during the afterschool program was an incredible opportunity to learn directly from the ELLs and recognize the need for specific teaching strategies in the classroom.” By providing a teaching opportunity, the pre-service teachers

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were able to put theory into practice, also known as praxis. Both math and ESL teachers reported increased confidence in seeking future collaboration and support. Session Three Discussion and reflection. For the final combined class, each group completed a PowerPoint presentation that included their lesson plans, a summary of the themes from their observations, the gaps identified between the math standards and the WIDA Can-Dos, and a reflection on the overall project they designed and implemented with the collaborative group. We designed this particular session to provide additional time for whole group discussion and reflection about the effectiveness of the strategies used throughout the entire project. By the end of the third session, many pre-service teachers shared the sentiment expressed by Carolyn: “[C]ollaboration with colleagues is paramount to your success! Together you can come up with lesson plans that are far better than those you could make alone.” We agree, and believe that the lesson plans our teachers produced collaboratively were superior to any one they could have written individually. Curriculum Revisions After each semester, using a combination of class discussion notes and laterassigned final reflection papers as feedback, we make appropriate revisions to our multicultural curriculum transformation project. In the fourth semester of our project, we decided that all pre-service teachers would benefit further from enrolling in a course about diversity and multicultural education, with a focus on working with ELLs. The shared course provided a space for prolonged collaboration, with weekly discussions that focused not only on working with ELLs, but also other marginalized groups. As part of the course, pre-service teachers also completed 20 hours of service-learning. At the end of the course, teachers expressed a deeper understanding of the needs of ELLs, a greater depth of knowledge necessary to conduct their own classes, excitement about being able to learn about a multitude of cultures, and greater confidence in their ability to create equitable classrooms. In addition to this course, pre-service ESL teachers are required to study methods for teaching math to middle school ELLs and within that respective course, each lesson plan they prepare must incorporate inclusive instructional strategies for ELLs (Weber & Crane, 2010).



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The Need for Collaboration Content teachers who strive to address the language gap need to seek support from ESL teachers or specialists because, “collaboration between ESL and content area teachers is essential if the immediate and long term needs of ELLs are to be addressed” (Pawan & Ortloff, 2011, p. 463). Within our extensive experiences in public schools as teachers and administrators, and within our current work with pre-service teachers, we observed many inservice teachers primarily performing their planning and lessons in isolation, seldom dedicating time or energy to interact with other teachers; collaboration and partnerships were rare. Nonetheless, research suggests “when teachers engage in collaborative practices, they experience a reduction in isolation, enjoy more occasions to share their expertise, and appreciate the opportunity to shape the way the ESL program operates in their schools” (Dove & Honigsfeld, 2010, p. 6). Furthermore, we frequently observed a tendency for teachers to believe their expertise is all that is necessary for meeting the needs of their students. Regardless of a teacher’s expertise in a given content area and in overall pedagogy, there is a body of knowledge and strategies with which teachers need to be familiar to be able to help ELLs be successful in the classroom. As Janet, a math pre-service student stated in her final paper, “[S]poken and written language[s] [are] such a large part of a mathematics classroom,” and all classrooms for that matter, “that it is absolutely necessary for us to be aware of our students’ language abilities so that we may cater and scaffold our instruction to them.” Since a number of teacher education programs do not incorporate courses on teaching content to ELLs, it is essential that teachers and ESL specialists establish much needed collaborations. Meeting with an ESL specialist. Even if you do not share a planning time, it is well worth the effort to find a common time when you can meet with an ESL specialist to discuss the best approaches for working with the ELLs in your classroom. To add, it is best to meet with an ESL specialist prior to the start of the school year so that you can incorporate new strategies starting at the beginning of the year. Before attending your meeting, you should find out pertinent details about your ELLs, such as their respective World-Class Instructional Design and Assessment (WIDA) proficiency levels, countries of birth, cultural traditions and perspectives, family structure, educational background, languages spoken in the home, past trauma, and any other information that could impact a student’s experience in your classroom. Ideally, you should ask the ESL specialist about alternative teaching strategies and discuss ways the ESL specialist might support your lesson and unit planning so that the material is more accessible to ELLs. To add, your collaboration should not end after the initial meeting, but should continue over

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the course of the school year and beyond. We suggest scheduled weekly meetings to discuss each week’s lesson because the more informed the ESL specialist is about your goals and objectives for students, the stronger and more targeted the ESL support can be. Since language barriers in no way indicate students’ inability to use critical thinking skills or to achieve academic success, the key to helping students reach their potential lies in understanding who they are, what they bring to the classroom, and the instructional strategies that will enable them to effectively acquire specific content knowledge. A curriculum based in multicultural transformation leads pre-service teachers through the process of recognizing the strengths of the students they teach, and developing their own curricula that foster empowerment in marginalized students, with the end result of providing equity and access for all students (Banks, 2013; Nieto & Bode, 2011). Addressing standards. Based on the assigned classroom standards, look up the verbs that describe how a student is expected to perform the acquired content knowledge (e.g., interpret or analyze), then use WIDA Can-Dos to figure out students’ proposed content knowledge, based on their language proficiency levels. For example, if a math standard specifies that students will be able to compare and contrast the properties/characteristics of polygon shapes and classify a given figure according to its properties, teachers would need to determine the proposed competency for an ELL student with limited English proficiency. Table 4.1 provides an example of suggested competencies adjusted for a student’s language proficiency level for provided math standard. In this example, we assume that from prior lessons the student knows certain math vocabulary (e.g., parallel, right angles, congruent) and the names for individual shapes from previous lessons. In this lesson, students are required to compare and contrast those shapes. In examining a math standard across the levels of language proficiency, knowledge acquisition occurs at all levels in varying ways. In Levels 1 and 2, ELLs have not yet developed the necessary vocabulary to create explanations and justifications. In Levels 3 and 4, ELLs have significant vocabulary at their disposal, but they still need supports that allow them to relate information in a step-by-step process. Upon reaching Level 5, most ELLs are able to complete tasks in a more independent way with fewer supports. The differentiation occurs in the way the task is structured and in the student work product. ELLs whose language proficiency is at a lower level are able to better deal with tasks that rely on modeling and scaffolding and that incorporate concrete language with visuals and manipulatives. As ELLs become more proficient in navigating language, the task can require the use of more abstract language skills, and in turn, more independence as they create a work product.

Select examples of shape manipulatives from or descriptions of shapes with multiple given properties. Organize shape manipulatives to determine shape properties.

Complete a chart of properties.

Match characteristics to shapes.

Point to examples of a specific property within a given shape.

Level 5 Bridging Organize the comparisons and contrasts of multiple shapes that share some, but not all, properties. Create an original chart showing these relationships (i.e. showing all the properties of each polygon).

Level 4 Expanding Analyze properties to determine the specific name for a given shape. Compare and contrast pairs of shapes that share some, but not all, properties.

Level 3 Developing Categorize a given shape according to its properties and defend/ explain categorization. Complete a provided graphic organizer to demonstrate the relationships between two polygons.

Note. Objective was to compare and contrast properties of polygons; classify polygons.

Sort provided shapes according to specific property.

Level 2 Emerging

Level 1 Entering

Table 4.1.   Projected competencies by language proficiency level

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After analyzing the gaps between the content standard you are teaching and the language proficiencies of the ELLs in your class, you can begin to incorporate this knowledge into lesson planning. Try to think of language objectives you would have for your ELLs. For example, based on the above example, what language skills would you want your ELLs to acquire? If you want them to be able to sort the various shapes and associate written and spoken words with each shape, state that as an objective. If you want them to be able to arrange shapes into a chart with a column for the shape and another for the characteristics, state that. In other words, state what performance standard would provide sufficient evidence that the student has learned the differences between various shapes. Keep in mind that you will most likely have differing language objectives across students. In addition to stating your language objectives, think about the types of activities that will lead ELLs through appropriate steps to achieve your desired result. Learn to ask yourself questions that will help you to design lessons that provide ELLs equitable access to your teaching. Also, if your language objective involves sorting, begin to think about whether you would provide manipulatives, word strips to sort, or possibly have the student draw the shape on a piece of paper and copy the correct word for the shape from the word bank. Similarly, when you assess student content knowledge, will your assessment match your instruction? Have you provided adequate supports for each step? Have you kept in mind that language acquisition moves from the concrete naming of objects to the abstract conceptualizations of ideas? In other words, be sure to reflect on each instructional step so that the progression is logical and appropriate for the language level. Also keep in mind what our math pre-service teachers learned from their collaborations with ESL pre-service teachers, as is articulated by Mary Ann in her reflection on implementing the group lesson plan: “[P]rior to implementing this lesson, we were warned by our ESL colleague that some of the students we would be working with may know what a square is, but not know how to describe it. To counteract this, she suggested we bring pictures that somehow incorporated squares. . . . This was incredibly beneficial because it gave students with limited English proficiency the opportunity to show what they know.” Leslie, another math pre-service teacher, commented, “Had we not brought manipulatives, it would have been difficult to keep students interested in what was going on because of the language barrier.” Reflecting on their experiences, pre-service teachers realized the importance of adapting their lessons to meet the linguistic needs of ELLs in the math classroom. All teachers can develop the knowledge, skills, and awareness that will help them to provide a quality education for the ELLs in their classes. STEM content is within reach of all students with appropriate supports that will



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bridge the linguistic gaps that create barriers to knowledge acquisition in a developing language. Just as we have the goal for our pre-service teachers to develop the habits of mind that lead to making adaptations for ELLs second nature, we believe that practicing teachers can also learn to keep linguistic gaps in mind throughout the planning and implementation of instruction to better meet the needs of ELLs in STEM classes (Costa & Kallick, 2009). REFLECTION BRIDGE From the beginning, we realized that seamless collaborations between preservice math and ESL teachers, while uncommon, are definitely possible. In addition, it became evident that we were experiencing significant enriching and broadening of our perspectives. Further, we are constantly reminded that our pedagogical and methodological beliefs are significantly different from the ways we were trained. We were trained to teach math as logical, linear, precise, and as right or wrong, and Spanish using lectures, drills, memorization, and regurgitation of information, respectively. However, throughout our teaching careers, we both have gained a better understanding of how students learn. We value the experiential knowledge we have gained in PK12 classrooms as even more important than the formal academic knowledge we have acquired in university classrooms. Based on those experiences, what has united us and enabled us to work so closely is our shared belief about the experiences students require for deep learning to occur. CRITICAL CONSIDERATIONS IN MATH MULTICULTURAL CURRICULUM TRANSFORMATION Even in suggesting a new process, we acknowledge the existence of certain challenges in implementing collaborative relationships with other teachers. Some of the roadblocks to this process include lack of common planning times, location in the school building, numbers of students, numbers of lesson preparations, and so on. Additionally, in a school with three math teachers per grade level, each teacher may have two or three ELLs in any given class, and each math teacher may have as many as five lessons to prepare for each day. If there is only one ESL teacher in the school, she may be responsible for all the ELLs, meaning that her time is limited for collaborating with each math teacher, while at the same time preparing her own language-specific lesson plans. The logistics of finding time to work collaboratively can be extremely complex. We are aware that a certain level of commitment to navigating these

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challenges is necessary for this kind of preparation to be possible, to say nothing of effective. Other challenges we encountered in our project include recognizing the importance of collaboration, finding time to collaborate, and working around the math frame of mind that knowledge of content assures the ability to teach all students. One prevailing challenge we have encountered with practicing math teachers concerns their anxiety to have their students perform well on the standardized tests. Some teachers tend to frame their instructional practices in preparing students to take standardized tests, so any strategies that veer away from multiple choice tests are met with suspicion. In turn, they regard collaboration as taking them away from the intense preparation necessary for their students to do well on the standardized exams. To cite Giouroukakis and Honigsfeld (2010), “Teaching to the test can be detrimental to ELLs who have unique cultural and linguistic needs . . . results in ‘lowered cognitive complexity of lessons for English learners, less meaningful instruction, and a lack of focus on the sociocultural context in which students are schooled’” (p. 473). Student individual needs cease to be the focus, being replaced by test preparation practices. This challenge reaches deep into habits of mind that may represent years of entrenched beliefs in appropriate delivery of instruction. Just as math pre-service teachers receive extensive preparation in their discipline prior to entering the teaching field, ESL teachers are also extensively prepared to understand and work with ELLs. In our experience, we have discovered that ESL teachers possess a wealth of information about their students, and they are eager to share their knowledge so that ELLs can access quality education. Our goal is for our pre-service teachers to enter the profession so convinced of the efficacy of working collaboratively that they seek creative ways of making it happen despite the challenges. Lee, a preservice teacher stated, I learned a lot of helpful math instruction ideas, like using the fraction tiles. I also got a brief view into their world, which was a unique opportunity, especially because they tend to think about things in a whole different way as mathminded people, and just as individuals with different perspectives than me. (Lee, personal communication, n.d.)

For a collaboration to be valuable, it must be reciprocal, with each group or individual participating in the learning and teaching process. When teachers work together without the element of reciprocity, they are not working in partnership and relationship. Instead, they are in a one-sided situation in which they don’t experience mutual gain, and most likely will not feel commitment to continuing with the attempted collaboration.



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SUMMARY Regardless of the challenges we face while doing this work, we continue to refine our process for preparing pre-service teachers to effectively help their ELLs achieve academic success. Our resolve is strengthened by comments such as this one, written by Jack, a math pre-service teacher who originally believed our project was unnecessary because, “[G]ood teaching is good teaching.” In his final paper, he wrote the following: Drawing pictures could have been an effective way of probing students’ thinking, yet I persisted in asking questions and trying to work with students’ limited answers. This is something I will need to grow in. . . . I need to stretch myself to accept and communicate with more representations. . . . Overall I feel that this project was a huge learning experience for me. Instructional strategies that I have come to rely on in planning and implementing lessons do not work very well for students who are learning English, so I need to provide other methods for students to demonstrate their understanding. (Jack, personal communication, n.d.)

We truly believe that this project with pre-service teachers with its parallel work in schools with in-service teachers takes multicultural education from “doing diversity” to the infusion and understanding of teaching that provides opportunities for ELLs to access knowledge in the math classroom. Multicultural curriculum transformation has developed from our years of working collaboratively to prepare our pre-service teachers to apply what they have learned to their own curricula. As Banks states, “The transformation approach [to multicultural curriculum] changes the basic assumptions of the curriculum and enables students to view concepts, issues, themes, and problems from several [. . .] perspectives from which problems, concepts, and issues are viewed” (2013, p. 189). Pre-service teachers develop Critical consciousness [that] represents things and facts as they exist empirically, in their causal and circumstantial correlations, naïve consciousness considers itself superior to facts, in control of facts, and thus free to understand them as it pleases. Magic consciousness, in contrast, simply apprehends facts and attributes them to a superior power by which it is controlled and to which it must therefore submit. (Freire, 1973, p. 44)

By spending a semester in the university classroom discussing the intersections of cultural perspectives, our pre-service teachers move closer to critical consciousness, which in turn, allows them to design and implement curricula that seek to provide an equitable and accessible education for all their students. Teachers “cannot rely on one-dimensional views of teaching

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and learning; rather, they must cultivate the capacity to view themselves, their students, and their learning and teaching as multidimensional” (Convertino, Levinson, & González, 2013, p. 39). Today’s multicultural classrooms demand that teacher education curriculum and that professional development for practicing teachers be infused with the many dimensions of multicultural education, and this can only happen through multicultural education transformation. REFERENCES Banks, J. A. (2013). Approaches to multicultural curriculum reform. In J. A. Banks, & C. A. McGee Banks (Eds.), Multicultural education: Issues and perspectives (eighth edition, pp. 181–99). Hoboken, NJ: Wiley. Clark, C. (2002). Effective multicultural curriculum transformation across disciplines. Multicultural Perspectives, 4(3), 37–46. Coltrane, B. (2002). English language learners and high-stakes tests: An overview of the issues. Center for Applied Linguistics. Retrieved from http://www.ericdigests. org/2003-4/high-stakes.html Convertino, C., Levinson, B. A., & González, N. (2013). Culture, teaching, and learning. In J. A. Banks, & C. A. McGee Banks (Eds.), Multicultural education: Issues and perspectives (eighth edition, pp. 25–41). Hoboken, NJ: Wiley. Costa, A. I., & Kallick, B. (2009). Habits of mind across the curriculum: Practical and creative strategies for teachers. Alexandria, VA: Association for Supervision and Curriculum Development (ASCD). Dove, M., & Honigsfeld, A. (2010). ESL coteaching and collaboration: Opportunities to develop teacher leadership and enhance student learning. TESOL Journal, 1(1), 3–22. Freire, P. (1973). Education for critical consciousness. New York, NY: Seabury Press. Giouroukakis, V., & Honigsfeld, A. (2010). High-stakes testing and English language learners: Using culturally and linguistically responsive literacy practices in the high school English classroom. TESOL Journal, 1(4), 470–99. Grant, C. A., & Sleeter, C. E. (2013). Race, class, gender, and disability in the classroom. In J. A. Banks, & C. A. McGee Banks (Eds.). Multicultural education: Issues and perspectives (eighth edition, pp. 43–60). Hoboken, NJ: Wiley. Kreye, B., & Tilley-Lubbs, G. A. (2014). Collaboration for authentic pre-service teacher experiences: Mathematics and English as a second language. International Journal of Teaching and Learning in Higher Education, 25(3), 4–5. Nieto, S. (2005). Teaching multicultural literature: A workshop for the middle grades. S. Burlington, VT: Annenberg/CPB. Retrieved from http://www.learner. org/workshops/tml/support/pdf/msmultilit_intro.pdf Nieto, S., & Bode, P. (2011). Affirming diversity: The sociopolitical context of multicultural education (6th ed.). Boston, MA: Pearson.



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Pawan, F., & Ortloff, J. (2011). Sustaining collaboration: English-as-a-second-language, and content-area teachers. Teaching and Teacher Education, 27(2), 463–71. Tilley-Lubbs, G. A. (2009). Good intentions pave the way to hierarchy: A retrospective autoethnographic approach. Michigan Journal of Community Service Learning, 16(1), 59–68. Turner, E., Domínguez, H., Maldonado, L., & Empson, S. (2013). English learners’ participation in mathematical discussion: Shifting positionings and dynamic identities. Journal for Research in Mathematics Education, 44(1), 199–234. United States Census 2010. Data. Retrieved from: http://2010.census.gov/mediacenter/awareness/minority-census.php Varghese, M. M., & Stritikus, T. T. (2013). Language diversity and schooling. In J. A. Banks and C. A. McGee Banks (Eds.), Multicultural education: Issues and perspectives (eighth edition, pp. 219–39). Hoboken, NJ: Wiley. Weber, C., & Crane, D. (2010). Making math accessible to English language learners, grades 6-8. Bloomington, IN: Solution Tree. World-Class Instructional Design (WIDA) (2014). Can-do descriptors. Retrieved from http://www.wida.us/standards/CAN_DOs

Part II

SCIENCE

Chapter Five

Teaching Biology in the Age of the Next Generation Science Standards Methodology for Teaching in High Needs Schools Antoinette Linton

INTRODUCTION Reform in science education has occurred in response to increasing demands for citizens who can solve practical health, political and social problems using science (Feinstein, Allen, & Jenkins, 2013). Beginning in the 1980s the demands for a scientific literate populous focused on preparing students to become science majors for colleges and universities, building student confidence, and developing students’ appreciation for the usefulness of science. Traditional science teaching met this demand by engaging students in artificial laboratory problems, exposing students to correct scientific information, and providing hands-on activities. Policy makers were disappointed when this effort did not generate the expected improvement in student science academic achievement. Of a particular concern was the underperformance of historically underrepresented minorities and students of low socioeconomic status in science coursework. This chapter examines an approach to teaching science for urban students in the era of the Next Generation Science Standards (NGSS). To accomplish this, an epistemic practice for NGSS teaching for urban secondary African American and Latina/o students was employed. Epistemic practice in this discussion refers to the processes and procedures explicitly taught to students, used over time to develop science knowledge that relates to real life experiences and the cultural values of urban students. The discussion of the proposed epistemic practice based approach to teaching the NGSS is presented in two parts. The first part includes the epistemic practices that 91

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support learning the NGSS in an urban science classroom. The epistemic practices include focus inquiry, directed observation, and guided practice (Hollins, 2011a). The second part includes the organizing ideas and principles for teaching the epistemic practice referred to as knowledge used for implementing NGSS (Hollins, 2011a). The organizing ideas for teaching the NGSS include knowledge of learning, curriculum, and argumentation. This discussion addresses in broad strokes what teachers need to know about NGSS, how to envision teaching within the NGSS, and why a vision is important (Hollins, 2011a). STORY OF SUCCESS The implementation of NGSS by an inner city biology teacher in a Southern California secondary high school was a project in which the curriculum was organized to make biology a holistic-practice based class grounded in the sociocultural perspective of learning. The biology teacher used the community as the text for extending the students’ knowledge and skills, rather than organizing the community around the topics introduced by the standards. The planning and enacting of the biology course for an urban high school began with contextualizing the standards in scenarios based on student reported experiences of science. The scenarios were then expanded to include essential questions and tasks that were deemed valuable by the students. For example, to introduce heredity to students, the biology teacher created the following scenario: You are a community member here in Los Angeles and you will need to go to the hospital, buy food and be a part of a family either as a child of someone or a future parent. You will need to make sophisticated judgments about the credibility of health, food, and citizen wellness claims by the local city, state and national government agents (for example, the Food and Drug Administration). As an informed community member you will need to design a rubric or criteria for judging the ethnical practices of local, city and state agencies now that you will be a primary consumer of their services. (J. Clark, personal communication, n.d.)

Here the students’ stories, reports, personal curiosities, and discourse were used as grounding for the scenario. The purpose of planning the next generation science standards in this way was to present the topics in a way that motivated students to act on their own behalf. In order to do this, the biology teacher had to value the stories, reports, personal curiosities, and discourse of the students as a way to support transforming the biological content to the



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sociocultural context of the urban community surrounding the school. The biology teacher intended for the students to interpret and translate the biological content based on the sociocultural discourse shared by other students. This course facilitated the sharing of ideas, stories, questions, and personal curiosities during the regularly planned academic routines. The course content was organized into three general sections for discourse: (a) the daily warm-up question, (b) what we are learning—a section of classroom discourse where students summarize and provide examples of their understanding of the topic, and, (c) and scenario discussion and question formation that began all units. The daily warm-up questions correspond to the discipline core ideas presented by the NGSS and were written in ways that were meaningful for students. The daily academic routine, what we are learning corresponded to student personal curiosities and questions they had at the end of class period. The scenario discussion that began each unit corresponded to the student reports and personal curiosities that students have shared in the course. Case studies and text assignments were modified in light of the student reports and personal curiosities shared over time during the school year. After taking note of student discourse, the biology teacher would interpret and translate the curriculum so that students would find meaning and purpose in their own lives, have opportunities to reflect, describe, and express their experiences and receive credit for these ideas in class. Organizing the classroom academic routines in this way opened up space for students to truly think about the biological content. No longer were they coming into the classroom everyday without a clue as to what was expected of them or where we were in their learning trajectory. Students were empowered to take charge of their own learning and help their classmates learn along the way. The empowerment of students comes with knowing how to begin, self-critique, and conclude investigation and negotiation of expository text. The teacher becomes effective when she explicitly gave creative freedom to students to modify and refine the practices so that students can act on their own behalves academically. By working together to create a community of learners that includes both teacher and student, student academic performance not only increased over time, but was intentionally and systemically placed under student control. CONNECTION TO MULTICULTURAL EDUCATION/ MULTICULTURAL CURRICULUM TRANSFORMATION Incorporating student discourse and inspiring personal curiosities and then using this discourse and curiosity as the context to interpret and translate

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curriculum and learning experiences for urban students is facilitated by the intentional development of mutually supportive relationship amongst the biology teacher and the students. The Science, Technology, Engineering, and Mathematics (STEM) learning experience described in this chapter demonstrates how a biology teacher promoted positive relationships between students, positive teacher-student relationships, and positive relationships between students and learning experiences. An examination of the conditions that support positive learning experiences in an urban science classroom reveals three essential practices: (a) putting yourself out there; (b) earning the trust of the students; and, (c) facilitating a community of learners. Putting Yourself Out There In order to build a community of learners, teachers need to put themselves out there. What is meant by out there is that teachers need to model the types of learning, listening, interpretation and translation of information that they want students to use. Some basic examples of this in the biology classroom were using personal family examples to explain biological phenomena, obeying classroom rules that students and teachers co-constructed, keeping one’s word, teaching fairness by being fair and teaching generosity by being generous. The biology teacher in this chapter went to great efforts to be a trustworthy content expert who used her integrity and intentionality of practice to facilitate the students’ learning. With that, she collaborated with students in constructing a mutually supportive context for learning. By designing meaningful epistemic practices and implementing academic routines that make social, academic, and cognitive sense to students, the teacher was able to create a safe space for students to express their concerns for the learning, add to and design part of their own learning experiences, and allowed students to express their ideas in ways that incorporated both the academic language and home language of students. Interacting with students in this way provided the teacher with the appropriate insights into how to bring in relevant aspect of students lived experiences into the biology course. Earning the Trust of the Students Urban students have experienced the most under prepared and inexperienced teachers in the profession. At times, students are negotiating the ongoing disappointments of going to school only to experience universalistic notions of learning that are used to deliver instruction and assess student performance. Often times, students are blamed for their lack of responding to these sub par learning experiences. The explanations used for student failure include no-



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tions of laziness, cognitive deficiencies and emotional behavior disorders. It is reasonable that urban students are skeptical of urban school environments and the adults who teach there. Knowing this, the biology teacher in this chapter had to earn the trust of the students in order to teach them. Earning the trust of the students includes engaging in explicit caring toward, and among, urban students with approaches that do not dismiss, reduce, or silence the humanity of the students. These approaches include investigating learning difficulties and taking what the students say about the difficulty of an assignment or learning experience seriously; maintaining consistent adult behavior so that you relate to students in such a way that they become more conscious of themselves; and demonstrating competency as a professional science educator. Investigating student academic difficulties entails understanding student attributes and believing that academic challenges result from issues with the approaches to classroom instruction as it is contextualized by students’ social and cultural backgrounds. Thus earning student trust in this area means making a conscious effort to connect students’ experiences and prior learning to the academic content. This requires the teacher to make careful and intentional observations of the students in school and outside of school settings, student learning preferences, interest and talents, to examine students’ previous work, and to engage in strategic discourse intended to provide insight into the nature of the challenge between the students’ knowledge and skills and the academic performance at hand. Facilitating students’ consciousness entails admitting to us that adult behavior is a powerful influence on student behavior. Telling the truth and admitting to mistakes, holds the teacher accountable to the social standards of behavior that students and teachers co-construct. Sharing thoughts and ways of thinking puts the teacher out there and situates the teacher as a safe knowledgeable other. This strategic demonstration of metacognition is not about facilitating students’ using their minds like the teacher, but making the teacher’s mind accessible in order to make decisions and act from their own minds. Finally, knowledge of student attributes, learning preferences, interests and talents enhance teaching practice and facilitate student success. In essence students agree to learn from a teacher and trust that the professional knowledge of teaching and learning is sound. Teachers secure student trust by demonstrating competent skills as a scientist, and creating systems of learning that enhances students’ awareness of their own ways of meaning making. At the secondary level this is facilitated by the strategic use of processes, procedures, and cognitive tools used to manage information and social interactions. The biology teacher in this chapter used conceptual matrixes to

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guide students’ understanding of biology. Well-planned social and academic experiences co-constructed with students provide the evidence that students need to trust and learn from the teacher. Therefore, it is to the teacher’s advantage to make teaching practice transparent and draw as many connections to students’ lives as possible. Developing A Community of Learners For the biology teacher in this chapter, creating a positive community of learners consistent with a sociocultural perspective of learning science is especially difficult when one considers the entrenched school culture that it must usurp. The predominant images of being students and teacher are some of the most persistent known in the social and behavioral sciences. To foster a sociocultural classroom, the biology teacher and students worked together to establish norms for discourse, working together, and sharing ideas; and practices (such as role responsibilities, looking over each other’s work with rubrics, and voluntarily assisting fellow students without needing the teacher’s permission). The objective of these norms and practices was to support students in supporting each other and taking intellectual risks. In this high support classroom, the biology teacher and students co-constructed a learning environment where complex scientific tasks could be operationalized using epistemic practices that were explicitly taught to students at the beginning of the year and used consistently throughout the year with intentionality and integrity. Students came to expect their peers to participate in consolidating scientific knowledge before investigations began, that at least one student in a group of students would help with learning the laboratory techniques and that all would challenge each other with making scientific arguments and claims. WORKING DEFINITIONS Apprenticeship in a Biology Course The National Research Council (NRC, 2012) document A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (hereafter referred to as the Framework) is the product of a committee of experts charged with developing a consensus view of what is important in K-12 science education. The Framework uses the logic of progressions to describe students’ developing proficiency in three intertwined domains—practices, cross-cutting concepts, and core ideas—in a coherent way across grades K through 12. The NGSS build on these intertwined domains and include tables that define what each practice might encompass and the expected uses



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of each cross-cutting concept for students at each grade level. Teachers are encouraged to emphasize the integration of core science concepts with one or more science practices such as modeling; evidence-based explanation and argumentation; and/or the design of investigations to test hypotheses, analyze results, and construct explanations of data (Pellegrino, 2013). These changes in the demand for science proficiency have shifted the focus from teaching science as a set of known ideas that can be divided into small pieces of information to an integrated field of knowledge with connections and themes that place an emphasis on specific science practices. Implementing the NGSS is a complex experience of learning and applying the processes needed to focus the content of the biology course. The processes needed to learn the discipline core ideas and cross-cutting concepts of the NGSS are embedded in the experiences. A three-part teaching sequence, used over a semester, is used in this discussion to illustrate this point. To ground the sociocultural perspective of teaching biology in the era of NGSS, I use the following concepts that characterized teaching and learning for urban student academic performance. They are derived from the broader literature on teaching and learning in multicultural societies and connect what we know about how people learn with the kinds of classroom conditions that optimize opportunities to learn in meaningful ways: Directed observation. An opportunity for students to engage in a predetermined conceptualization of a skill or process that is enacted by a teacher or a fellow student. Epistemic practice. Processes to be used for the benefit of student learning, this empowers students to take charge of their academic performance by teaching a process that makes sense to them. Earning students’ trust. Purposefully and intentionally displaying teacher competence, care, and trustworthiness with the ability to teach. This includes having an effective way of collecting information on students’ background and community; the ability to use student discourse as a source of curriculum. Focused inquiry. An investigation into particular phenomena that influence the processes and conditions for learning within and outside of classrooms. Guided practice. Student-to-student or teacher-to-student opportunities to approach learning segment under the watchful eye of a more experience other. Putting yourself out there. A teacher putting one’s cultural frame out in the forefront not as a model, but a frame of reference on how to negotiate internal conflict, not knowingness, perspective taking and positionality as key tool for community building and caring in the classroom. Rigor. When the learning experience allows for frequent opportunities to engage in complex, meaningful, problem-based activities where students are

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routinely asked to apply knowledge, in diverse and authentic context, explain ideas, interpret texts, predict phenomena, and construct arguments based on evidence. Sociocultural perspective (socioculturalism). A learning perspective that states that learning happens when students advance their skills and understandings through participation with others in culturally organized activities. FOCUS INQUIRY INTO TWO LEARNING PROCESSES (THE PRACTICE) In discussing the development of positive science classroom environments three essential practices where identified: (a) putting yourself out there; (b) earning the students’ trust; and, (c) and developing a community of learners. These practices were essential in the development, planning and enacting epistemic practices for investigation and negotiating expository text. The following description of the two learning processes provide insight into the roles of teachers and students, and how the instructional practices and content are directly related to the local community which the students reside. The initial activity of the school year is focused inquiry into text-study and experimentation processes. Text-study and experimentation processes are approaches to teaching that are grounded in the NGSS science and engineering design practices. The text study is an assignment where students advance their ideas about biology using biological text. Here students engage in a six-step expository process where: (a) they create research questions based on question frames; (b) infer the scientific methods presented in the text; (c) determine data sources; (d) analyze the text organizational features; (e) answer the research questions from the first step; and, (f) create a summary of the section assigned. The purpose of this focus inquiry is to teach students the science and engineering design practices. The materials needed for focus inquiry include a course outline with a calendar of topics aligned to the NGSS, rubrics for self assessment, past student work to grade using the rubrics and to initiate student generated questions about how to start the processes, what the components of the process are, and how to know when the process is completed. Direct instruction is used to introduce the focus inquiry process. In the first part of focus inquiry experience, students begin learning the text-study and experimentation processes by receiving opportunities to examine the materials needed for the processes (see Appendix A). The text-study learning experience includes: (a) requirements for developing research questions to guide inquiry into the different types of text students will be exposed



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to (textbook, laboratory protocols, supplemental science readings; (b) a list of research methods; (c) examples of data sources; and, (d) instructions on how to write the data analysis, findings and summary of science text. The findings portion of the text study is the answers to the research questions that students are required to write at the beginning of the process. During this portion of focused inquiry students are encouraged to use their background and experiences with science in everyday situations to make sense of the tools. It is stressed that this process will not change only the content of the process. In this way urban students are acquiring important prerequisite skills for science literacy development. Allowing students to express their knowledge, in their own way, grants them access to learning the process. In the second part of the focus inquiry experience, students learn the experimentation process, a five-step process that mirrors the text study which includes a document called the KQL (What We Know, What We Question, and What We Learned) (see Appendix B). The KQL is likened to the KWL (What We Know, What We Wonder, and What We Learned), but there are significant changes. First, students work together in research groups where they highlight the background knowledge of the laboratory activity and any connecting background information that they know. Then they consolidate this information under the K portion, much like the K portion of a KWL. Second, students use the same question frames from the text-study process to formulate five research questions that can be used to create hypotheses. The hypotheses are possible answers to a research question and are testable. Next, students set up their laboratory activity according to the hypothesis that is to be tested, collect their data and then organize the data for analysis. Then students are to make claims about what they know from the laboratory experience and support what they know using components of the text study. These claims are written on the L portion of the KQL. Finally, students are to support or reject their hypotheses based on the analysis of the data and the support of their claims. When students are learning this process they: (a) examine the instructions on how to share their experiences with their peers in the K section; (b) examine guidelines for constructing five questions about the laboratory topic; (c) learn how to choose a question from the previous step to formulate a hypothesis in the if . . . then statement format; (d) learn how to collect, organize and analyze data; (e) learn how to use data to support or reject a hypothesis; and, (f) learn how to construct an argument by using information from the data analysis and supporting textual information from the text study. This process is conducted for every laboratory activity. The second part of the sequence for the text-study and experimentation processes is directed observation. First, students use the text-study and experimentation rubrics to grade prior student work kept from previous years.

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Students take note of how the completed assignment is organized and how it relates to the reading or laboratory activity. Directed observation is particularly important because students need to understand the qualities of the processes as they relate to the NGSS and all students need guidance in learning what to attend to and how to make sense of the assignments (Hollins, 2011a). Students are allowed to use, critique, and suggest modifications to the processes as their understanding of the principles that guide text-studies and experimentation becomes deeper. Transforming biology content knowledge into two sociocultural processes for learning addresses the second element of providing positive learning experiences for urban students by developing cognitive practices that facilitate the development of trust for the students. By teaching the epistemic practices as skills to be used for the benefit of student learning students are empowered to take charge of their academic performance by teaching a process that makes sense to them. By planning a focused inquiry into the two practices, the biology teacher increases the authenticity and connectedness of the learning experiences to students’ prior knowledge and experience; the rules and directions of the epistemic practices are clarified, and students are provided opportunities to practice how they will engage in discourse concerning the practices. Using focused inquiry in this way is intended to increase student confidence in learning science and in the teacher’s ability to teach science. During instances of focused inquiry and directed observation, students discuss and co-create the classroom routines; the academic processes, and the collaboration strategies used. This supports the students learning and influences the norms for engaging with the teacher, with other students, with curricular materials, and text-study and experimentation processes. Through focused inquiry and directed observation students take ownership of the approaches to science and engineering design, discipline core ideas, and crosscutting concepts. Using these sociocultural approaches for teaching science, focused inquiry and directed observation introduce and set standards and procedures for the learning science (Hollins, 2011a). GUIDED PRACTICE Over time students are given opportunities to approach the assignments on their own and the teacher guides brainstorming and discussion among the whole class; interactions are student-to-student and teacher-to-student. By the end of the first semester small groups of students interact and learn in teams through collaborative and cooperative participation with the KQL and use the text study to form arguments. Students self-assess and peer review using the



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rubrics. Students use these processes throughout the school year, teach new students the processes, and apply the processes with each new topic. First Five Weeks into the Semester During the focus inquiry portion of the semester, the text-study and experimentation processes were taught. Students discussed their challenges concerning the processes. Generally, students were concerned with the methods, data sources, and data analysis portion of the text study, as well as with constructing a hypothesis and argument for the experimentation process. For the text study, many students would copy the captions beneath the figures and graphs found in the textbook and use this information as the methods portion of the assignment. Other students would leave the data source portion of the text study blank. During small group and individual discussions about the processes, many students expressed confusion and frustration about what to write and the sections were related. Students explicitly requested examples, one-on-one instruction, and wanted immediate feedback concerning their efforts to practice on their own. It was important to take these concerns seriously and to express to the students that their concerns were heard and that changes to the delivery of the approaches would change. Early teacher-to-student discussions about the assignment revealed that students did not know the differences between methods and sources of data, and many students often wrote duplicates within these two sections. For the experimentation process, students were challenged to write a hypothesis that could be tested. For example, during a photosynthesis laboratory assignment where students were examining the effects of sunlight on carbon dioxide consumption of elodea plants, some students wrote an untestable hypotheses concerning plant growth. Students were taught that a hypothesis must be testable and to review the materials and methods of the laboratory assignment to determine why they could not measure plant growth. During these discussions, multiple analogies constructed from understanding students’ cultural, social, and academic experiences were used to develop a conceptual understanding of the process. Over the next several weeks of the first semester, guided practice was used to facilitate the learning experiences of the students. Some students continued to have difficulties distinguishing methods from data sources. At times, students would revert back to copying the captions from the figures diagrams and tables located in the readings. This led to one-on-one sessions with students on making sense of what they were reading and developing the ability to infer what the authors of the text were thinking in order to present the picture or table in which the methods were based.

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Some students questioned whether or not the text-study and experimentation processes were needed to truly learn biology. These questions would lead to the discussion about what makes science different from history, math, and language arts. The processes of developing questions, planning out investigations, analyzing data, constructing claims and arguments defines what scientists know and do. It is the science and engineering practices that provide opportunities for students to share what they know and what their challenges are. Gradually, by the end of the semester, students began to see the connection between the different dimensions of the NGSS. Midsemester At the midsemester point, it was time to reflect on challenges from the first half of the semester, and it was also time to refine approaches. After exploring students’ initial responses to guided practice, the teaching focus shifted from teaching the science and engineering practices to the challenges identified during the first half of the semester. A response to challenges in the experimentation process was the KQHL (What We Know, What We Question, How We Find Answers, and What We Learned). This tool was developed to help students organize their responses to laboratory work. Using the graphic organizer increased dialogue during the experimentation process. Confident students began to assist other students with finding text-based information for question construction, formulating testable hypotheses and carrying out investigations. The fact that students began to help one another as different students began to master the epistemic practices employs the third dimension of facilitating a positive learning environment for science learning by empowering students to facilitate the learning of their peers. By promoting a communal atmosphere where everyone benefits when everyone learns, students were facilitated to learn deeper knowledge of the subject matter by helping another student. Students mentioned how they would have ah-ha moments when they began to explain how to use the epistemic practices to learn a topic. New students would enter into the classroom from another classroom, school or district and students were encouraged to teach the routine so that the new student would be included in the classroom community. As more students began to master the epistemic practices, a community of learners began to grow and the learning challenges of a few were not only addressed by the biology teacher but by their peers as well. Although the practices were not learned to mastery at the same rate for all students, students realized that by helping each other they began to understand the material at a deeper level. In short, different than the competitive, teacher-centered environments that reproduce student divisiveness, developing an epistemic practice based approach to learning science helped students use their experiential knowledge to help themselves learn the material as they were facilitated to help each other.



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The implementation of a reading guide was also introduced at the midsemester point in response to the text study. Students had difficulty inferring the methods and data sources presented in the figures and diagrams in text. Students did not know what to attend to while reading the text to construct the text study. The purpose of the reading guide was to provide a way for students to ask questions about specific components of the text-study process that were difficult. The reading guide provided facilitative questions, in student everyday language, so that student self-confidence in using the process would improve. Refining the practices to facilitate student-learning employs the first dimension of facilitating a positive learning environment for science by allowing the teacher to put themselves out there and exposing one’s thinking about the changes that were needed to improve student learning. By paying attention to students’ learning challenges the teacher was empowered to change the materials and curriculum to increase access to science learning. Student culture, questions, feedback, discourse were viewed as curriculum that were used to change the KQHL document. By midyear, students had mastered the language around using the tools and could make suggestions and changes to the documents. As a fellow community member, the teacher made meaning of the student feedback and made changes that were linked to the learning that was already in progress. Valid knowledge about students learning needs and thinking about the practices allowed the teacher to contextual the changes to the practices so that students academic improvement could occur. Four Points Assessment Rubric Evaluation of the KQHL and reading guide was facilitated by a four points assessment rubric (see appendix C). According to the rubric, students’ responses on the KQHL indicated that students could express their understanding of the discipline core ideas, express their thoughts either orally or in writing and draw conclusions based on evidence with guidance. Students were able to successfully pose research questions, participate in investigations, and collect and analyze data. Students could write, speak, and follow directions, read from the textbooks and participate in using quantitative reasoning in a step-by-step teacher intensive format. By the end of semester one, students were able to independently perform the text-study and experimentation processes and use the processes to develop understanding the discipline core concepts and cross-cutting ideas. Qualitative Data End of semester analysis of student work was used as a quantitative indicator of the connection between changes in pedagogical approaches and the

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academic performance of students. Scores on text studies and laboratory write-ups from the first five weeks of the semester served as baseline data. Overall, the greatest improvement in academic performance was in the experimentation process. During the first five weeks of the semester, 30% of the biology students scored 75/100 or higher on the laboratory write-up. By the twentieth week of school 54% of students scored 75/100 or higher on the laboratory write-up. This is a 24% overall gain. Student gains for the text study were more modest. During the first five weeks of the semester, 33% of the biology students scored 65/90 or higher on the text study. By the 20th week of school 45% of students scored 65/90 or higher. This is a gain of only 12%. These scores are gathered from students who received guided practice or clarifying questions from the teacher to complete the assignments. It is believed that the data indicate that close to 50% of biology students are still in need for focused inquiry and directed observation of the science and textual practices used in the course. In addition, continuous dialogue with students who are struggling with the practices is needed in order to improve, modify, and refine the practices so that all students have access to science learning in the biology course. REFLECTION BRIDGE Listening and truly hearing students discourse and making changes to the epistemic practices contributed to the understanding of the relationship between using students’ sociocultural knowledge and facilitating the academic performance of students. The biology teacher in this chapter (a) put herself out there, (b) earned the trust of her students, and (c) intentionally facilitated a community of learners in her classroom. That is, when putting herself out there she readily admitted when she did not know particular content outside of her class or when she was open to suggestions by the students. She earned the students’ trust by being fair (rewarding and correcting mistakes without discrimination), designing well-planned and well-enacted lessons that connected to students lives, and intently listening to students when they were talking about their lives. As the year progressed, she encouraged student experts, individuals who mastered the epistemic practices, who volunteered to help their peers, and made note of at least one strength that every child demonstrated. In order to facilitate the development of a community of learners, the biology teacher made every possible effort to ensure that all students in the classroom felt safe and supported with her as well as with each other. Challenges arose when students were first introduced to the coconstruction of the learning environment in this way. Students have spent many years in learning environments characterized by teacher-centered, com-



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petitive, and assessment-driven classrooms where their voices are not heard. They are not accustomed to teachers adjusting instruction to accommodate differences in how students learn and so may see these adjustments as not being fair to other students. To address this, the biology teacher explicitly taught the idea of fairness for classroom learning as the act of doing everything in her power to help a student learn. Not all students need the same things, not all students have the same strengths or challenges, and so it is her responsibility as a professional educator to make sure that everyone’s academic needs are met. The idea that creating a even playing field so that all students had access to learning was viewed by students as favoritism because it lacked the factor of sameness they were familiar with. ESSENTIAL KNOWLEDGE USED FOR TEACHING THE NGSS (THE THEORY) The essential knowledge for implementing the NGSS included (a) a constructivist-sociocultural perspective to teaching urban students; (b) a perspective of curriculum referred to as the Nature of Science to organize discipline core ideas, engineering and science practices and cross-cutting concepts; and, (c) a four-points rubric for assessment and argumentation (see appendix D). In the previous discussion, the approach to teaching the NGSS was presented. This discussion presents a vision of how students learn, how curriculum should be organized and using argumentation as assessment. A SOCIOCULTURAL VISION OF THE NGSS Making sense of how to prepare the NGSS for urban students is at the heart of articulating a vision of learning. Urban students construct their school experiences using social and cultural tools for making meaning. Understanding and using these tools is key to facilitating deep and durable student involvement in science. Understanding and facilitating this multidimensional process requires the use of a tool for organizing discipline core ideas and cross-cutting concepts of the NGSS. This tool can be used to guide the designing of curriculum and develop learning experiences that guide students’ understanding of new science skills. These tools need to focus student dialogue, learning experiences, and thinking in ways that develop a more sophisticated application of science ideas. Hollins (2008) states that facilitating meaningful learning in schools requires three practices: (1) empowering students to direct their own learning,

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(2) linking learning experiences with cultural values and practices; and, (3) directly linking learning experiences to real life situations such as those found in the workplace. She pointed out that teachers can design meaningful learning experiences for specific groups of students by using culturally appropriate communication, ways of socialization that are familiar to students, information processing strategies such as text-study and experimentation processes, and culturally valued knowledge and skills in curricular content. Hollins (2011b) described a sociocultural apprenticeship approach to learning how to teach that involved three well-interrelated learning experiences, focused inquiry, directed observation and guided practice. Here, teachers learned how to investigate, attend to, and practice the skills and knowledge needed to learn how to teach. These three apprenticeship practices were referred to as focused inquiry, directed observation, and guided practice (Hollins, 2011b). Hollins’ (2011b) approach to learning how to teach was applied to the process of learning science. Learning science was viewed as an apprenticeship where students participated in well planned, culturally valued learning experiences for the purpose of developing the skills and understanding of science and engineering practices, discipline core ideas, and cross-cutting concepts. In this conceptualization, students were given the opportunity to: (a) investigate a particular learning process for a component of NGSS; (b) provide guidance for investigating particular aspects of science and engineering practices, discipline core ideas and cross-cutting concepts; and, (c) give guided opportunities to participate in authentic real-life science activities under careful supervision of an experienced classroom teacher. In this experience, students were engaged in interrelated and sequenced processes that support communication and learning for both teachers and students. The practices of focused inquiry, directed observation, and guided practice incorporate student cultural and experiential background knowledge and what they need to experience to develop the new skills and understandings related to NGSS. It provides opportunities for students to use what they have learned in science to plan and enact an investigation. After the investigation students were expected to be able to interpret data through a specific discipline core idea and cross-cutting concept and establish a sound argument to communicate to their peers. Taking a sociocultural approach to teaching biology in the era of NGSS is no easy task. Operationalizing the learning by using focused inquiry, directed observation, and guided practice was the approach taken to tie back to meaning making that is intended to become a habit of mind for students. This tying back is grounded in students’ lived experiences. However, this does not mean that students will always be motivated to fully engage in the learning processes. Students may have tremendous difficulties with the processing needed to engage in science learning grounded in this learning perspective due to the



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lack of experience they have with learning in classrooms that require them to critically think about their experiences. It seems that whenever there are new ideas presented within this learning context there is always a need for focused inquiry. For example, when the KQL was modified into the KQHL, students needed to engage in focused inquiry in order to practice working with the tool and working together around the processes within the tool. Facilitating the use of this tool with its modifications required that the teacher be versed in ways of asking questions, plan and enact lessons that have opportunities to make careful observations of students’ academic performance in-the-moment of the lesson, and be able to make modifications that incorporate aspects of students’ cultural and historical factors, learning theory, choices in pedagogy, alterations in curriculum materials, and facilitating/interrupting social dynamics. Organizing Curriculum for NGSS The interrelatedness of focused inquiry, directed observation, and guided practice that Hollins (2011a) emphasized was incorporated into the design of the curriculum. In this example, focused inquiry was used to shape the structure of the discipline and to design learning experiences for students that include but go beyond standards and objectives. The primary focus of having a progressive view of the curriculum is to provide focus, purpose, and structure to the learning experiences of all students. Focused inquiry into curriculum development for the NGSS included an examination into: a) what types of problems students are required to solve; b) how content and curriculum are presented to students; c) how instruction is to be adapted in light of NGSS; and, d) how to structure the learning environment for NGSS, including approaches to teach science thinking, engineering design, the use of technology, inquiry, and about student development. These elements of the curriculum were examined and compared in relationship to the current textbook offered by the district and supplemental material used in teaching biology. Knowledge about the curriculum from these different sources provided a framework that organized and operationalized the NGSS (Hollins, 2011c). Appendix C provides answers to these questions and frames the overall perspective of the new curricular approach to NGSS. By understanding the types of problems students will solve, the thinking we want students to engage in, and how students will use materials and technology in science, teachers were better equipped to provide opportunities to plan for problem solving and inquiry. The curriculum perspective provided guidance on how the NGSS was organized and operationalized the curricular scope and sequence. Once the scope and sequence was mapped out, the

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guiding questions and answers were used to refine the details of each NGSS performance expectation for life science. As a result of focused inquiry, the stance that science is an integrated field of knowledge with connections and themes that might be hierarchical or web like and incudes discipline core ideas, engineering practices, and crosscutting concepts was taken (Schneider & Plasman, 2011). As a science teacher, I viewed the curriculum and the work as representations of canonical science knowledge, and as such, the curriculum is a disciplinary tool and the teacher is a disciplinary practitioner who models intellectual skills and dispositions for the student (Windschitl, 2002). The perspective is progressive in that the problems and student performance expectations planned are connected to the values, language, and everyday experiences of the students and the surrounding community (Hollins, 2008; Parkay, Anctil, & Haas, 2005; Duschl, 2008). This progressive perspective enables teachers to plan and enact learning experiences that are relevant to the discipline, engages students in scientific discussions that are relevant to their lives and experiences. When engaging students with curriculum, grounded in a sociocultural perspective, the classroom will be characterized as one where students are talking, walking about, building, arguing, and at times fussing with one another. Heterogeneous grouping with students taking on roles to play is common. During the semester in which this study was conducted, students resisted the new ways of engaging with the curriculum. Students are familiar with using curricular materials to find the right answers. Having discussions about big ideas and playing with different points of view are cognitively foreign in the public school classroom. In order to address this student phenomenon, the classroom and the use of curriculum had to be recultured; that is, the ways of being, speaking, writing, and hearing had to be discussed at the beginning of the school year. Epistemic practices were explicitly taught as skills, and then consistently assigned so that students could develop the habits of mind to refer to them when new problems arose (a key component of the tying back process). At every opportunity it was important for students to engage in group work that facilitated meaningful discussions, laboratory investigations that incorporated the investigation epistemic practice, and readings that incorporated the use of the text study. Students were encouraged to use these tools outside the classroom if it helped with other coursework. In addition, students were encouraged to modify the practices as they saw fit to improve their academic performance. Argumentation and Assessment Hollins (2011a) contends that integrity and trustworthiness are two essential elements of high-quality teaching. Integrity exists in the appropriateness of



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the teaching practices for urban students, and the strength of the learning and curricular perspectives that inform teaching. Under these conditions, trustworthiness exists when students consistently achieve the performance expectations. Quality science teaching is maintained through accountability for the integrity and trustworthiness of teaching practices based on evidence from assessments of students’ progress in relationship to the performance expectations. In cases where students do not accomplish the performance expectations, the teacher assumes responsibility for making adjustments in practices based on evidence from appropriate assessments of performance assessments (Southerland, Smith, Sowell, & Kittleson, 2007). Meaningful assessments within NGSS provide evidence that students are able to a) make meaningful connections between their everyday experiences and discipline core ideas and performance expectations; b) use the crosscutting ideas to help students frame the big ideas across disciplines and make applications in new and novel situations, c) engage in science and engineering practices and determine the legitimacy of particular claims and evidence, and d) communicate and present ideas using elements of argumentation (Duschl, 2008; Ford & Forman, 2006; Gipps, 1999; Jordon, 2010; Lee, 2002; Moje, 2007). The purpose of this type of assessment is to ensure that students develop deep understandings of discipline-specific knowledge and practices, that students can apply what they know in different situations, and that teachers have important information in which to base interventions for supporting the correction of misconceptions and understanding. Teachers need to be able to identify and develop appropriate approaches to assessment that will provide the evidence necessary to determine the integrity and trustworthiness of their teaching practices and that the students make consistent progress in meeting expected learning outcomes (Graue & Johnson, 2011). Appendix B provides a rubric to frame the development of assessments in the era of NGSS. One approach to assessing students’ ability to apply the knowledge of NGSS is engaging students in a process of argumentation from evidence. In order to facilitate students’ ability to engage in argumentation from evidence teachers are encouraged to design analytical tasks that use receptive language and productive language functions. Analytical tasks involve distinguishing between a claim and supporting evidence or explanation (Lee, Quin, & Valdes, 2013). Students do this by analyzing whether evidence supports or contradicts a claim. Students are given opportunities to analyze how well a model and evidence are aligned. From these tasks students can construct an argument (Lee, et al., 2013). Students use receptive language functions when they are given a task that allows them to comprehend and critique arguments made by others both orally and in writing. Students will use productive language functions when

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they communicate ideas, concepts, and information related to the formation, defense and critique of arguments orally and in writing. (Lee et al., 2013). Appendix D is a rubric that students and teachers can use in order to measure whether or not students can engage in argumentation from evidence. SUMMARY The biology teacher in this chapter intended for students to develop questioning skills, critical thinking, and to work towards developing a community of learners in the classroom. Developing these skills is not a one-size-fits-all endeavor. Classroom communities and learning are as diverse and complex as the student bodies that make them. Taking a sociocultural stance to learning biology means that teachers will need to learn a great deal about their students and the communities in which their students live in order to provide for and support authentic opportunities to learn. This chapter presents a perspective of science learning that is counter to the conventional wisdom of teaching, were students engage in activities in order to receive the transmitted information in the format of an elite class. Instead, what is presented is a systematized and operationalized way of encouraging students to participate in inquiry and interrogate expository text in real ways. In this type of classroom, the teacher intentionally critiqued her cultural script, shared it with her students, and asked for student input in the scope and sequence of the learning activities. In order to do this, the teacher needed a holistic practice based approach to teaching and learning. This approach included the planning, enacting, interpretation, and translation of student learning outcomes in response to the learning event planned. The use of focused inquiry, directed observation and guided practice as epistemic practices for teaching created the foundation to this holistic-practice based approach to teaching and learning. Over the course of a semester, use of focused inquiry, directed observation, and guided practice was documented. Students’ elicited responses were taken into account and changes in features of the tools were used during the three-part apprenticeship practices for facilitating science learning. These responses revealed the challenges in student thinking—from the beginning of the school year to the end of the first semester—regarding the components of the assignment that were confusing and needed more guided practice. The documentation of the relationships students have with the curriculum, with the teacher, and with each other revealed insights on the dynamics within each class period such as which students have more confidence with the



Teaching Biology in the Age of the Next Generation Science Standards 111

processes, which students can work independently, and what analogies, examples, and cultural references were used by the teacher and by the students. At the beginning of the semester, classroom discussion centered on the process components taught during focus inquiry. Discussions ranged from expectations for knowing when an assignment was complete, defining each step of the text-study and experimentation processes, operationalizing the processes and determining the level of rigor. As the teacher, I made special efforts to provide culturally and socially relevant examples and facilitating student sharing of understanding. By midsemester, enough performance data had been gathered to implement strategic changes to the assignments and rubrics to grant more access to the students constructing of the reading guide, adding the argumentation process to the KQL and modifying the rubrics to clarify details of the process for easy use are examples of the changes and modifications. The student dialogue during class time progressed from a focus on the procedures of the text-study and experimentation process to seeking assistance with the content of hypotheses, the connections between the methods of the text study to the procedures for the laboratory activity, seeking approval for modifying laboratory procedures and using data to support or reject hypothesis. The quantitative data from student work scores indicate that the two practice-based approaches contributed to students’ ability to improve their academic performance over time. What specific factors may contribute to academic improvement students’ performance increasing is speculative, however, it is evident that there is improvement by the end of the semester and that this improvement is increasing. The findings from this study suggest that the use of epistemic practices to teach learning processes has a positive effect on high school biology student academic performance. Taking time to plan an investigation into a process used to provide coherence and continuity between topics and units, providing guidance during the investigation in order to specifically make connections between the discipline core and the cross-cutting concepts, and allowing for guided practice of the processes seems to increase the confidence and collaboration of the students. For many students the teacher takes the role of facilitator and elder in the room, which indicates that the process has potential for empowering students to direct their own learning. Monitoring student performance on the products of epistemic practices is one indication that the students’ participation in focus inquiry, directed observation and guided practice has potential for supporting positive learning outcomes in the era of NGSS.

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REFERENCES Duschl, R. (2008). Science education in three-part harmony: Balancing conceptual, epistemic, and social learning goals. Review of Research in Education, 32(1), 268–91. Feinstein, N., Allen, S., & Jenkins, E. (2013). Outside the pipeline: Reimagining science education for nonscientists. Science, 340(6130), 314–19. Ford, M. J., & Forman, E. A. (2006). Redefining disciplinary learning in classroom contexts. Review of Research in Education, 30(1), 1–32. Gipps, C. (1999). Socio-cultural aspects of assessment. Review of Research in Education, 24(1), 355-92. Graue, E., & Johnson, E. (2011). Reclaiming assessment through accountability that is “just right.” Teachers College Record, 113(8), 1827–62. Hollins, E. R. (2008). Culture in school learning: Revealing the deep meaning. New York, NY: Routledge. Hollins, E. R. (2011a). Teacher preparation for quality teaching. Journal of Teacher Education 62(4), 395–407. Hollins, E. R. (2011b). The centrality of a theoretical perspective on learning to teach. New York, NY: Nova Science Publishers, Inc. Hollins, E. R. (2011c). The meaning of culture in learning to teach: The power of socialization and identity formation. In A. Ball and C. Tyson (Eds.), Studying diversity in teacher education (pp. 19–61). Lanham, MD: Rowman & Littlefield. Jordan, N. C. (2010). Early predictors of mathematics achievement and mathematics learning difficulties. In R. E. Tremblay, R. G. Barr, R. D. Peters, and M. P. Boivin (Eds.), Encyclopedia on early childhood development (pp. 1–6). Montreal, Quebec: Centre of Excellence for Early Childhood Development. Lee, O. (2002). Science inquiry for elementary students from diverse backgrounds. In W. G. Secada (Ed.), Review of research in education: Volume 26 (pp. 23–69). Washington, DC: American Educational Research Association. Lee, O., Quinn, H., & Valdes, G. (2013). Science and language for English language learners in relation to Next Generation Science Standards with implications for Common Core State Standards for English language arts and mathematics. Educational Researcher, 42(4), 223–35. Moje, E. B. (2007). Chapter 1: Developing socially just subject-matter instruction. A review of the literature on disciplinary literacy teaching. Review of Research in Education, 31(1), 1–44. National Research Council (NRC). (2012). A framework for K-12 science education: Practices, crosscutting concepts, and core ideas. Washington, DC: The National Academies Press. Parkay, F., Anctil, E., & Haas, G. (2005). Curriculum planning: A contemporary approach. Boston, MA: Allyn and Bacon. Pellegrino, J. (2013). Proficiency in science: Assessment challenges and opportunities. Science, 340(6130), 320–23. Schneider, R., & Plasman, K. (2011). Science teacher learning progressions: A review of science teachers’ pedagogical content knowledge development. Review of Educational Research, 81(4), 530–65.



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Southerland, S., Smith, L., Sowell, S., & Kittleson, J. (2007). Resisting unlearning, Understanding science education’s response to the United States’ national accountability movement. Review of Research in Education, 31(1), 45–72. Windschitl, M. (2002). Framing constructivism in practice as the negotiation of dilemmas: An analysis of the conceptual, pedagogical, cultural, and political challenges facing teachers. Review of Educational Research, 72(2), 131–75.

Needs improvement

The report does not contain a title

0

No questions are written

0

Does not contain methods, procedures or possible activities that scientists used.

0

Contains no mention of the sources of data.

0

Sections

Title

5

Key concept questions

10

Methods

10

Data sources

5

3

Contains only an incomplete list of the sources of data used

Contains only an incomplete summary of the methods. Does not reference the diagrams, figures, or tools used. 7

7

Some questions are written but do not relate to the topic of the reading or do not allow for reading in order to answer them.

The report contains a title but lacks one or more of these: Chapter section Section Title Page numbers 3

Contains: all possible sources of data. (macromolecules, cells, tissues, organisms, etc.) 5

Contains a complete summary of the methods used based on the diagrams, figures, and pictures presented in the chapter. 10

All questions are presented. Uses key concepts, may include their own questions. Apparent that reading is needed in order to answer the questions. 10

The report contains a title with all the components: Chapter section Section Title Page Numbers 5

Excellent

Period______________________

Satisfactory

Name______________________________________________________

Appendix A:   Text Study Rubric

0

No questions are answered

0

No summary

0

10

Findings

40

Summary

10 7

The summary is unclear, contains little scientific information, or is not relevant to the topic

Some questions are answered correctly 30

7

Contains an incomplete explanation of how the section of the reading is organized

Total earned _________ Comments _________________________________________________

Explanation of how scientists presented and analyzed data is absent

Data analysis

Clearly and completely explains the topic of the section, includes references to approaches and findings 10

All questions are answered correctly 40

Contains a detailed and accurate explanation of how the section is organized, including a brief summary of each section 10

Period__________________________

Needs Improvement

“What you already know” or hypothesis is missing

0-2 points

Does not consider materials that were used in the lab for construction of research questions

0-2 points

Does not consider the methods, procedures and safety issues

0-2 points

Sections

KQL & Hypothesis (Pre-lab)

10 points

Materials (Pre-lab)

10 points

Methods, Procedures, & Safety Issues (Pre-lab)

10 points

3-7 points

Contains only a few questions that relate to the procedures and safety issues

3-7 points

Contains only a few questions that related to the materials needed for the lab

KQL does not connect to the topic discussed or there are insufficient areas such as: One or two questions are missing from the “Q” portion. Hypothesis is not written as an “If . . . (conditions), then . . . (cause) statement. The hypothesis is not testable according to the laboratory conditions. 3-7 points

Developing

All questions relate to the methods, procedures and safety issues. Methods have been modified to test the hypothesis. 8-10 points

Materials align with the topic of the lab. All questions are related to the material used in the lab. 8-10 points

8-10 points

The background information is relevant and provides examples of how the laboratory relates to the theme science as a process and connects to at the discipline core idea. The hypothesis is written correctly and is testable.

Satisfactory

Self-Assessment: You have to self-assess before you turn the document in. If your score is too far off from the teacher’s score, 10 points will be deducted.

Name______________________________________________________

Appendix B:   KQL Rubric

Does not consider hypothesis, sources of error, and concepts learned

0-2 points

Conclusion

10 points

Total earned _________ Comments _________________________________________________________

Clearly states whether hypothesis is accepted or rejected. Identifies: 1) sources of error; 2) concepts learned 8-10 points

11-19 points

0-10 points

25 points

Accepts or rejects hypothesis but lacks adequate support. Attempts to explain: 1) sources of error; 2) concepts learned points

Back of KQL Contains a detailed and accurate account of the data as it related to the hypothesis. There are two or more references to the text study. Argument for or against the hypothesis is well supported. 20-25 points

Gordo

Back of KQL Contains partially accurate explanations of the data, has little reference to the text study material, and the hypothesis is weakly supported.

0-2 points

10 points

Back of KQL Explanation of the data is inaccurate or absent. Hypothesis is missing and here are is support from background reading (text study)

No questions are answered

Questions “L”

All questions are answered correctly 8-10 points

6-9 points

0-5 points

15 points

Contains: all data tables and graphs are drawn neatly, calibrated appropriately, presented scientifically, and reported in SI units 10-15 points

Some questions are answered correctly 3-7 points

Contains: all data tables and graphs are labeled and represented appropriately

Contains: some but not all the tables and/or graphs; it has them all, but they are not labeled or filled in correctly

Data tables and/or graphs

Needs Improvement

The assessment tests known ideas that are divided into right and wrong answers. Assessment is presented in the traditional format (i.e., multiple choice, short answer).

Students are not presented with opportunities to provide evidence-based explanations.

Category

Integration of core science concepts

Opportunity to give evidence based explanations Students express their understanding of a developmental component of a science concept (predator) or inquiry (models building and testing) but cannot make meaning or draw conclusions.

The assessment attempts to cover the appropriate NGSS and core standards. The assessment may focus on scientific methods or content. Assessment is presented in a mixed method format (performance and traditional)

Developing

Appendix C:   Four Points NGSS Assessment Rubric

Students express their understanding of a scientific concept or process by finding patterns in the data and making meaning of the pattern, or constructing conclusions, refining models, and rejecting or supporting hypotheses based on evidence. This information is then used to make a claim. Students have satisfactorily been given opportunities to communicate this orally, or in writing.

The assessment covers the appropriate NGSS and provides students opportunities to demonstrate performance skills. Assessment posses more performance skills opportunities than traditional.

Satisfactory

Students express their understanding of a scientific concept or inquiry by finding patterns in the data, making sense of the pattern, constructing a claim, rejecting or supporting a hypothesis, and evaluating the usefulness of the claim with other variables, factors and student derived claims. Students have been given an opportunity to satisfactorily communicate this orally and in writing.

Core concepts assessed are integrated and connected to themes that are webbed throughout students’ lives. Thinking is likely to follow one or several integrated episodes of inquiry.

Excellent

Assessment presents questions, hypotheses, and procedures are already planned. Students are to enact the plan. The plans are based on past scientists’ work and activities that have been officially sanctioned as correct.

Students are not expected to engage in design challenges. There is just one correct solution to an engineering design and the teacher presents it that way.

Science practices

Engineering design Students are presented with a design and are expected to use it as a template to develop their own (but similar) design.

Assessment presents student opportunities to collect data through observation or experimentation or presents scenarios where students re already familiar. Details are teacher-guided in that the assessment is for students to understand on their own.

Students are given problems that are relevant and found in current events. Presenting models that are found in the text and are easily replicable or modified for the assigned problem.

Assessment components include students’ posing questions, designing investigations that are meaningful to them, collecting evidence, and making claims (with instruction). Inquiry is a first-hand experience where students engage in developmentally appropriate approximations of practice within the discipline such as a performance assessment.

Students engage in design (models, posters, processes, etc.) and relate design to human problems. Students have opportunities to revise the design as learning occurs.

Science questions, hypotheses and experimentation assessed contain connections to the material and other subjects that may or may not be scientific.

Needs Improvement

Students recognize vocabulary on the assessment.

Assessments present problems that students are familiar with or problems are decontextualized.

Little to no information about student prior learning or performance based skills can be gathered from the assessment.

Category

Student communication

Quantitative reasoning

Overall quality of assessment

Appendix C:  (Continued)

Assessment tasks are appropriate and teacher can justify why previous learning tasks are appropriate for student learning.

Assessments allow students to collect data use quantitative reasoning is a step-by-step teacher presented format.

Students are given opportunities to write, speak, read and hear scientific discourse. Students follow instructions, read from textbooks, online sources, science journals and supplemental readings.

Developing

Assessment satisfactorily meets all criteria for high quality assessments and can be used to measure student performance and inform future teaching and learning.

Assessment presents opportunities for students to use quantitative reasoning to solve relevant problems.

Students write, speak, read, hear and critique each others’ work. Students are given opportunities to express their understandings of how science changes during group endeavors.

Satisfactory

Assessment surpasses the criteria for high quality assessments and can be used to measure and improve student performance and inform teacher practice.

Assessment presents students with novel problems to solve with no prescribed way to use quantitative reasoning.

Students actively apply what they have read, heard, and written to human issues in the community. Students are given opportunities to have first hand approximations to produce scientific writing and other forms of communication.

Excellent

Lee, et al. (2013)

Total

Components of an Argument

3

4

Students express their understanding of a scientific concept or inquiry by finding patterns in the data, making sense of the pattern, constructing a claim, rejecting or supporting a hypothesis, and evaluating the usefulness of the claim with other variables, factors and student derived claims. Students have satisfactorily communicated this orally and in writing.

Students express their understanding of a scientific concept or process by finding patterns in the data and making meaning of the pattern, or constructing conclusions, refining models, and rejecting or supporting hypotheses based on evidence. This information is then used to make a claim. Students have satisfactorily communicated this orally, or in writing.

Students express their understanding of a developmental component of a science concept (predator) or inquiry (models building and testing) but cannot make meaning or draw conclusions.

1-2

Excellent

Satisfactory

Unsatisfactory

Appendix D:   Four Points NGSS Rubric for Assessment and Argumentation

Chapter Six

LGBT-Inclusion across the Life Science Curriculum Mary Hoelscher

INTRODUCTION This chapter aims to encourage life science teachers’ transformation of their existing curriculum such that it is inclusive towards lesbian, gay, bisexual, and transgender (LGBT)-identified people in both the content that they teach and the pedagogical strategies that they utilize to teach that content. In this chapter, I share my experiences transforming my curriculum as a high school life science teacher compelled by my students and my own personal identities. My experiences as a teacher educator partnering with teachers as they pursued LGBT-inclusive curriculum transformation are also included. When appropriate, this chapter connects to education research that supports LGBTinclusive curricular transformation. This chapter focuses on standards that are most relevant to secondary grades, but elementary science teachers may find opportunities to promote greater inclusion that are relevant to their own context. STORY OF SUCCESS When I became a teacher, I had considered proactively addressing gender and sexual diversity, but I had never seen it done. I had the impression that inclusion of topics related to sexual orientation and/or gender identity was taboo in science education. No one had told me that, but the silence was deafening. I feared the possibility of angry parents complaining to my principal. I 123

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feared being fired if I stepped outside of the bounds of business-as-usual for a science teacher. I feared that proactive support of LGBT-identified people would make me suspect. I feared that someone might discover my own identities. I feared becoming a thirty-second inflammatory news story. During my first year of teaching, my students transformed my cautious and somewhat traditional curriculum through their questions and comments. I consented by responding to their questions about lesbian and gay people openly and honestly when they brought them into the classroom. By my third year of teaching, I had observed patterns and become emboldened (no one had stopped me.) I had found that genetics was low hanging fruit for discussions about chromosomal differences that challenged traditional thoughts about the alignment between sex and gender and the gender binary of male and female in conditions such as Klinefelter’s (XXY) and Turner’s (XO) syndromes. But, my students were still surprising me with new opportunities for inclusion. My classroom was arranged in stations one particular late winter day. Organisms from across the animal kingdom were lying in dissection pans around my room: a hagfish, a leopard frog, a pike, a pigeon, a fetal pig, and, uninterestingly, I had presumed, an earthworm. The faint smell preserving solution pervaded the room. Students’ comparative anatomy observation charts littered the tables. A question rang out from a student reading the dissection guide at the earthworm station: “Hermaphrodite? Is that what transgender people are?” The students and I proceeded to discuss the difference between biological hermaphroditism in animals that are able to produce both sperm and egg; and in animals, like humans, that cannot because the tissues that either become testes or ovaries are the same. That fact about humans alone was captivating to many. We continued to discuss the cultural terms transgender and transsexual openly and respectfully. However, like so many things in the sciences, there are very rare exceptions. I later learned that true human hermaphroditism was documented in the case of an individual with a mosaic karyotype that consisted of three cell types and a translocated SRY gene sequence (Modan-Moses, Litmanovitch, Rienstein, Meyerovitch, Goldman, & AviramGoldring, 2003). Later that day, I took note in the slides that kept my teaching units structured to intentionally address this topic in the future. As had been the case in the past, my frankness and openness was well received by my students. I had the intuitive sense that what I was doing was right. I felt that I was earning the trust of my students regardless of their sexual orientation or gender identity. I intuitively felt that what I was doing would help my LGBT-identified students. Further, as a bisexual-identified queer person myself, I also felt



LGBT-Inclusion across the Life Science Curriculum 125

more whole as a teacher and person as I transformed the curriculum to make it inclusive of my own experience as a human being. WORKING DEFINITIONS LGBT-inclusive curriculum is used to describe teaching content and pedagogy that proactively, intentionally, and positively create spaces for LGBT people and topics. The term inclusive is drawn from special education, which has worked for decades to create opportunities for students of all abilities to participate fully in classroom learning environments. There are differences between a person’s biology and behaviors, identities, and labels relative to sexual orientation and gender identity. Biology and behaviors include what chromosomes or anatomy a person possesses and what they chose to do with their body. Identities are the complicated perceptions of self that a student develops as they experience the world socioculturally. Finally, labels are applied to people as members of oversimplified groups for the purposes of evaluation and research (see figure 6.1). There are correlations between identities and actual sexual behaviors, but they are not absolute. The specific sexual behaviors of a particular person are generally outside of the business of a classroom teacher. Labels are important for teachers to consider as they and others evaluate their own teaching to ensure that there is not an opportunity or learning gap between different groups of students. At this time, many life science teachers are provided with data that may guide their evaluation of such gaps vis-à-vis labels constructed around numerous student characteristics including gender, ethnicity, class,

Figure 6.1.  This figure clarifies the distinction between behaviors, identities, and labels.

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home language, qualification for special education services, and/or enrollment in free and reduced lunch services, but very few schools are presently collecting student demographic information related to sexual orientation and/ or gender identity. Thus, at this time, classroom teachers should largely be concerned about the gender and sexual orientation identities of their students in shaping their curriculum. Gender and sexual orientation identities may be fluid during an individual’s life. More complexly, at the same time, the same individual may take on one or some of these identities in one space and others in a different space. This speaks to the sociocultural nature of the identities; they are relative and individuals navigate them in complicated ways for a variety of reasons including safety, acceptance, and, sometimes, resistance. A wider net of identities may include gender queer, undecided, pansexual, pan fluid, fluid, heteroflexible, asexual, and intersex to name a few. As a classroom teacher, I did not seek to know the gender and sexual orientation identities of my students. When they did share such identities with me, I sought to ensure the privacy of that information. Sometimes a Q is added to LGBT, which may denote questioning or queer, depending on the particular nature of a study or program. Questioning is an increasingly recognized process that many people experience as they develop an awareness about their sexual orientation and/or gender identity. Some individuals prefer the term queer to broadly denote not necessarily straight while others who identify within LGBT may find the term queer offensive or pretentious. I personally prefer LGBTQ+, the Q here for queer, to make space for this complexity. However, this combination is infrequently used in education research or school contexts and thus I will use LGBT. As I refer to research and scholarly work conducted by others, I will clarify the subject of their work as LGBT; LGBT and queer; and LGBT and questioning. CONNECTION TO MULTICULTURAL EDUCATION/ MULTICULTURAL CURRICULUM TRANSFORMATION The curriculum transformation described in this chapter aligns with Banks (2004) framework of multicultural education including the five elements of content integration, knowledge construction process, prejudice reduction, equity pedagogy, and empowering school culture and social structure. The pursuit of this transformation goes beyond exposing students to LGBTidentified people or topics. The hope for this transformation is that students and whole school communities will be more respectful, safer, and enjoyable environments that are conducive to learning. My own curriculum transformation in the classroom began around the relationships I developed with my students as I answered their questions about



LGBT-Inclusion across the Life Science Curriculum 127

gender and sexual diversity. That prompted adjustments to the language I used, my classroom management techniques, and, as my confidence grew, the content that I planned. Clark (2002) encourages that teachers should “take into account their personalities, their discipline, their specializations within their disciplines, and the information they glean from curriculum transformation research in determining a unique course for their curriculum transformation undertaking” (p. 45). LGBT-INCLUSIVE CURRICULUM TRANSFORMATION: THE PRACTICE Standards are pervasive in the present era of education at the national, state, and local level. Usually, standards set the minimum of what must be taught. Rarely do they set bounds regarding what may not be taught. It has been argued that extensive lists of standards leave little room for adding more, but I found that curriculum transformation was not a simple additive process. As one life science teacher said, “I could do this [LGBT-inclusion] anywhere.” Indeed, there are opportunities throughout the traditional life science curriculum for LGBT inclusion. Though scientists speak of averages, almost every characteristic of living organisms exists along a continuum. There are always deviations and outliers. It is that diversity which is the site of potential for evolution by natural selection. Life is, truly, a queer (resisting normal) thing full of complexities and exceptionalities such as male pregnancy in seahorses (Wilson, Ahnesjo, Vincent, & Meyer, 2003), human mothers who are not the genetic parents of their own embryonically conceived and live-birthed children (Noble, 2014), and overlooked same-sex pairs of nesting albatross (Young, Zaun, & VanderWerf, 2008). The particular curricular opportunities life science teachers have to create LGBT-inclusive curriculum are plentiful. The full transformation requires revising both what is taught in life science courses—the content, as well as how it is taught—the pedagogy. This combination of inclusive content combined with inclusive pedagogy is necessary to create a whole LGBT-inclusive life science curriculum, but this transformation does not have to happen all at once (Clark, 2002). The following includes ideas for life science teachers as they pursue LGBT-inclusive life science curricular transformation. Pitfalls to Consider My experiences as a teacher educator suggest that life science teachers may be hesitant to engage in any diversity topic because they worry about saying the wrong things and offending the very students they are hoping to help.

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The best way for a life science teacher to gain confidence in avoiding the general pitfalls and biases related to addressing LGBT topics is to attend a workshop or participate in a similar program designed to increase awareness and respect for LGBT people. Many college campuses and, increasingly, school districts offer these programs through their offices of student diversity. While these courses provide an immersion into the language and sensitivities of many LGBT-identified people including the need for privacy, as a teacher it remains important to be responsive to the reactions of the students in the classroom. A frank check-in with students should a surprising response occur is likely to assist in the development of inclusive language and simultaneously build trust with students. Further, nonheterosexual or non-gender-conforming identities ought to be discussed as naturally occurring differences and never as pathologized abnormalities (Mohr, 2008). For life science teachers, this suggestion is especially relevant as biology textbooks often speak of chromosomal abnormalities rather than differences. This change in a life science teachers’ language will benefit students whose lives are touched by chromosomal differences including intersex conditions. For example, trisomy-21 and Klinefelter’s syndrome should not be addressed in unique ways, as there ought to be nothing more or less embarrassing about a trisomy of the sex chromosomes than of any other chromosomes. These syndromes ought to be addressed with sensitivity on the teacher’s part with the teacher demanding respectful language from their students. Oversimplification should be avoided. Just as trisomy-21 impacts individuals differently, intersex conditions also impact individuals differently. Students may respond to learning about chromosomal sex differences with statements such as “does that relate to being gay?” A short answer I utilized was “no more than being human relates to being gay.” Similar reactions may be anticipated when discussing earthworms. For instance, when students encounter the term hermaphrodite, which refers to organisms with both male and female sex organs, they may ask if transgender people are hermaphrodites. This is an outright misconception. It is important that science teachers are ready to lead their students in learning activities that will help them differentiate between sociocultural (e.g., transgender) and scientific (e.g., hermaphrodite) words. Discussions of human developmental biology may help students understand the process by which humans develop ovaries, testes, or, in very rare cases, both (see the case described in ModanMoses, et al., 2003). Classroom Leadership and Management Life science teachers, like all other teachers, must develop strategies that address bullying language and specific harassment of LGBT students. Some



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attention has now been given to students’ use of the term gay in a derogatory manner (Meyer, 2011) prompting responses such as GLSEN’s ThinkB4YouSpeak campaign. Life science teachers’ inclusion of LGBT students ought to go beyond simply responding to students’ negative comments to proactively reframing classroom spaces through LGBT-inclusive curriculum. Student group assignments are another classroom management topic that science teachers should consider transforming. For instance, group assignments based solely on gender present several barriers to LGBT-inclusiveness. One problem with sorting students in this manner is that it reinforces the sociocultural gender binary. Additionally, sorting students in this manner forces them to identify their gender to others (or have it identified by others) creating a potential cascade of outing non-gender-conforming students. Further, sorting students based on one biologically determined characteristic sets-up students to pit their traits vs. those of others. Male vs. female groups should be as unthinkable as groups based on other physical characteristics (e.g., black vs. white, short vs. tall, etc.). Science teachers should select more pedagogically meaningful group determinants based on student interests, classroom participation, and/or learner readiness. Life science teachers are likely to encounter unique curricular-related opportunities to set an inclusive and accepting tone to their classroom environment. For instance, some lab activities may produce opportunities for homophobic remarks such as those that model genetic inheritance requiring students to pretend to be male or female parents. Life science teachers may proactively address this potential for bias and reduce the display of prejudice that might occur as they provide their students with the instructions for an activity of this nature and be prepared to respond to bias if it is expressed. Similarly, the Latin prefix homo often generates snickers from students (e.g., homozygous) because of the homophobia-based discomfort with the term homosexual. A positive example I have seen a teacher candidate use is matter-of-factly clarifying for students that the prefix homo means same in this instance just as it does in the word homosexual. If students respond negatively, a direct discussion about acceptance and inclusion of LGBT people is warranted. Scientific and Engineering Practices The National Research Council (NRC) emphasizes student learning centered on scientific and engineering practices to develop students’ grasp of the breadth and flexibility of the work which scientists and engineers engage in with the hope that, the actual doing of science or engineering can pique students’ curiosity, capture their interest, and motivate their continued study

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(NRC 2012, p. 43). The Framework for Science and Education clarifies this intention: The focus here is on important practices, such as modeling, developing explanations, and engaging in critique and evaluation (argumentation), that have too often been underemphasized in the context of science education. In particular, we stress that critique is an essential element both for building new knowledge in general and for the learning of science in particular. Traditionally, K-12 science education has paid little attention to the role of critique in science. However, as all ideas in science are evaluated against alternative explanations and compared with evidence, acceptance of an explanation is ultimately an assessment of what data are reliable and relevant and a decision about which explanation is the most satisfactory. (NRC 2012, p. 44)

Life science teachers may lead their students in critical discourse around texts through the analysis of heteronormativity in the curriculum materials readily available in their classrooms. Critical analysis might focus on who is being left out of science and the impacts heteronormativity may have on scientific research. For instance, consider the Laysan albatross long studied by scientists who never realized that many of the nesting pairs were femalefemale as they sought other complicated theories to explain how birds who could not physiologically lay two eggs often sat upon nests with two eggs (Young, Zaun, & VanderWerf, 2008). In such cases, human bias stymied accurate scientific understanding. This pedagogical approach empowers students as it “places the students into the real world of science-in-the-making and teaches them to broaden their approach on analyzing controversial topics that require a scientifically literate populace to influence policy. Science as inquiry extends students’ views beyond the ‘what’ of science and transports them into science that is fallible, self- correcting, and progressive” (Snyder & Broadway, 2004, p. 632). Transformative Opportunities Across the Life Science Content Nature and history of science. The history of science is full of scientists whose personal lives have been erased or quietly disregarded due to their known or perceived sexual orientation or gender identity. For instance, Merkle (1997) recommended including more details about the personal life of Sir Francis Bacon who is often thought of as the father of modern scientific thinking. Other famous LGBT scientists and engineers include Alan Turing, Alexander von Humboldt, Rachel Carlson, Sally Ride, and Margaret Mead. The Equality Forum (2011) provides an extensive list of LGBT biographies as part of its LGBT history month, observed each October. Science teachers



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may engage students in thinking about how science and engineering may be impacted by the exclusion of people with certain characteristics. Animal diversity and behavior. There are numerous examples of same-sex mating behavior across many non-human animal species including African bat bugs, bonobo chimpanzees, bottlenose dolphins, common toads, garter snakes, and fruit flies (Bailey & Zuk, 2009). This calls into question the traditional assumption that mating or sexual behavior is just for reproduction as there is evidence that there are other selective pressures contributing to the evolution of same-sex sexual behavior. (Note, the terms lesbian, gay, bisexual, and transgender describe human identities or labels, not animal behaviors.) The book Gay, Straight, and the Reason Why: The Science of Sexual Orientation (LeVay, 2011) provides an overview of scientific theories explaining sexual orientation among humans including in utero exposure to varying levels of steroidal hormones, childhood experiences, genetics, and structural differences in the human brain. Critically, science teachers may be encouraged to address how science related to sexual and gender diversity is presented in the general media with their students. Heredity and genetics. Life science teachers may examine sex chromosome combinations and the traditional male/female binary related to the X and Y chromosome as their students learn to make a distinction between sex (e.g., male/female/intersex) as biologically determined, and gender (e.g., man/woman, boy/girl, gender queer) as socially constructed (Meyer, 2011). This leads readily to discussions about the role of environment in the phenotypic expression of genetic variations (Kumashiro, 2004). Such questioning could be extended to research about gender and sexual diversity in other cultures. For instance, students could learn about the two-spirit identity, those who have the spirit of both men or women, among some Native American people (Cameron, 2005). Additionally, life science teachers may lead class discussions about the persistence of the sexual binary despite the scientific complexity of chromosomal differences (e.g., XO, XXY, and XXX; Kumashiro, 2004). Similar consideration could be given to why genes carried on the X-chromosome are called sex-linked traits instead of X-chromosome-linked traits. Terms such as male-pattern baldness, which may affect women and intersex individuals are similarly problematic and could be discussed. Cellular and molecular biology. Spanier (1995) noted how scientists had labeled E. coli with plasmids male and those without them female. When learning about cells, the mitochondria—often thought of as the power plant of the cell—is often noted as being of maternal ancestry. Science teachers may lead students in discussions about what it really means for molecules to be maternal or sexed at all.

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Epidemiology. Another possibility is inquiry into the history of public health by studying the emergence of the AIDS epidemic and the role that wide-spread homophobia played in researching and responding to the disease (Britzman, 1995). Several books detail these events including Science Fictions by John Crewdson and And the Band Played On by Randy Shilts. For a more modern example, students could critically examine the persistence of a policy from 1983 that prevents men who have ever had sex with a man, since 1977, from donating blood even as the American Red Cross indicates the policy should be changed (Darling, 2013). Classroom discussion could focus on whether or not the policy is scientifically justified and what effect such policies have on LGBT-identified people and society at large. Endocrinology. Teachers may bring in whole texts or sections from medical books that discuss the role of estrogen and testosterone in the human body and compare those to how the same molecules are discussed in secondary life science textbooks. Nehm and Young (2008) completed a detailed analysis of commonly used secondary life science textbooks finding that they reinforce misconceptions about gender binaries that are not scientifically accurate. For instance, students could explore why their textbooks edit, reduce, and/or simplify the varied tasks these proteins perform in human bodies as compared to college and professional-level textbooks. They could then consider how the different representations contribute to scientific misconceptions of sex and gender and how those misconceptions might affect LGBT-identified people. Human reproduction. My experience as a life science teacher and my experiences as a science teacher educator indicate that students frequently bring questions related to sexually transmitted illnesses and human reproduction to biology teachers. These topics are included in most life science textbooks. While these topics are often addressed in health classes in more detail, life science teachers should be prepared to respond with medically and scientifically accurate information and/or should be comfortable referring students to additional resources in a nonjudgmental and supportive manner. Addressing LGBT-Inclusion and Religious Objections Life science teachers must be prepared for responding to religious diversity in their classrooms in order to teach many topics in biology that may raise objections from religiously fundamentalist students and their families. While students and parents have a right to express their views about same-sex relationships and marriages, teachers have a responsibility to ensure that all of their students are accepted in their classroom and promote student learning. I urge life science teachers to apply the same pedagogical thinking and strategies that they use to attend to religiously-based concerns about evolution by natural selection to situations related to LGBT-inclusion. My own experi-



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ences as an LGBT-inclusive science teacher and science teacher educator responding to religious-based objections have been overwhelmingly positive. I do not seek to change the perspectives of those who raise objections. I respectfully listen and consider the concerns of administrators, colleagues, families, and students, and respond by stating the reasons and evidence behind my pedagogical decisions. I often include the five arguments for LGBTinclusive curriculum presented earlier in this chapter: (a) it’s just and right, (b) improves LGBT students’ learning, (c) avoids legal repercussions, (d) improves my relationships in the classroom with all of my students, and (e) there are potential benefits for the whole school community. REFLECTION BRIDGE I entered my journey as an education researcher planning to address achievement gaps broadly. That intention was narrowed to focus on LGBT people and topics when I learned of the harsh school realities experienced by LGBTidentified youth in the United States. I felt simultaneous pain about the suicide rates and lost opportunities, anger that I had never known about them before, and relief that my efforts in the life science classroom had likely been of some benefit. I dove into the research more deeply, and learned that “at least twentyfive years of research document the pedagogical, social, and economic value of incorporating lesbian, gay, bisexual, transgender, and queer (LGBTQ) content into curriculum and policies and using sexual orientation and gender identity as frameworks to seek educational and social justice” (Quinn & Meiners, 2011, p. 135). Yet, the status quo of LGBT and queer exclusion in teacher education had likely persisted because “personal behavior weighed more heavily than personal professional competence in determining a teacher’s fitness to serve in a given community” (Quinn & Meiners, 2011, pp. 136–37). Kevin Jennings (1994) gave voice to the psychological and professional toll of this exclusion on LGBT and queer-identifying teachers in One Teacher in 10, including stories of depression, anxiety, and jobs lost. In the new edition of the book, he begins by noting a change, “On the whole, more LGBTQ teachers are able to be open and honest about their identities” (Jennings, 2005, p. xiv). He cites a surprising common reason and one that resonated with my own experience—the teachers’ students themselves seemed to be encouraging LGBT and queer teachers to do more. Despite hints of positive change in the voices Jennings captured, large quantitative studies indicate that LGBT and questioning students struggle as many experience hostility and violence regularly, which correlate to poor attendance, suicidal ideation, and limited plans for postsecondary education

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among others (Kosciw, Greytak, Bartkiewicz, Boesen, & Palmer, 2012; Robinson & Espelage, 2011; Robinson & Espelage 2012). Gay-straight alliances; school policies that explicitly protect LGBT-identified students; supportive educators; and LGBT-inclusive curricula have been found to correlate to improved outcomes for LGBT-identified students (Kosciw et al., 2012). Kosciw et al. (2012) found that just 1.6% of their sample of LGBT-identified secondary students had experienced LGBT-inclusion in science. There is little other research documenting the experiences or needs of LGBT-identified science students. LGBT-INCLUSIVE CURRICULUM TRANSFORMATION: THE THEORY The theory behind transforming the existing secondary life science curriculum begins by understanding that many teachers overlook the possibility that they may have a student who is other than straight in their classroom (Young & Middleton, 1999). Biegel (2010) suggests that “often without realizing it, public schools are sending youth LGBTs the message, at best, that something is wrong with them, or at worst, that they do not exist” (p. 136). This is heterosexism and may be regarded as the result of heteronormativity, the pervasive socioculturally constructed and systemic bias towards heterosexuality and cisgender people at the expense of nonheterosexual and/or gender nonconforming people (Meyer, 2011). For instance, the tendency of textbooks to note marriage in human family trees instead of matings or pairings, as is more typically represented for other animal species, is an example of heteronormativity because many LGBT people in the United States cannot be legally married to their partner and thus cannot be represented in this manner. Additionally, this is biased and unwelcoming to students who do not have married biological parents. In contrast to heterosexism, homophobia is regarded as the person-located thoughts or actions generated from individuals’ direct fear or hatred of homosexuality or people who are homosexual. Heterosexism is the individual’s bias towards heterosexuality. Thus, for instance, a teacher might make homophobic comments such as, gays have no place in school, or a heterosexist comment such as, the girls need to ask the guys out to the Sadie Hawkins dance. Socioculturally, homophobia and heterosexism may be thought of as the psychological, therefore individually embodied, manifestations of systemic heteronormativity. Many scholars have noted that homophobia and heterosexism are common in education (Pinar, 1998). Importantly, though, it is evident that the majority of LGBT students are successful in school (Robinson & Espelage, 2011). Gay, Lesbian and Straight



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Education Network’s (GLSEN) research suggests that supportive educators, gay-straight alliances (GSAs), comprehensive bullying/harassment policies and laws that explicitly indicate protections for sexual and gender diversity, and LGBT-inclusive curriculum are correlated with better outcomes and experiences for LGBT youth (Kosciw et. al, 2012). No single element from this list is likely to be enough to improve outcomes for the most severely impacted LGBT youth. Indeed, hostility and victimization do not explain all of the variation in LGBT and questioning students’ outcomes. Robinson and Espelage (2012) used multilevel covariate-adjusted models and propensityscore-matching models to compare LGBT and questioning students’ experiences to those of their peers and found that students who were LGBT and questioning were, “3.3 times as likely to think about suicide (p < .0001), 3.0 times as likely to attempt suicide (p < .007), and 1.4 times as likely to skip school (p = .047)” (p. 309). These findings emphasize the need for truly systemic transformation across educational and social contexts to ensure social justice for LGBT students. There are five clear arguments for life science teachers to make their curriculum LGBT-inclusive. First, all students ought to have the opportunity to experience a safe and nurturing learning environment free from harassment and discrimination that accepts and includes them in all of their courses. Thus, it is the just and right thing for life science teachers to be fully inclusive of all students (Meyer, 2011). Second, LGBT students are learners counted in schools and teachers’ classrooms like any other students. Educational outcomes including GPA and pursuance of higher education for some of these students are impacted by hostile school climates (Kosciw et al., 2012). In this era of high stakes testing and accountability, life science teachers are challenged to do everything they can to improve all students’ school outcomes. There is evidence that LGBT students who experience more LGBT-inclusive curriculum have better outcomes (Kosciw et al., 2012). Thus, establishing LGBT-inclusive curriculum may be regarded as necessary for science teachers to do their job effectively. Third, it is increasingly clear that school districts may face legal and financial repercussions should their teachers fail to provide safety, inclusivity, and adequate instruction for their LGBT students (Biegel, 2010). Thus, life science teachers must consider the possible financial and legal repercussions should they fail to provide for the safety and well-being of their LGBT-identifying students. Fourth, LGBT-inclusive practices may improve relationships and trust in the classroom benefiting students who do not identify as LGBT (Sears, 1997). This may be understood by widening the understanding of which students may be positively affected by LGBT-inclusive curriculum. While LGBT students are easily considered as benefiting from this curricular transformation, there are also students from LGBT families who would

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benefit. Additionally, and all of those students have friends who care for them. These associated students may find bias towards LGBT people unacceptable (see figure 6.2). In addition to the benefits for students who identify as LGBT or who are associated with LGBT-identified people, school communities consist of many more individuals whom are likely to benefit from LGBT-inclusive life science curriculum than students, including school employees (teachers, administrators, counselors, and other staff) some of whom identify as LGBT and, similarly to the case with students, many more who may see themselves as LGBT allies or have families that include LGBT-identified adults and children (see figure 6.3). While research about the influence of LGBT-inclusive curricula on LGBTidentified students is somewhat understood, there is almost no research about the influence of such curricula on school wide communities. Anecdotally, I can share that a colleague of mine, upon seeing an inclusive project I had planned for my life science students running off the copier, thanked me in a deeply emotional moment in which she shared her recent diagnosis with a rare form of an intersex condition, which had left her doubting and questioning her own gender identity and self-worth. She commented to me that she was grateful that my students were learning about these biological variations and discussing the more complicated social aspects of sexual and gender diversity, as she wondered out loud how her own present experience might have been altered had she participated in a similar learning experience while she was a student. Intuitively, I feel that there may be positive and quantifi-

Figure 6.2.  This figure suggests an expanded notion of how many students may be positively affected by LGBT curricular inclusion.



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Figure 6.3.  There are many people in school environments who may be positively affected by LGBT curricular inclusion in the life sciences.

able impacts on the whole school community, and perhaps for public health outcomes throughout society, which may arise from LGBT-inclusion in the life sciences, should research in this area be pursued and adequately funded in the next decade. In the meantime, I encourage life science teachers to transform their curriculum and experience its benefits for their students, their schools, and themselves. CONCLUSION As discussed throughout the chapter, the reasons to transform life sciences curriculum such that it is LGBT-inclusive abound. Not only will it help to make the classroom a more just and safe place for students, but as evidence

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suggests, it will likely improve students’ learning outcomes. Life itself is far more complicated and diverse with regard to sexual and gender diversity than the traditional high school curriculum has historically reflected. As life science teachers, LGBT-inclusive curriculum also brings our teaching closer to reflecting the true diversity of life. REFERENCES Bailey, N., & Zuk, M. (2009). Same-sex sexual behavior and evolution. Trends in Ecology & Evolution 24(8), 439–46. Banks, J. A. (2004). Multicultural education: Historical development, dimensions, and practices. In J. A. Banks & C. A. McGee Banks (Eds.), Handbook of research on multicultural education (second edition, pp. 3–29). San Francisco, CA: Jossey-Bass. Biegel, S. (2010). Creating change in the classroom: Curriculum, pedagogy, and LGBT content. The right to be out: Sexual orientation and gender identity in America’s public schools. Minneapolis: University of Minnesota Press. Britzman, D. (1995). Is there a queer pedagogy? Or stop reading straight. Educational Theory 45(2), 151–65. Cameron, M. (2005). Two-spirited Aboriginal people: Continuing cultural appropriation by non-Aboriginal society. Canadian Women Studies, 24(2–3), 123–27. Clark, C. (2002). Multicultural curriculum transformation across disciplines. Multicultural Perspectives, 4(3), 37–46. Darling, M. (2013, July 14). Banned for life: Why gay men still can’t donate blood. Men’s Health. Retrieved from http://www.msnbc.msn.com Equality Forum. (2011). LGBT history month. Retrieved from http://www.lgbthistorymonth.com/ Jennings, K. (1994). One teacher in ten: Gay and lesbian educators tell their stories. New York, NY: Alyson Books. Jennings, K. (2005). One teacher in ten: LGBT educators share their stories. New York, NY: Alyson Books. Kosciw, J. G., Greytak, E. A., Bartkiewicz, M. J., Boesen, M. J., & Palmer, N. A. (2012). The 2011 National School Climate Survey: The experiences of lesbian, gay, bisexual and transgender youth in our nation’s schools. New York, NY: Gay, Lesbian, Straight Educator Network (GLSEN). Kumashiro, K. (2004). Against common sense: Teaching and learning towards social justice. New York, NY: RoutledgeFalmer. LeVay, S. (2011). Gay, straight, and the reason why: The science of sexual orientation. New York, NY: Oxford University Press. Merkle, D. G. (1997). Inclusive science education: What does it look like? Confronting homophobia and providing equity for homosexuals in our science classrooms. Paper presented at the Annual Meeting of the Association for the Education of Teachers in Science, Cincinnati, OH. Meyer, E. J. (2011). Gender and sexual diversity in schools. New York, NY: Springer.



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Modan-Moses, D., Litmanovitch, T., Rienstein, S., Meyerovitch, J., Goldman, B., & Aviram-Goldring, A. (2003). True hermaphroditism with ambiguous genitalia due to a complicated mosaic karyotype: clinical features, cytogenetic findings, and literature review. American Journal of Medical Genetics 116A(3), 300–3. Mohr, J. M. (2008). Oppression by scientific method: The use of science to “other” sexual minorities. Journal of Hate Studies 7(1), 21–45. National Research Council (NRC). (2012). A framework for K-12 science education: Practices, crosscutting concepts, and core ideas. Washington, DC: The National Academies Press. Nehm, R., & Young R. (2008). “Sex hormones” in secondary school biology textbooks. Science and Education 17(8), 1175–90. Noble, G. K. (2014). Pregnancy no proof of motherhood; Woman was her own twin-and the twin was the mother of her children. Guardian Liberty Voice. Retrieved from http://guardianlv.com/2014/01/pregnancy-no-proof-ofmotherhood-woman-was-her-own-twin-and-the-twin-was-the-mother-of-herchildren/#Fsh3ZXO3W50hxQrm.99 Pinar, W. F. (1998). Introduction. In W. Pinar (Ed.), Queer theory in education. Mahwah, NJ: Lawrence Erlbaum Associates, Inc. Quinn, T., & Meiners, E. (2011). Teacher education, struggles for social justice, and the historic erasure of lesbian, gay, bisexual, transgender, and queer lives. In A. Bell and C. Tyson (Eds.), Studying diversity in teacher education. Lanham, MD: Rowman and Littlefield Publishing, Inc. Robinson, J. & Espelage, D. (2011). Inequities in educational and psychological outcomes between LGBTQ and straight students in middle and high school. Educational Researcher 40(7), 315–30. Robinson, J. & Espelage, D. (2012). Bullying explains only part of LGBTQheterosexual risk disparities: Implications for policy and practice. Educational Researcher 41(8), 309–19. Sears, J. T. (1997). Thinking critically/ intervening effectively about heterosexism and homophobia: A twenty-five year research retrospective. In J. T. Sears, & W. L. Williams (Eds.). Overcoming heterosexism and homophobia: Strategies that work (pp. 13–48). New York, NY: Columbia University Press. Snyder, V., & Broadway, F. (2004). Queering high school biology textbooks. Journal of Research in Science Teaching, 41(6), 617–36. Spanier, B. (1995). Impartial science: Gender ideology in molecular biology. Bloomington: Indiana University Press. Wilson, A. B., Ahnesjo, I., Vincent, A. C., & Meyer, A. (2003). The dynamics of male brooding, mating patterns, and sex roles in pipefishes and seahorses (family Syngnathidae). Evolution, 57(6), 1374–86. Young, A. J., & Middleton, M. J. (1999). “It never occurred to me that I might have a gay student in my K-12 classroom:” An investigation of the treatment of sexual orientation issues in teacher education programming. Paper presented at the Annual Meeting of the American Educational Research Association Montreal, Quebec, Canada. Young, L. C., Zaun, B. J., & VanderWerf, E. A. (2008). Successful same-sex pairing in Laysan albatross. Biology Letters 4(4), 323–25.

Chapter Seven

Earth Shaking Dragons and Orphan Tsunamis Transforming Middle School Earth Science and STEM through Studying Ancient Science Inquiry and Multicultural Collaborations in Earthquakes, Tsunamis, and Disaster Preparedness Marna Hauk and Adam Masaki Joy INTRODUCTION This chapter explores the content areas of earth science and geophysics (early detection of earthquakes) and physical sciences (inertia) for grades 6–8. Furthermore, this chapter offers two examples of how multicultural STEM education can transform learning by integrating storytelling, inductive reasoning, and hands-on collaborative science learning in a multicultural context, and by extending science learning into community emergency response planning and disaster resilience. Multicultural education researchers and practitioners have developed approaches for transformation and empowerment that can be extended into approaches for multicultural science, technology, engineering, and math (STEM) education. At its best, multicultural STEM learning does more than highlight cultural heroes or tack a lesson plan onto the existing frameworks of science. Multicultural STEM education has the ability to regenerate science inquiry into more inter- and transdisciplinary, systemic, creative, connective, holistic, and experiential approaches. These approaches, including storytelling, engage deep learning, expand learners’ worldviews, and transform their engagement with their colleagues and the planetary systems. This chapter offers a different approach that STEM educators can take to teaching about earthquakes via two storylines and activity streams. First, how First Nations storykeepers, geologists, and Japanese scientists collaborated to piece together historical geologies, and then how a Han dynasty Chinese scholar invented the world’s first seismograph. From these appealing inquiries, 141

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students can engage with community emergency preparedness and disaster resilience. The chapter concludes with the theoretical underpinnings of this approach, and how it can be extended for different learners and technologies, as well as how it is relevant for civic engagement and family and community contexts. This chapter hopes to illustrate the promise of how deeply transformational, experientially immersive, cross-disciplinary, rigorous, and insightful multicultural STEM can be. STORY OF SUCCESS In 2010, Discovery Middle School was designated as an Adequate Yearly Progress (AYP) Tier 1 school, one that was supposedly “failing” its students. Its state standardized test scores were among the lowest in the district and state, the science scores abysmal. The administration and faculty knew we had a great, dedicated staff, but according to the data, something was amiss and we were threatened with state intervention. The district mandated change, and so Discovery began its school improvement plan (SIP). Administration and staff looked at what we were doing right and what challenges we faced. We looked at our demographics and observed some of the lowest scores came from students on free and reduced lunches, students of color, and our English language learners (ELL). We reflected much and knew we had the resources to reach all our students. One plan of action included our own ELL teachers leading workshops. They reminded us that as teachers and facilitators of learning, relationships and relevance were imperative if we were to be effective. The ELL instructors encouraged the staff, among other suggestions, to show our students in ELL and students of color that they and their culture were assets to our success in school learning by infusing multicultural perspectives in our practices. Implementing multicultural and inclusion strategies, the staff improved our personal relationships with all of our students. Our intent was for students to see that their voices, and that of their culture, were important, and that we valued them. Furthermore, our curriculum started to become meaningful as students found relevance. Our students saw how learning and advancement were a collective effort, embarked upon by all of us without homogenizing unique and different perspectives. Staff and faculty affirmed that students from non-Western cultures were a key part of this collective effort. School stopped being the place where we learned of just Eurocentric values, and instead Discovery came to represent a shared endeavor of learning. By 2012, Discovery became an exemplar in the district. Our standardized state language and math scores jumped 15%–20%. Science though left all in awe as



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our scores rocketed up 31%. We ranked near the top or at the top across the district. One reason science led the way was because earth science studies naturally lent itself to multicultural STEM instruction. Starting in 2010–2011, coauthor Joy changed to teaching only science at Discovery Middle School. He began teaching more than 70% of all incoming students. As a multicultural education faculty of color, he was committed to proactively teaching integrated multicultural STEM not as an add-on but deeply embedded within a transformative STEM curriculum. This chapter features two example study lessons from this multicultural STEM initiative. The sociocultural context of learning planetary geological dynamics combined with student and community resilience empowerment honoring multiple voices and cultures was a part of the culture change leading to better standardized test scores at Discovery Middle School. CONCRETE EXAMPLE OF MULTICULTURAL CURRICULUM TRANSFORMATION IN MATH EDUCATION: THE ORPHAN TSUNAMI OF 1700 The most common approach to teaching earth science involves describing Earth’s layers, plate tectonic theory, and then earthquakes. This common method is like telling a great story while giving away the punch line at the beginning. It mostly disregards the diverse body of discovery and knowledge that led to these great ideas. The goal of learning through the lens of multicultural and geographical perspectives is to engage the student in the relevance and the process of the science learning. The story of relevant Earth studies can begin with the question, “Why are there blue tsunami warning signs along the beaches of Washington, Oregon, and Northern California? In particular Long Beach, Washington, the nearest resort town to Vancouver?” In fact, some students might have participated in local drills held regularly by well-visited coastal communities. This line of questioning leads to a discussion of how this pending catastrophic disaster was revealed, and the story of the Orphan Tsunami of 1700 (Atwater, 2005). Students role-play scientists of different fields and historians who had multiple mysteries and shed light on an unknown potential catastrophic disaster in the Pacific Northwest. The students represent the geobiologists who investigate the strange deposition layers of sand and diatoms, or the biologists who try to unravel the mystery of dead spruce groves along the same coastal stretch, or the Pacific Northwest Native American anthropologists documenting oral stories of a great disaster many generations ago in the

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region, or the Japanese historians telling of an “orphan tsunami” that struck the coastal lands of Japan without the usual warning of an earthquake. As these role-playing investigators begin communicating their conundrums to each other, the mystery begins to clarify the seismic and geological situation: to tell of periodic, catastrophic earthquakes and tsunamis along the Pacific Northwest—occurring every 300–800 years, the last of which occurred 300 years ago. This learning can be reinforced, showing animated visualizations of the geoscientific dynamics of this historical tsunami, including how the exact date and time of the tsunami can be determined because of the speed of tsunami waves traveling over the ocean (IRIS, 2014). DETECTING EARTHQUAKES THAT CAUSE TSUNAMIS Our discovery of periodic tsunamis leads to the query, what are earthquakes and why do they happen? Here, students begin their investigation by studying how scientists need to gather data and how earthquake data has been collected throughout history. For example, students examine the first seismographs designed by the Chinese. This lesson touches on the scientific journey of Zhang Heng considered one of the eight most brilliant scientists of all time (Graham, 2010; Howell, 2003), acknowledged even in Eurocentric historical scientist resources (Balchin, 2003). Students design seismographs and explore how they detect earthquakes. Zhang Heng’s approach could detect directionality based on poised marbles falling into one of four axes of directionality (see figure 7.1). Studying actual seismograms, students see patterns that infer multiple types of earthquake waves that help determine location of earthquakes. Students then use these patterns and triangulation (compass constructions) to actually determine earthquake origination. The location patterns of earthquakes lead to the unveiling of great fractures in the Earth and the culminating plate tectonic theory. These patterns also reveal the hidden inner layers of the Earth. Curriculum and Activities Related to Emergency Preparedness for Earthquakes and Tsunamis (See also Appendix C) Students can research and present at several scales about how earthquake and tsunami science connects with disaster preparedness and resilience. Understanding the relevance of the threat that earthquakes pose, students research and present what they and their communities can do to prepare for catastrophic earthquakes. Students research and present the liquefaction threat using geological surveys. Students research and present community mitigation plans for earthquake/tsunami, including disaster resilience strategies. They



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Figure 7.1.   Zhang Heng’s seismograph. Wikimedia Commons, 2004

also research and present how homes can prepare for earthquakes/tsunamis. Finally, students research and present how, individually, they can prepare for an earthquake/tsunami. REFLECTION BRIDGE Sample curricula discussed in this chapter include collaborative multicultural tsunami science inquiry and the re-creation of an early Chinese seismograph,

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along with their community learning and disaster resilience planning correspondents. Such curricula offer dynamic, experiential, cross-cultural, and narrative engagements with transformative multicultural STEM learning. These unique types of curricular engagements provide bridges for border crossings for students for whom Western science is itself a new culture (Aikenhead, 2001). The approaches also embody how science actually represents a plurality of epistemologies (Kawagley, Norris-Tull, & Norris-Tull, 1998) while acknowledging scientists positioned from multiple cultures within their inquiry processes. Mercer (2011) calls for a glocalized science education approach which “aims to synthesize the global (in all of its diversity of contexts) from a specific local perspective primarily for the purpose of local, not global, understanding” (pp. 300–1). Carter (2011) confirms that moving beyond Eurocentric assumptions of universalism and homogenizing normalization of Western science cultures is vital to critical multicultural STEM pedagogy (p. 317). These kinds of curricular approaches in one middle school in Vancouver, Washington, embedded inside of a larger school initiative around multicultural engagement, culturally responsive curriculum, and relationship building, did see a significant rise in test scores. These approaches are compatible with rigor in science teaching and suggest community engagement and multiple applications in and beyond the STEM classroom. THE CRITICAL CONSIDERATIONS IN STEM MULTICULTURAL CURRICULUM TRANSFORMATION STANDARDS AND RIGOR IN STEM LEARNING FOR MULTICULTURAL STEM These lesson approaches satisfy rigor in science, technology, engineering, and math learning. The Next Generation Science Standards (2013) provide one view of rigor in STEM. See table 7.1 for comparisons of how the curriculum we are describing, for example, aligns with generalized science standards. In brief, studying historically complex geologic instability in the field elucidates the interconnected nature of science and its real-world applications. Creating contexts in which students use models to collect earthquake data, predict earthquake epicenters, and represent and describe plate tectonics and inner-Earth layers satisfies student performance expectations which can further build coherently from earth dynamics into inertia, thermodynamics, and wave theory. This type of deepening of science learning in both content and method, such as students looking at how evidence supports the theory of plate tectonics and how layers of the Earth were determined, allows advanced



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theorizing and hypothesis building and testing. Furthermore, the curriculum that involves studying how seismographs detect and determine location of earthquakes allows an integration of science and engineering learning. This helps students prepare for college and career. Further, the applications into community emergency preparedness contained in this unit involve civic engagement. Finally, we would suggest that meeting the learning needs of all students involves both, moving towards social action transformation (see section below), and including embodied, experiential, and immersive approaches that deeply engage learners. The multicultural elements, which include multimodal approaches such as narrative-history-science-collaboration elements, expand and connect learners’ capacities in a transdisciplinary fashion, and help prepare students for the needs of planetary citizenship, or what Sterling (2009) calls an ecologically connective consciousness. .

Table 7.1.   Relationship of science standards and suggested curricular approaches Sample standards (Adapted from Next Generation Science Standards, 2013) Interconnected nature of science as experienced and practiced in the real world Standards are student performance expectations

Science standards build coherently

Focus more on deeper understanding of content as well as application of content Integrate science and engineering Designed to prepare students for college, career, and citizenship Alignment across standards (including Common Core)

Application related to suggested curricula How the Pacific Northwest has a history of geological instability and will experience that in the future Students use models to collect earthquake data, to predict earthquake epicenters, to represent and describe plate tectonics and inner-Earth layers Students create a more sophisticated understanding of dynamic Earth, leading to even more in-depth exploration of topics such as inertia, thermodynamics, and wave theory Look at how evidence support theory of plate tectonics and how layers of the Earth were determined How seismographs detect and determine location of earthquakes Students research, find patterns, infer, apply technology to answer questions and solve problems Students are required to read and interpret higher-level scientific resources

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Educational Context Adam Joy (one of the authors) teaches in a multicultural school in suburban Portland metropolitan area in Vancouver, Washington. Seventy-six percent of students are on the free and reduced program; the student body is 45% non-white, including over 31% Latina/Latino student populations. This curriculum can be adapted to specific teaching and learning settings. For example, in community learning contexts, the disaster preparedness portion can fit well with a community participatory action research approach to setting up emergency preparedness, with potential connections to public health, neighborhood watch, and neighborhood organizing. Cities with transition movements are particularly well positioned for this kind of connective learning. Coastal communities might also find this material relevant. It can be adapted for other ecosystems and geological dangers such as fault lines, hurricanes, tornados, and flooding zones. The themes of community preparedness can connect this approach to integrated learning with climate change resilience curriculum (Kagawa, 2009). Relationships with and Among Students and Their Families The content builds relationships with and among students and their families both in the project-based learning and community approaches that are emphasized. In particular, curricular extensions proposed in the sections “Designing Earthquake-Resistant Building,” and “Colliding, Sliding, and Separating Plates” of the Catastrophic Events book include having students engage with their families to prepare an emergency plan (National Science Resources Center [NSRC], 2006). Students complete an evaluation form with their families checking how earthquake-resistant their home might be (NSRC, 2006). Checks may include how secure internal fixtures in their homes, such as bookshelves, televisions, hot water heaters, and external concerns, such as brick chimneys, large windows, power lines, and large trees. More in-depth examination may include soil type, how the home roof is anchored, or whether foundations have earthquake mitigation. The discussion should lead to how families may improve their home to be more earthquake-resistant and contingency plans in case of an earthquake. Civic Engagement These approaches increase civic engagement in two ways. First, they relate to sending help to people in a crisis and the detection of earthquakes. Second, they relate to community emergency preparedness planning, with potential



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relation to transition towns and emergency preparedness planning at larger scales. Kagawa (2009) emphasizes that multicultural education, inclusive of and valuing cultural diversity, can support building “disaster resilient communities . . . characterized by mutual trust, respect for cultural diversity (including indigenous knowledge), and active community participation and self-reliance . . . address[ing] underlying vulnerabilities comprehensively” (p. 114). One of the authors is part of an emergency response team, the triage team and this topic touches on how schools are being asked to triage for the community in emergency situations. A further topical extension is how science can serve the public interest and how inventions can be put to service for the good of the community. This brings in ethical dimensions into this multicultural education approach. Another way that these units relate to civic engagement is to model how groups of information-sharing and collaborative scientists can develop technologies and how they undertake multifaceted research in order to help keep communities safer. Additional Considerations Gifted student extensions. Potential extensions for talented and gifted (TAG) students include units on using the compass to triangulate epicenters, and more difficult math to figure out how far away the earthquake happened, the speed of the earthquake waves, and their differential speed—using those three places. Additional directions for curricular extensions include working in teams to build the tipping dragon Chinese seismographs (see appendix B, section 6, “Experiment: Building a Pendulum for Detecting Earthquakes”), as well as field trips to walk in the muck and see the soil layer inversions. Student teams could discuss what these mean in terms of seismographic history on a geological scale, with extensions into local history to imagine what differently sized seismological events might have meant for denizens of the time. Additionally, students could study the inventions of Zhang Heng to learn about inter- and transdisciplinary inquiry, similar to Leonardo daVinci and other great thinkers. Suggestions for curricular integration. Another additional possibility would be to integrate learning approaches, including to social studies/city planning/emergency preparedness, history, as well as literature. Further curriculum connections could extend to oral history traditions in social studies and literature, which could include having students write stories situating them as if back in the 1700s during the tsunami.

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Content Linked to Pedagogy and Assessment Critical theorizing about multicultural education gives us the opportunity to offer frameworks for depth, rather than surface, multicultural approaches that are relevant for multicultural STEM education. Approaches including curricular transformation and reframing, social action, indigenous ecological knowledge models, developmental phasing, cultural commons, and group creativity, all contribute to culturally responsive curricular development. For example, Vold, Ramsey, and Williams (2003) describe Banks’s (1999) four-level framework for multicultural curricular transformation approaches. The approaches range from Level 1, the Contributions Approach, which focuses on holidays, heroes, and particular events, to Level 2, the Additive Approach which would, for example, append multicultural STEM onto current STEM structures without actually changing core structural approaches to science, technology, engineering, and math education. Transformation of curriculum and multicultural STEM. Banks’s (1999) Level 3, the Transformational Approach, actually involves allowing the multiple perspectives of multicultural education to restructure core knowledge conceptions and approaches. The example Vold et al. (2003) offer is the connection between historical slavery and the general concept of the process of enslavement. Cajete’s (2000) articulations regarding the process of Native science exemplify this transformative, deep, restructuring in both framing and process: “The perspective of Native science goes beyond objective measurement, honoring the primacy of direct experience, interconnectedness, relationship, holism, quality, and value” (p. 66). Cajete goes on to argue against disciplinary divisions: “Science cannot divide its applications into departments; it is integrated into the whole of life and being and provides a basic schema and basis for action” (p. 66). Social action approaches to multicultural STEM. Cajete’s (2000) insights, in fact, extend into Banks’s Level 4 approach to multicultural education, namely the Social Action Approach, in which students are empowered to take action themselves on real-world situations. Certainly, many different forms of multicultural STEM traditions involve more holistic approaches including storytelling, inductive reasoning, and hands-on collaborative science. The potential group collaboration practices, even for western scientists as described in Sawyer (2007), can be extended into group collaboration processes as demonstrated by the cross-cultural synergies of the orphan tsunami discoveries, resulting in what Sawyer (2007, 2010) terms group genius and collaborative emergence. Ample resources exist to shed multicultural perspectives that move away from the idealization of a solo scientist as a “lone genius” (Montuori & Purser, 1995; Richards, 2007) and toward community, group, tribal, and cultural approaches (Cajete, 1999), emotionally and socially intelligent



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Table 7.2.   Correlations between Multicultural Transformation Approaches and Suggested Curricular Ideas in this Article Curricular idea Learning about seismic events through multicultural insight, storytelling, and the geologic record, integrated in such a way that it refigures how we understand earth events Studying Zhang Heng as a scientific innovator Reading this chapter and tacking this unit onto the existing curriculum Students researching for multicultural evidence and storytelling regarding other major seismic or geologic events Students getting involved in emergency response planning for their community, including accessibility for students and families from different backgrounds and privilege

Multicultural Transformation Approach (From Banks, 1999) Social Transformation Approach (Level 3)

Contributions Approach (Level 1) Additive Approach (Level 2) Social Action Approach (Level 4)

Social Action Approach (Level 4)

ecoliteracy (Goleman, Bennett & Barlow, 2012), and the ecological intelligence of the commons (Bowers, 2006). Maturing the developmental phases of multicultural education. We would suggest a corollary to Level 4, Social Action Approaches in multicultural education. Our suggestion will have particular relevance for refiguring STEM, bringing into question the idea of curriculum design that is handed across to teachers, and instead moving into models that empower teachers and learners to adapt and invent culturally relevant and culturally responsive offerings leveraging the cultural strengths, continuities, and relevancies in the local student and cultural population. This would be in alignment with what Vold et al. (2003) discuss as the more mature developmental phases of multicultural education. This approach allows the teachers to move from being technicians to being co-constructors, and allows multicultural STEM to move from approaches that are tokenizing and additive to allowing multicultural STEM to refigure and galvanize across the curriculum. Some of these curiosities and suggestions are in accord with pedagogical approaches such as sociocultural approaches to science education (Lemke, 2001). Limitations. These theories shed light on some potential limitations of our proposed curricular ideas in this chapter. For example, is Zhang Heng being upheld as a lone genius and Level 1 multicultural/science hero? Does the

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idea of providing any curriculum contribute to and reaffirm the idea of the teacher as technician, rather than promoting culturally responsive curricular innovation? Table 7.2 offers some insights into how the ideas discussed in this chapter align with multicultural maturity models, and offers some caveats and suggestions. Another potential limitation of our proposed curricular ideas in this chapter is that, from the point of view of relevance and cultural responsiveness, these particular lesson ideas are most likely relevant for Pacific coastal communities or areas with earthquake danger. By extension, however, ideas from this chapter could spark emergency preparedness and disaster resilience integrated across the curricula for many communities. Additionally, as the unfortunate practice of petroleum fracking becomes more pervasive, and climate change continues to accelerate destabilization of core earth systems, earthquake education and emergency preparedness become ever more relevant. Evaluation. Assessment particulars might include evaluating effectiveness of group collaborative learning (Sawyer, 2007; 2010), evaluation of test trials with student-built seismographs, and evaluation of accuracy of triangulation math. Integrated Use of Technology Technology can be integrated into earthquake detection, including the use of the older seismographs. There are websites that will plot earthquakes and the student-researchers can look at patterns across the earth, revealing fault lines and plate boundaries (see earlier section on earthquake detection, including www.iris.edu). This type of cross-correlation can help students understand that the long-standing keeping of manual records has now been extended through technological modeling. Recording locations of earthquakes helps develop these long-term models. SUMMARY Multicultural STEM approaches, such as teaching about earthquakes and tsunamis through earth shaking dragons and orphan tsunamis, demonstrate that scientific rigor can be deeply engaging. Furthermore, it can model and catalyze collegial creative collaboration, storytelling, civic engagement, and social relevance. Multicultural STEM has the potential to move beyond heroes, holidays, and lesson plan add-ons, toward deeply transformative and socially engaging curricular approaches that reveal the dynamic and integrated connectedness and wholeness of vibrant planetary processes through cultur-



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ally responsive science inquiry. During this time of great need for insight and committed collaborative engagement for the thriving of planetary systems, multicultural STEM can help catalyze middle school science learners to “social learning for a connective consciousness” (Sterling, 2009) to foster the next generation of integrated earth inquiry. APPENDIX A Unit Plan Sample 1: Orphan Tsunami Unit Question: Why are there blue tsunami evacuation signs along the Oregon-Washington-California coastline? Material for this lesson plan are drawn from Atwater (2005); IRIS (2014; 2015a, 2015b); Oregon Department of Geology and Mineral Industries (n.d.a, n.d.b); UNAVCO (2014a, 2014b). A. Introduction. There has been no major historical earthquake or tsunami since Europeans first started to explore and migrate to the Pacific Northwest in the 1780s. B. Relating it to students’ experiences. Students are asked if they have traveled to beaches and observed “blue tsunami evacuation signs” (show pictures, as in UNAVCO, 2014b). Some students may have been present for coastal community tsunami drills. C. Three mysteries and a cultural legacy. The goal is to understand the patterns from different sources and traditions. The science learning goal is to find evidence that there have been historical “great” earthquakes strong enough along the Pacific Northwest coast to cause land deformation and catastrophic tsunamis. Students break into small groups to read four separate mysteries/ sources (there can be multiple groups that share their mysteries). Students are asked to read and examine the information provided for each mystery and find a reasonable explanation. 1.  Group 1: Groves of ghost spruce along the Pacific coastline. Groves of dead spruce trees are found right next to healthy trees. The difference: waters. Students look at the tree ring (dendrochronology) to date the event. 2.  Group 2: Strange deposition patterns along the Oregon, Washington, and California coastlines. Students examine pictures of soil layers showing sand on top of organic material, soil, and mud. The images also show fire pits under the sand layer, which is under a mud layer.

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Usually organic material (plants) can be found growing on soil on top of sand layers along coast. This layering is found along the Oregon, Washington, and California coastline. Carbon dating from organic material and fire pits point to an event around 1700. 3.  Group 3: Orphan tsunami strike in Japan in 1700. Students read about an “orphan” tsunami that struck Japan around January 27–28, 1700, wrecking death and destruction. Why this was considered an “orphan” tsunami was because Japanese noted earthquakes occur prior to tsunamis and there were no recorded earthquakes associated with this tsunami. The question of this mystery was where did this earthquake happen that caused this 1700 tsunami? 4.  Group 4: Native American oral accounts of the tsunamis. Students read about Makah traditions regarding going to high ground after an earthquake, as well as reports of Makah oral accounts of the waters receding for four days and then rising again without wave or breakers submerging the land around. The water surge took many lives. It took four more days for the water to return to normal. Students also read other accounts including the Hoh and the Quilleute stories of the Thunderbird and the Whale (SODGMIa, SODGMIb). D. Scientific exchange. After coming to their conclusions, students simulate being scientists who share their findings and suppositions. Each group breaks up and separates. Within each group, students adopt different roles. One is an “expert” of their topic and is stationary as other members of their team go to the other groups and collect information in regards to their “mysteries.” Afterwards, group members recollect and discuss the information and reassess their suppositions. Through collaborative discussion, student-scientists piece together the patterns of Japanese earthquake genesis and West Coast landfall of the tsunamis. E. Supplemental information. First Nations peoples had oral history of the 1700 tsunami that was conveyed in the James Swan’s diary entry in 1864 (Atwater, 2005). More information on the oral accounts is also available at (Oregon Department of Geology and Mineral Industries, n.d., a). Also, going more deeply into coastal depositions indicates cyclical patterns of repeated great earthquakes and tsunamis evidence every 300–800 years. The last one occurred just over 300 years ago (Atwater, 2005). F.  What are tsunamis and their effects? What caused the tsunamis along Oregon, Washington, and California coastlines? Once students have established that there are paired earthquakes-tsunamis, they start to learn about their causes. 1.  Students read articles (textbook or United States Geological Survey (USGS) Internet articles) and watch videos (YouTube or video) regarding tsunamis.



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2.  Students access Internet resources on the 2004 Indonesian and 2012 Japanese tsunamis. Scientific factors to consider: speeds over the open ocean versus speed in shallow coastal areas; height over the deep ocean versus shallow coastal waters; indicators prior to tsunami appearance; threats of incoming and outgoing waves; wavelengths and number of waves. 3.  Students explore causes of earthquakes, landslides, volcanoes, or meteorites based on extent of effect, earthquake must be source of tsunamis along Oregon, Washington, and California coastlines. G. If earthquake caused this tsunami, what causes earthquakes? Why along the Oregon, Washington, and California coastline? Goal: introduction to plate tectonic theory H. Patterns of seismic activity: Where do earthquakes happen? How are they detected? 1.  Historical investigations. Chinese seismograph. Students read and discuss how it worked (Note: Chinese seismograph works because they knew earthquakes were directional! Students should discuss how this was determined). See appendix B for more details. 2.  Seismographs. Students can explore how seismographs work by setting up a seismograph (Carolina’s Catastrophic Events science kits or create own using designs available on Internet). Compare the differences and similarities of their own and the Chinese design. 3.  Seismograms. Read seismograms for patterns (S- and P-waves). Students examine real seismographs from University of Portland seismographs (IRIS, 2015b). Students should observe there is an initial earthquake detection and a secondary spike(s), indicating two types of waves. 4.  S- and P-waves. Students study the differences and similarities. Key concept used is that these waves travel at different rates (P-waves travel faster than S-waves). Teachers can avail themselves of IRIS (2015a) for videos. 5.  Properties of earthquakes. Determine distance from earthquake epicenter using S- and P-waves. Students role-play S- and P-waves in class. Two students “race” over a three-meter distance. One takes one step for an interval while the other student takes two steps. Students measure the time difference between the two “S- and P-waves.” Repeat the race, now over six meters, nine meters. Students analyze the data to see a connection between time difference and distance. Key idea: the farther the finish line from the start the time difference between the S- and P-waves becomes larger. This time difference indicates the distance a seismograph is from the epicenter—not the location.

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6.  Triangulation and locating epicenter. Class explores using triangulation in determining earthquake epicenter (IRIS, 2015a). Students can use triangulation to determine the epicenter of an earthquake (web source). Students simulate the detection of an earthquake from three seismograph stations (there are many throughout the world, see USGS for maps of stations). Using a compass to measure distances on a map, Students use distance data form three seismograph stations to determine the epicenter of earthquakes. Key idea: Scientists now have a way to document where earthquakes happen. 7.  Plotting. Students can plot world earthquakes to identify fault lines and plate boundaries. Students can use Tarr et al. (2010) and UNAVCO (2014a) websites to see historical earthquakes and/or can plot historical earthquakes (100+). Key idea: earthquakes tend to happen in a pattern, a contiguous one, implying the Earth’s crust is “broken” into pieces. 8.  Pattern extension. Students can also conduct this same exercise done at a larger scale. They compare frequency of earthquakes over longer periods of time and greater spans of locations (Simkin et al., 2006). I. Learning about plate movement: What is happening at boundaries and fault lines? 1.  How are earth movements determined? Use GPS and LADAR to determine movement (USGS, 2015; UNAVCO, 2014a, 2015). Students look up information from GPS sensors and other instruments (laser distance finders) from plate boundaries to show movement direction at plate boundaries. 2.  How does earth move at plate boundaries? Students identify how plates are moving at different boundaries. These are given descriptive names [transform, divergent, convergent]. 3.  What geographical features do plate movements form? Students look at physical features along plate boundaries (mountains, volcanoes, plains, rifts, islands, trenches, etc.). 4.  What area type of plate movements is associated with tsunamis? Students examine the type of boundaries and geographical features from the recent Indonesian and Japanese tsunamis (convergent/subduction, trenches). Students predict the type of boundary and features around the Pacific Northwest coast. 5.  How does the earth move along the coastlines of Oregon, Washington, and California? Students look at GPS data from the Pacific Northwest and conclude that earthquake/tsunami conditions exist off its coastline. J. Interior earth: Why do plates move and cause earthquakes? What else do earthquakes reveal?



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1.  Properties of S- and P-waves (transmission and reflection). Students can simulate the type of waves S- and P-waves. A student can simulate a sinusoidal (S-) wave by moving their hand across his/her body quickly while holding a stretched out slinky. A student can simulate a compression wave (P-) by moving their hand back and forth quickly while holding a stretched out slinky. With controls, students can time S- & P-waves to show P-waves are faster. Using a bowl of water, students can also show that while P-waves travel across liquids, S-waves do not. 2.  World detections patterns (Simkin et al, 2006; UNAVCO, 2014a). Students examine profile of the Earth to observe patterns that now all seismograph stations detect S- and P-waves. All detect P-waves, but not all S-waves. This S-wave bind zone is dependent on how far from the epicenter. Students should speculate why? (Earth has liquid material deep near its core.) 3.  Multiple layers. Because of reflection of waves, scientists infer multiple layers (Pp-waves, Ppp-waves, etc., as shown from seismograph stations at University of Portland; see IRIS, 2015b). 4.  Center of earth solid metal. Because of Earth’s gravity, we know the center of Earth has to be made of more dense material (metal), and if it is metal and liquid, it must be hot. Infer that very center is solid metal because of the pressure (material science). 5.  Convection’s involvement in Plate Tectonic Theory. Because of intense heat, scientists infer convection occurring in the rocky layer causing the Earth’s crust to move. Key idea: Plate Tectonic Theory: Earth’s crust is broken into “plates” and these plates move because of convection of the rocky layer (mantle) in the Earth. K. Empowering students: Earthquakes and tsunamis can happen. What can be done? 1.  Dangers. What are the dangers of earthquakes and tsunamis? Students can read/watch videos. 2.  Community disaster resilience. Access resources for community-scale preparatory actions and community building for proactive resilience (Kagawa, 2009) 3.  Community evacuation routes (blue tsunami warning signs), emergency response plans. Students revisit earthquake and tsunami preparedness. 4.  Preparing structures. How are structures made tsunami- and earthquake resistant? 5.  Preparing homes. What needs to be done to homes to make them safer during an earthquake?

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6.  Preparing households. Emergency strategies: food, water, injuries, meeting places, and so forth. APPENDIX B Lesson Sample 2–Earthquake Detection and Zhang Heng Zhang Heng and the Chinese Dynasty Earthquake Detection Materials used to create this lesson plan include Balchin (2003); CCTV (1995, 2008); Forensic Geneaology (2012); Graham (2010); Howell (2003); IRIS (2014, 2015a), Kagawa (2009); MacArdle, Miles, Campbell, Chakton, & Farsarakis (2008); Quoi (2010); Riveland (2013); Tarr et al. (2010); Wikimedia Commons (2004). A. Engaging question for learning: Why do we care about earthquakes? Because they are destructive and kill many lives. To better understand the science earthquakes and the dynamic Earth. To find patterns and predict earthquakes. B. Prompt for discussion: Do you or someone you know live in an earthquake zone? In Southern California, it’s the Big One. In the Pacific Northwest, it’s Cascadia Subduction Zone. In the Midwest, it’s the New Madrid fault system. On the Eastern Seaboard, it’s the Ramapo Fault. There exists numerous threats to life and infrastructure throughout the United States, yet earthquakes strike with devastating effects around the world. An article on earthquake risk in the United States can spark discussion (Quoi, 2010). C. Prompt for discussion: Why would you care where an earthquake happens? Do you have friends or family living at a distance from you? Today, modern seismology uses arrays of seismographs can determine the intensity and location of any major earthquakes. Once an earthquake occurs, regional emergency offices can offer assistance and aid to the stricken area. Telecommunication systems allow for immediate contact to nearly anywhere in the world to see how your loved ones fared. Increasingly, disaster resilience models involve proactive readiness and communitybuilding (Kagawa, 2009, p. 114). D. Prompt for discussion: What happened before technology allowed the pinpoint location and offer of assistance to a stricken area? Nearly 2000 years ago, Zhang Heng, a bureaucrat, astrologer, mathematician, inventor, and poet, devised a seismograph that could tell the direction of earthquake epicenter (MacArdle, Miles, Campbell, Chakton, & Farsarakis, 2008).



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E.  How did Zhang Heng do this? First, he needed a device that only detected earthquakes and their horizontal motion, not the general vertical motion caused local earth displacements (such as like those caused by a semitruck or a herd of cattle running by). He knew that vertical earth motions were created by earthquakes and were directional. As an instructional example, share CCTV (1995) video of the Kobe earthquake showing the motion of display cases in convenience stores’ surveillance cameras. Zhang Heng’s famous device works on the principal of a pendulum. F. Experiment: Using a pendulum to indicate the direction of an earthquake. Experiment question: How can a pendulum indicate the direction of an earthquake? Set up a pendulum (string hanging from a fixed point above the table or desk) with a marker suspended from its end and a piece of paper underneath it on a table. Provide a horizontal strike on the table to initiate a swing of the pendulum. Strike from different directions. How can a pendulum indicate the direction of the earthquake? What are its limitations? Can it determine intensity? What if you used sand (place sand in a suspended funnel)? Would there be a way for a sand pendulum to indicate direction of force (e.g., sand dispersed farthest from the center). Zhang Heng used a metal drum, a pendulum, and brass balls. Look at a diagram or photo of his seismogram. Have students try to figure out how it worked inside. Provide hints if needed (inside was not flat; it was divided into 8 sections; and there was another brass ball in the middle). Videos are available online (CCTV, 2008). G. Why did the Chinese feel a need for such a device? During China’s Han Dynasty, Zhang Heng’s device could detect major earthquakes hundreds of kilometers away. The government’s territory was quite large. They could send aid to affected locations before receiving requests for aid by messenger (via ship, horse, runner; no telephones). What if the Hans detected an earthquake in a rival’s territory? How else might cultures use such information? APPENDIX C Teacher Resources Teaching about Emergency and Disaster Preparedness and Community Resilience Teacher Resources for Teaching about Tsunamis Teacher Resources for Teaching about Zhang Heng and Earthquake Detectors and Plate Tectonics

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Teaching about Emergency and Disaster Preparedness and Community Resilience Resources on how to inspect and mitigate home hazards related to earthquakes and tsunamis: Center for Disease Control and Prevention: http:// www.bt.cdc.gov/disasters/earthquakes/inspecting.asp Federal Emergency Management Agency Earthquake Publications: http:// www.fema.gov/earthquake-publications USC/Earthquake Country Alliance Seven Steps to Earthquake Safety: http:// earthquakecountry.org/sevensteps/ Examples of Locality Based Emergency Preparedness Resources (teachers will want to select resources relevant for their own locality related to disaster and emergency preparedness): City of Cannon Beach Emergency Action Plan (including evacuation routes): http://ci.cannon-beach.or.us/community/evacuationmaps.html Oregon Tsunami Clearinghouse: http://www.oregongeology.org/tsuclearinghouse/ Kagawa (2009). Learning in emergencies: Defense of humanity for a livable world. In D. Selby and F. Kagawa (Eds.), Education and climate change: Living and learning in interesting times (pp. 106–24). Provides a useful reframe and articulates the need for a transformative and community empowering emergency education. Provides a model of emergency education and disaster resilience that can help science educators proactively build collaborative community capacity. Theoretical and practical rigor. Teacher Resources for Teaching about Tsunamis Animations of the Orphan Tsunami from the IRIS Geology site (IRIS, 2014): http://www.iris.edu/hq/programs/education_and_outreach/animations/22 This resource offers animated visualizations of the geophysical dynamics of the science of these tsunamis. Teachers can use this to reinforce the underlying science behind the collaborative, scientific, cultural-historical role-play. IRIS (2015a) also has educational videos useful for supporting student visualization of emergent learning. Atwater, B. F. (2005). The orphan tsunami of 1700: Japanese clues to a parent earthquake in North America. Reston, VA: U.S. Geological Survey. This resource tells the story of how scientists discovered episodic, catastrophic earthquake/tsunamis along the Pacific Northwest coast. It includes pictures, diagrams, and the diverse scientific and cultural data that, through



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systemic understandings and systematic collaboration, allowed the discovery. Teachers would photocopy from the book’s documents and data as handouts to the different science inquiry teams. UNAVCO (University NAVSTAR Consortium)/University of NAVSTAR (Navigation Satellite Timing & Ranging) Consortium (2014b). Episodic tremor and slip: The case of the mystery earthquakes. Geodetic Educational Resources. Retrieved from http://www.unavco.org/education/ resources/educational-resources/lesson/ets-mystery-earthquakes/ets-mystery-earthquakes.html This resource provides scientific information, curriculum, teacher materials and Powerpoint presentations and student worksheets regarding the “mystery tsunami.” Teachers would use this resource to prepare their dynamic lesson plans. UNAVCO (University NAVSTAR Consortium)/University of NAVSTAR (Navigation Satellite Timing & Ranging) Consortium (2015). Educational resources. Retrieved from http://www.unavco.org/education/resources/ educational-resources/educational-resources.html This resource offers information about current scientific processes for collecting data and interpreting information, such as GIS, LIDAR, and how current technology is used to understand geology. Teachers can use this resource to demonstrate how modern geologists do their jobs. They might also find it useful to generate collaboration contacts and for their own professional development. Teacher Resources for Teaching about Zhang Heng and Earthquake Detectors and Plate Tectonics Incorporated Research Institutions for Seismology (IRIS). (2014). Education and public outreach. Retrieved from http://www.iris.edu/hq/programs/ education_and_outreach Incorporated Research Institutions for Seismology (IRIS). (2015a). Education and outreach videos. Retrieved from https://www.iris.edu/hq/programs/education_and_outreach/videos Incorporated Research Institutions for Seismology (IRIS). (2015b). Recent earthquake teachable moments. Retrieved from http://www.iris.edu/hq/ retm/event/1328 Viewers can see the world seismic monitor, lessons and resources, educational software, public displays and teacher development. Teachable Moments—for example, Teachable Moments PDF in English and Spanish. Teachers will feel confident in using IRIS, which has high-quality science and STEM teaching materials and represents membership “from virtually

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all US universities with research programs in seismology plus international affiliates.” China Central Television America (CCTV) (2008). Han Dynasty seismograph in 132AD [Video]. Retrieved from http://www.youtube.com/ watch?v=GcVFuIccf5c#t=20 Teachers might find this brief, ten-minute explanatory video about the Han Dynasty seismograph useful in preparing their own lesson plans, and/or for student-directed inquiry. Riveland, C. (2013). Zhang Heng’s famous ancient Chinese inventions: China gaze. Retrieved from http://www.chinagaze.com/2013/05/01/famous-ancient-chinese-inventions/ Teachers might find this resource useful as it also describes Zhang Heng’s many (polymathic) accomplishments across disciplines, giving a flavor of why he is described as the Leonardo DaVinci of his day, although technically he predated DaVinci by 1400 years. We might better say, Leonardo DaVinci was the Zhang Heng of his day. This could lead into a discussion of how Chinese cosmologies of his time did not make the same kinds of distinctions between science and literature, for example, that modern Western culture reinforces. Forensic Genealogy. (2012). Quiz 359: Ancient Chinese seismograph. Retrieved from http://www.forensicgenealogy.info/contest_359_results.html Aggregated website with many sources on Zhang Heng and the seismograph. A site aggregating resources on Zhang Heng’s invention, framed as a STEM quiz. Teachers might find this useful for learning context and background information. REFERENCES Aikenhead, G. S. (2001). Students’ ease in crossing cultural borders into school science. Science Education, 85 (X), 180–88. Atwater, B. F. (2005). The orphan tsunami of 1700: Japanese clues to a parent earthquake in North America. Reston, VA: U.S. Geological Survey Balchin, Jon. (2003). Science: 100 scientists who changed the world. New York, NY: Enchanted Lion Books. Banks, J. A. (1999). An introduction to multicultural education (2nd ed.). Boston, MA: Allyn & Bacon. Bowers, C. A. (2006). Revitalizing the commons: Cultural and educational sites of resistance and affirmation. Lanham, MD: Lexington Books. Cajete, G. (Ed.). (1999). A people’s ecology: Explorations in sustainable living. Santa Fe, NM: Clear Light Publishers. Cajete, G. (2000). Native science: Natural laws of interdependence. Santa Fe, NM: Clear Light Publishers.



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Carter, L. (2011). The challenges of science education and indigenous knowledge. In G. J. Sefa Dei (Ed.), Indigenous philosophies and critical education (pp. 312–29). New York, NY: Peter Lang. Center for Disease Control and Prevention (CDC). (2014). Inspecting for home hazards. Retrieved from http://www.bt.cdc.gov/disasters/earthquakes/inspecting.asp China Central Television America (CCTV) (2008). Han Dynasty seismograph in 132AD [Video]. Retrieved from http://www.youtube.com/watch?v=GcVFuIccf5c#t=20 China Central Television America (CCTV) (1995). Great Hanshin/Kobe earthquake 1995 [Video]. Retrieved from https://www.youtube.com/watch?v=LkZLjH2yUo4 City of Cannon Beach. (n.d.). Tsunami evacuation: Pedestrian route maps. Retrieved from http://ci.cannon-beach.or.us/community/evacuationmaps.html Federal Emergency Management Agency (FEMA). (2015). Earthquake publications. Retrieved from http://www.fema.gov/earthquake-publications Forensic Genealogy. (2012). Quiz 359: Ancient Chinese seismograph. Retrieved from http://www.forensicgenealogy.info/contest_359_results.html Goleman, D., Bennett, L., & Barlow, Z. (2012). Ecoliterate: How educators are cultivating emotional, social, and ecological intelligence. San Francisco, CA: JosseyBass and The Center for Ecoliteracy. Graham, A. (2010). Astonishing ancient world scientists: Eight great brains. Berkeley Heights, NJ: Enslow Publishers. Howell, B. F. (2003). Biographies of interest to earthquake and engineering seismologists. International Geophysics, 81(B), 1725–89. iLookChina (2011). Ancient Chinese inventions that changed the world: The seismograph. Retrieved from ilookchina.net/2011/07/24/ancient-chinese-inventions-thatchanged-the-world/ Incorporated Research Institutions for Seismology (IRIS). (2014). Education and public outreach. Retrieved from http://www.iris.edu/hq/programs/education_and_ outreach Incorporated Research Institutions for Seismology (IRIS). (2015a). Education and outreach videos. Retrieved from https://www.iris.edu/hq/programs/education_and_ outreach/videos Incorporated Research Institutions for Seismology (IRIS). (2015b). Recent earthquake teachable moments. Retrieved from http://www.iris.edu/hq/retm/event/1328 Kagawa, F. (2009). Learning in emergencies: Defense of humanity for a livable world. In D. Selby and F. Kagawa (Eds.), Education and climate change: Living and learning in interesting times (pp. 106–24). New York, NY: Routledge. Kawagley, A. O., Norris-Tull, D., & Norris-Tull, R. A. (1998). The indigenous worldview of Yupiaq culture: Its scientific nature and relevance to the practice and teaching of science. Journal of Research in Science Teaching, 35(2), 133–44. Lemke, J. L. (2001). Articulating communities: Sociocultural perspectives on science education. Journal of Research in Science Teaching, 38(3), 296–316. Macardle, M., Miles, E., Campbell, E., Chakton, N., & Farsarakis, J. (2008). Scientists: Extraordinary people who altered the course of history. London, UK: Basement Press

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Mercer, O. R. (2011). “Glocalising” indigenous knowledges for the classroom. In G. J. Sefa Dei (Ed.), Indigenous philosophies and critical education (pp. 299–311). New York, NY: Peter Lang. Montuori, A., & Purser, R. E. (1995). Deconstructing the lone genius myth: Toward a contextual view of creativity. Journal of Humanistic Psychology, 35(3), 69–112. National Science Resources Center (2006). Catastrophic events: Student guide and source book. Burlington, NC: Carolina Biological Supply Company. Next Generation Science Standards (NGSS). (2013). Retrieved from http://www.k12. wa.us/Science/NGSS.aspx Quoi, C. Q. (2010). Earthquake threat lurks for the United States, too. Live Science. Retrieved from http://www.livescience.com/8011-earthquake-threat-lurks-unitedstates.html State of Oregon Department of Geological and Mineral Industries (SODGMI) (n.d.a). Geologic hazards on the Oregon coast: Prehistory and historic tsunamis. Retrieved from http://www.oregongeology.org/sub/earthquakes/oraltraditions.htm State of Oregon Department of Geological and Mineral Industries (SODGMI) (n.d.b). Oregon tsunami clearinghouse. Retrieved from http://www.oregongeology.org/ tsuclearinghouse/ Richards, R. (Ed.). (2007). Everyday creativity and the new views of human nature: Psychological, social, and spiritual perspectives. Washington, DC: American Psychological Association (APA). Riveland, C. (2013, May 1). Zhang Heng’s famous ancient Chinese inventions: China gaze. Retrieved from http://www.chinagaze.com/2013/05/01/famous-ancient-chinese-inventions/ Sawyer, R. K. (2007). Group genius: The creative power of collaboration. New York, NY: Basic. Sawyer, R. K. (2010). Individual and group creativity. In J. C. Kaufman & R. J. Sternberg (Eds.), The Cambridge handbook of creativity (pp. 366–80). New York, NY: Cambridge University Press. Simkin, T., Tilling, R. I., Vogt, P. R., Kirby, S. H., Kimberly, P., & Stewart, D. B. (2006). This dynamic planet: World map of volcanoes, earthquakes, impact craters, and plate tectonics (third edition.). Retrieved from http://pubs.usgs.gov/ imap/2800/ Sterling, S. (2009). Riding the storm: Towards a connective cultural consciousness. In E. J. Wals (Ed.), Social learning towards a sustainable world: Principles, perspectives, and praxis (pp. 63–82). The Netherlands: Wageningen Academic Publishers. Retrieved from http://www.wageningenportals.nl/sites/default/files/resource/ sociallearning-e.pdf Tarr, A. C., Villaseñor, A., Furlong, K. P., Rhea, S., & Benz, H. M. (2010). Seismicity of the Earth 1900-2007: U. S. geological survey scientific investigations map 3064, sheet 1, scale 1:25,000,000. Retrieved from http://pubs.usgs.gov/sim/3064/ UNAVCO (University NAVSTAR Consortium)/University of NAVSTAR (Navigation Satellite Timing & Ranging) Consortium (2014a). Earthquakes, epicenters, hypocenters, magnitudes, and earthquake catalogs. Retrieved from https://www. unavco.org/software/visualization/idv/UNAVCO_IDV_datasource_eqs.html



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UNAVCO (University NAVSTAR Consortium)/University of NAVSTAR (Navigation Satellite Timing & Ranging) Consortium (2014b). Episodic tremor and slip: The case of the mystery earthquakes. Geodetic Educational Resources. Retrieved from http://www.unavco.org/education/resources/educational-resources/lesson/ ets-mystery-earthquakes/ets-mystery-earthquakes.html UNAVCO (University NAVSTAR Consortium)/University of NAVSTAR (Navigation Satellite Timing & Ranging) Consortium. (2015). Educational resources. Retrieved from http://www.unavco.org/education/resources/educational-resources/ educational-resources.html University of Southern California (USC)/Earthquake Country Alliance. (2015). Seven steps to earthquake safety. Retrieved from http://earthquakecountry.org/ sevensteps/ United States Geological Survey (USGS). (2015). Educational resources. Retrieved from http://education.usgs.gov/ Vold, E., Ramsey, P. G., & Williams, L. R. (2003). Multicultural curriculum and teaching. Multicultural Education: A Sourcebook (pp. 147–205). New York, NY: Routledge. Wikimedia Commons (2004). A replica of an ancient Chinese seismograph from Eastern Han Dynasty (25–220 CE). Oakland, CA: Chabot Space & Science Center. Retrieved from http://en.wikipedia.org/wiki/File:EastHanSeismograph.JPG

Chapter Eight

Classroom Meteorologists Transforming Science Content in a Dual Language Second Grade Classroom Sandra Lucia Osorio

INTRODUCTION Currently teachers are being bombarded with standards that they must have their students meet in their classroom, including Common Core and the new Next Generation Science Standards. While it is beneficial to have a common goal for students nationwide to achieve, these standards lead to a use of curriculum that is “white, middle-class” oriented. This curriculum misses out on the rich diversity children bring to most of today’s classrooms, and it does not acknowledge individual student’s knowledge base, identities, and backgrounds (Nieto, 2000). This can have a detrimental effect on students’ learning. All students have various starting points that must be taken into consideration when teaching any content area. This is why there is a need for multicultural curriculum transformation as a way of leveling the playing field. This chapter focuses on science instruction in a second grade dual language classroom, in which Sandra was assisting in the implementation of science notebooks as a formative assessment, specifically looking at the development of academic language. Science notebooks were chosen because it gave each student the opportunity to show knowledge they had and information they were learning in any format chosen. In addition, this chapter will describe how two teachers saw challenges in how science was being taught to their second grade dual language students and decided to transform that instructional practice. This particular chapter focuses on the beginning of the school year topic of weather in which students were learning about research and inquiry through hands-on activities. 167

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STORY OF SUCCESS The classroom at focus contained twenty-six students, twenty of which were Spanish-dominant students and six of which were English dominant students. The content of science was taught in English. There were a wide range of English language proficiency skills as well as content knowledge held by the students in the class. There was also a range of social economic levels in the classroom that affected the types of opportunities students had been exposed to outside the classroom. Twenty of the students in the classroom were considered from a low socioeconomic level because they qualified for free and reduced lunch program. All the students, but one, had been together during their first-grade year with their teacher, so they had well-established relationships. Their existing relationship aided in the instruction and implementation of science notebooks because the teacher knew a lot about student individual backgrounds and students knew a lot of information about each other. This environment enabled students to feel comfortable and forthcoming during classroom discussions around science. Since a majority of the students in the classroom were emergent bilinguals (García, Kleifgen & Falchi, 2008; Teachers College, 2008) with English being their second language, a variety of resources were used during the science instruction. For example, the teacher utilized a think-pair-share exercise in which students were expected to talk with a partner about a question or topic given by the teacher or brought up from student conversation before speaking to the whole group. They were also allowed to share in their native language if they were not comfortable in sharing English. Additionally, the teacher also modeled how ideas could be translated. Finally, a word wall with visual representations of words, as well as sentence starters written on the board were always present to help students in the process of writing their ideas. The most important aspect of the science unit was valuing the funds of knowledge students brought to the classroom, and using the science-centered activities to build students’ existing knowledge base (González, Moll, & Amanti, 2005). The investigations my co-teacher and I decided to conduct in class related to the topic of weather were based upon students’ interests and knowledge. We wanted to give students agency and involve them in problemposing dialogue. The formative assessment practice we implemented this year was the use of science notebooks (Aschbacher & Alonzo, 2006; Black, 1998; Fulton, 2012). Students were allowed to record their ideas in any way they chose. This allowed for individualization. Allowing for individualization in the science notebooks was important to us because, having had students the year prior, we knew the vast differences among students and how they may choose to represent their learning. An additional advantage of the science



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notebook was that all the information from throughout the year was contained in one central location so the teacher could easily see the student’s growth and struggles. Toward the end of the unit, students were allowed to research and investigate different ways that humans can affect the weather and the environment in an effort to promote higher-level thinking and allow students to apply their newly acquired information. Students came up with a problem they saw and researched various solutions. Some of the topics investigated were the greenhouse effect and the plastic pollution in the oceans. The students then made video clips explaining the problem they studied and what we, as citizens of the Earth, could do to begin to remedy some of these problems. The student that researched the greenhouse effect promoted the idea of biking or walking to school and work in order to reduce emissions. The student that investigated the floating garbage patches in the oceans promoted the importance of recycling. She even shared information she researched about our city’s local recycling efforts. This application lesson was a way to get students involved in activism in their current political context. Just as we had done with the implementation of the science notebooks, we were trying to take students background and interest into account as we individualized the science instruction as much as possible. Throughout this entire unit, the teachers were serving as facilitators. We were moving away from the banking-model of education in which students were seen as empty vessels and instead positioning students as the knowledge holders and leaders (Freire, 1970). This is very different from the norm of teacher-directed instruction and can be rather uncomfortable for teachers in the beginning. Although we recognize that teachers are pressured to meet the standards and assess the learning of all students throughout the school year and we acknowledge that moving to a more student-directed format can be difficult and overwhelming, we feel that giving students authorship and agency makes them grow in so many ways while still accomplishing these goals. Some of the ways we saw students grow were that students were more engaged in the topics since they directly related to their interests. Also, students who were on the shy side were getting more opportunities to converse with their peers, and some were becoming comfortable with taking on a leadership role and sharing their ideas. CONCRETE EXAMPLE OF MULTICULTURAL CURRICULUM TRANSFORMATION IN SCIENCE EDUCATION During this weather unit we knew that all students had to learn about past weather patterns and how they affected various Earth processes. Instead of

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treating all the students as if they were the same, we started with what they knew, their funds of knowledge (González et al., 2005). We sent home cameras for students to take pictures of weather, pictures of how weather affected their lives and home environment. An example of a picture we received back was of one student’s home garden. By receiving this picture, we knew that particular student had knowledge related to seasons and their relation to planting as well as how weather could affect the outcome of their planting. We used this information to aid us in our decision to make this student a leader of a group where they could share their expertise with other members of the class. Instead of taking a science unit and teaching it to our students, we constructed our unit by beginning with the standards, asking ourselves and the students what they know related to those standards, and considering student interest. This means that every time we teach this unit it could be different given that the students would be changing from year to year. Reflection Bridge We were able to accomplish all that we have just described because we engaged in multicultural education transformation. Instead of viewing multicultural curriculum as an add-on when the ideas were convenient, we created our curriculum with multiculturalism as a primary focus. This required us to go well beyond the superficial, in learning to think comprehensively about what and how we teach, and then to apply this thinking to our teaching praxis. KEY DILEMMAS IN SCIENCE EDUCATION Too often, multicultural education is discretely presented as on additive to what is already in the curriculum. In science education one way this is seen is by introducing students to a scientist of color. For example, if we would have just shared with students a picture and description of a meteorologist of color and some of the amazing things he or she was doing in the world this would not have been transformative because there was no real change in our day to day instruction or in the lens through which we deliver curriculum. In order for us to truly transform our science instruction, we had to rethink how we even began planning the unit as well as the way it was going to be taught and assessed. SUMMARY By changing the way we began planning the weather unit, linking the activities to students’ personal interests, and changing our assessment tools,



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we were able to transform our science instruction in our second grade dual language classroom. Students were more motivated to engage in the various activities and students who rarely shared in our whole group began to speak up in large groups and were now taking on leadership roles in the classroom. This lead to better academic performance as demonstrated in our evaluation of the science notebooks. Students became the experts. They were asked to go beyond just answering the question, by really becoming scientists. REFERENCES Aschbacher, P., & Alonzo, A. (2006). Examining the utility of elementary science notebooks for formative assessment purposes. Educational Assessment, 11(3/4), 179–203. Black, P. (1998). Formative assessment: Raising standards inside the classroom. School Science Review, 80(291), 39–46. Freire, P. (1971) Pedagogy of the oppressed. New York, NY: Seabury. Fulton, L. (2012). Science notebooks: Teachers’ developing beliefs, practices, and student outcomes. Action in Teacher Education, 34(2), 121–32. García, O., Kleifgen, J., & Falchi, L. (2008). Equality matters: Research review no. 1. From English language learners to emergent bilinguals. New York, NY: Teachers College, Columbia University. González, N., Moll, L., & Amanti. C. (2005). Funds of knowledge: Theorizing practices in households, communities, and classrooms. Mahwah, NJ: L. Erlbaum Associates. Nieto, S. (2000). Affirming diversity: The sociopolitical context of multicultural education. New York, NY: Longman. Teachers College. (2008). Equity matters: Research review No. 1 [Peer commentary on the paper “From English Language Learners to Emergent Bilinguals” by O. García, J. Kleifgen, & L. Falchi]. Retrieved from http://files.eric.ed.gov/fulltext/ ED524002.pdf

Part III

MATHEMATICS AND SCIENCE

Chapter Nine

Rethinking Art in Mathematics and Science Jeff Sapp

INTRODUCTION I didn’t come to art naturally. I taught high school math and middle school math and science for years before I ever considered art as a comrade. Two things caused me to embrace art. First, I noticed how students valued artistic expression in how they dressed and put themselves together each day, how they decorated their textbook covers and notebooks, and how they doodled during lectures. Secondly, I increasingly became aware that when I did anything artistic—whether it was through assigning graphic organizers, using posters with colored markers for students to show comprehension, incorporating music as a way to show the relevance of math, or showing pictures of Fibonacci patterns in nature—whatever artistic outlet I used suddenly increased attention, motivation, and comprehension. I became a STEM teacher increasingly intrigued by the power of art. I wanted to learn more. In many ways the arts continue to be an equity issue for children. I currently work with California State University Dominguez Hills’ Urban Teacher Residency (UTR) and Transition to Teaching (TTT) programs that place math and science teachers in the lowest performing schools in Los Angeles Unified School District (LAUSD). One of the goals is to get competent and dedicated educators to stay in these high-needs schools, as there is a high attrition rate for professionals. The arts are around, but the drive in many schools is still singularly focused on increasing standardized test scores. Period. In the schools I work with, many of which are in working class areas, the arts are often considered the “fluff” mentioned earlier. I was intrigued to 175

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Table 9.1.   Percentage of K-8 Students in After School Art Programs What is the percentage of K-8 students in after school arts programs? Households that make under $15K $15–30K $30–50K $50–75K $75K+

= = = = =

6% 9% 14% 20.3% 30%

find a study that looked at arts and affluence (McMullen, 1968). What the study found was that the wealthier the household the more the children in that household were given opportunities to immerse themselves in art. Okay, so what do wealthier households know about art that I don’t know and how will it benefit students? For one, students who study art have higher grades, score better on standardized tests, have better attendance records and are more active in their communities. Why? One reason is that the arts change the brain by strengthening students’ ability to focus, keep their attention on a task, delay gratification, and manage their emotional states of patience, flow, and self-discipline. These are all skills that our LAUSD students need desperately and I was “in” about the power and impact of art and have spent years integrating art into mathematics and science. STORY OF SUCCESS Ladson-Billings (1995) coined the term culturally relevant pedagogy and defined it as a way of teaching that “not only addresses student achievement but also helps students to accept and affirm their cultural identity while developing critical perspectives that challenge inequities that schools (and other institutions) perpetuate” (p. 469). I certainly saw this play out well with one of my university student-teacher candidates. He taught in a predominantly Latino community (98% of his high school students were Latinos) and he developed a set of primary documents showing Mayan mathematics. Because it was his own culture as well as the culture of most of his students, and because he hand-drew beautiful and intricate pieces highlighting various contributions of the Mayans, he stated, “I could actually see my students literally lean in to math for the first time. Honestly, I’ve never seen my students be more engaged and curious about math as I did the day I used my set of primary documents.” The personal and cultural aspects of his set of primary documents—a set that beautifully affirmed his and his students’ cultural identity—unleashed a number of critical questions from his students: “Why have I never seen this before in a math class?” “Who writes the math books and



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why did they leave us out?” “What else are they not telling us?” “How can we find out more about what the Mayans did?” A group of students decided to explore these questions with their teacher after school and then report back to the class. Over the course of several years, this has led to the walls of the classroom becoming an exploration of “mathematics outside the textbook,” as the students have named it. CONNECTION TO MULTICULTURAL EDUCATION/ MULTICULTURAL CURRICULUM TRANSFORMATION The critical multicultural aspects of these sets of primary documents lie in students questioning, confronting, and challenging why their cultural identity groups might not be represented in mathematics and science, what Gay (2004) refers to as “curriculum desegregation.” The engaging reality that their identity group is suddenly visible in an otherwise invisible curriculum is simply the hook, but not the reason for the use of these primary documents. One teacher showed numerous women in the historical canon of science, most of whom students had never heard of before. The teacher listens for the “Why?” question and can facilitate conversations around patriarchy, misogyny, and sexism—conversations not often happening in math and science classrooms. This further moves the teaching of mathematics and science to an “equity pedagogy” that Gay (2004) describes as an education that “places value on how to effectively teach diverse students as well as what to teach them.” Furthermore, besides curriculum desegregation and equity pedagogy, there is a humanizing pedagogy surrounding the use of these primary documents as well. This humanizing pedagogy can be seen by students’ responses to seeing their cultural identities in the classroom, but perhaps more so by looking at more personal aspects of important people in the mathematics and science canons. One teacher, for instance, included the love letters written between Charles Darwin and his partner Emma Wedgwood, with whom the father of evolution spent over forty years with and raised ten children alongside (Burkhardt, 1994). No one in the class had ever heard of Wedgwood or that Darwin had children. Suddenly, Darwin was a person and not just a topic (Buber, 1971). A humanizing pedagogy moves topics from an “it” (an object) to a “thou” (a subject). CONCRETE EXAMPLES IN STEM MULTICULTURAL CURRICULUM TRANSFORMATION Primary documents and sources are snippets of history and life. They are often incomplete and come with little context and, consequently, they require

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students to be analytical, to examine sources thoughtfully, and determine what else they need to know to make inferences from the materials. Primary documents and sources also help students relate in a personal way to events of the past and help them come away with a deeper understanding of history as a series of human events, often of which they themselves are a part. Many textbooks today are full of colorful visuals that are nothing more than window dressing. Teachers can go far beyond window dressing and have students focus on the symbols and metaphors in editorial cartoons, dramatic qualities of photographs, the potential of images to make abstract ideas and concepts become concrete, and interrogate the implicit biases and stereotypes in certain images. Used these ways, the implementation of primary documents in mathematics and science easily meet many curriculum standards required of professional educators today. Inviting students to bring in their personal “funds of knowledge” (Moll, 2005) allows for important family and community conversations to occur. It never ceases to surprise me when students bring in primary documents related to a topic we are studying and I find out that they have a close relative who has played a key role in the topic at hand, like a recent student who shared that his uncle is a Nobel Prize–winning chemist. One of the reasons students are thrilled to be creating primary documents themselves is the availability of technology today. Students can scan photographs and documents, leaving the originals safe at home. They can print famous documents—easily accessible through dozens of museum archives online—and use sepia tones and different paper stock to make them look and feel authentic. I stand in awe of the creative power that becomes unleashed when I invite students to create documents around a mathematics or science topic. Anticipatory Activities and Primary Documents Anticipatory activities are meant to elicit curiosity, provoke questions, and activate students’ background knowledge. I find them a wonderful place to infuse art with mathematics and science. A favorite anticipatory activity involves creating a set of primary documents around a concept as a way to introduce and intrigue students about the topic. This anticipatory activity is meant to grab students and “hook” them into a topic they’ve been reluctant about in the past. Some of the primary documents are hand drawn, others are photographs that are printed out on photo paper so as to make them feel more authentic, others are printed on card stock, and some are soaked in tea to give them both an aromatic and textural feel. Students go wild for the visual and kinesthetic feel of these documents and, even more so, they feel like they’re pryingly getting into someone else’s personal property, which engages them in math and science in ways I’ve not seen before.



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I teach methods courses for math and science teachers. It is the work of our beginning math teachers that I wish to share with you. As always, the quality of work students provide inspires me. The ones in this chapter are examples that demonstrate how mathematics can be infused with elements of race, ethnicity, and gender. Curriculum Overview This particular assignment was left open and broad so as to invite as much creativity as possible. The only requirements were these: 1.  Create a minimum of ten primary documents. 2.  Place a notation on the backside of each document giving as much content as possible about it. 3.  You must vary the documents so that the set contains different visual and tactile pieces to engage your peers. For instance, some photographs, use different stocks of paper, soak a document in tea, burn the edges of one, hand write or draw others. 4.  Write a one-page description of how the documents fit within your teaching. 5.  Place all items in a large self-contained envelope. 6.  Be sure to make a copy of your work to keep as you’ll be donating the set you hand in “to the cause.” Curriculum Specifics What I love about the first primary document below is that Jessica included an actual example of a simple quipus as well as the photograph of an older example with more cords. I love the color-coded visual and accompanying explanation because simply reading the description I can see the values, but it’s even more fun to kinesthetically handle an actual quipus. The next set of primary documents introduces five great women of mathematics in a way that would reach reluctant readers as well as reluctant mathematicians. Students learn about Maria Gaetana Agnesi, Caroline Herschel, Florence Nightingale, and Sofia (or Sonya) Kovalevskaya. This pink set of documents was presented as a booklet that students could easily flip through and Veronica mentioned that she “created several sets so that when my students finished their seatwork, they could flip through these and learn about these great women.” I love how she wrote in the voice of each of these important women. In figure 9.3 you see the work of Jose, who hand-drew these original, intricate drawings. He was so engaged with this activity because it invited him

Figure 9.1.   Set of primary documents on Ancient Number Systems. Created by Jessica Guyon. Written on the back: Quipus or khipus (sometimes called talking knots) were recording devices used in the Inca Empire and its predecessor societies in the Andean region. A quipu usually consisted of colored, spun, and plied thread or strings from llama or alpaca hair. It could also be made of cotton cords. The cords contained numeric and other values encoded by knots in a base ten positional system. Quipus might have just a few or up to 2,000 cords. Each cluster of knots is a digit, and there are three main types of knots: simple overhand knots, “long knots” consisting of an overhand knot with one or more additional turns, and figure-of-eight knots. In the Aschers’ system a fourth type of knot—figure-of-eight knot with an extra twist–is referred to as an “EE.” A number is represented as a sequence of knot clusters in base 10. The example is a simple example where the blue cord represents 41, the red represents 111, the turquoise represents 1, and the yellow represents 22.

Figure 9.2.  Set of primary documents on Famous Women Mathematicians You Probably Never Heard of. Created by Veronica López. What it says: Sophie Germain (1776–1831) “Since my parents opposed my studies, I was left no choice but to sneak books into my room. Eventually, smuggling candles and books became more difficult. But hey, if there is a will, there is a way! I had to come up with the pseudo name M. le Blanc to be taken seriously in the math community. Unfortunately, men in my time couldn’t handle what I brought to the table! After working in number theory, I gained interest in Chladni figures (patterns produced by vibrations). My work here was foundational to applied mathematics, and it is even used in the construction of skyscrapers today.”

Figure 9.3. Set of primary documents on Mayan Mathematics. Created by Jose Antonio Casillas. Top: What it says on the back: The map of Central Mexico and the main pyramids of the Mayans. Bottom: What is says on the back: The Temple of Kukulcan was built 91 steps high. It had 4 sides bringing it to a total of 364 (91 x 4 = 364) plus the top platform to a total of 365. The temple was a calendar for the Maya and served as a guide for the Maya to harvest and plant.



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to show how his own cultural heritage has impacted mathematics. They were drawn on hard stock paper. Figure 9.4 adds the culture of many of this teacher’s students into mathematics. Sheeveta stated that she works “with a Latino population of 98%, so I knew these documents would make a good engagement activity to teach students about distant descendants from their culture and how they used math during that time.” I particularly liked what she did with the Mayan Dresden Codex (figure 9.5) by dipping the crinkled paper into tea to give it both smell and texture. Figure 9.6 includes a simple, but effective idea of making a Xerox copy of a document and then posting the copy onto cardboard in an effort to give the document texture. Jessica and the others created comprehensive packets of primary documents on the Mayans and it was one of the more popular sets to create. In figure 9.7, it is the intention of the educator, January, that she “show these to students to show how different the number systems were in the past from different cultures and different countries. We think that it’s important that students see how the numbers evolved over time.” KC writes that he’d use the documents to “help students gain an historical and cultural perspective on the history of math.” Over a dozen different cultures were represented in their documents.

Figure 9.4.  Set of primary documents on The Cultural Histories of the Aztecs and Mayans. Created by Sheeveta M. Jackson. What it says on the back: Maya numerals (otherwise known as Mayan numerals) were a vigesimal (base-twenty) numeral system used by the Pre-Columbian Maya civilization. The numerals are made up of three symbols: zero (shell shape), one (a dot), and five (a bar).

Figure 9.5.   What it says on the back: The Mayan Dresden Codex is the oldest known book written in the Americas. This is the document that contains the Mayan numerals of bars shells (meaning “zero”), dots (meaning “one”), and bars (meaning “five”). The Dresden Codex also contains amazingly accurate astronomical tables.

Figure 9.6.   Set of primary documents on Ancient Number Systems. Created by Jessica Guyon. What it says on the back: The Mayan had a second Number System that they used for dating buildings and on calendars. This would be a more formal system rather than a number system used for calculation. The numerical glyphs can be seen on monuments and codices as normal-form (bar-and-dot) glyphs, or as glyphs known variously as head-variant glyphs or portrait glyphs. Portrait glyphs are just that, portraits of the gods that are the integers. They’re also called head variants because only the head is shown. In the vast majority of cases, only a portion of the head is shown, although full heads do exist.

Figure 9.7.   Set of primary documents on The Evolution of the Counting Numbering System. Created by January Camero and K. C. Gobble. What it says on the back: Chinese Numeral Systems. The Chinese had one of the oldest systems of numerals that were based on sticks laid on tables to represent calculations.

Figure 9.8.   Set of primary documents on The Evolution of the Counting Numbering System. Created by January Camero and K. C. Gobble. What it says on the back: A cuneiform tablet of Babylonian mathematics depicting the Pythagorean theorem. The tablet shows an approximation of the square root of 2 in the context of Pythagoras’ theorem for an isosceles triangle. The original tablet is in the Yale Babylonian Collection.

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Figure 9.9.   Set of primary document on The Pythagorean Theorem. Created by Jazmin Rodríguez and Chris Torres. What it says on the back: A photo of a famous book named The Pythagorean theorem, a 4,000 year history. It goes through the development of the proof by Pythagoras.

After creating their primary documents, January and KC were approached by a peer in our class who offered to reconstruct their work using clay. Because of this collaboration January and KC now have a clay representation of their work for their classrooms. This is just another extension of what is possible when educators begin to focus on artistic expressions in the history of mathematics. The best cut comes of this assignment is the diverse collection of documents the educators gathered, from ancient art, various proofs from different cultures and times, and selections from important books. Jazmin Rodriguez states, “Showing ancient documents to my students gave them a sense of credibility of how the Pythagorean theorem proof was created. It was really interesting to see my students excited and engaged when they saw realistic copies of the primary sources. This introduction was a great way to start the conceptual lesson and engagement. My students were able to debrief after they analyzed the documents and write a paragraph of the importance of such documents and formulas.” Chris Torres uses his set of primary documents as a self-discovery activity. “The only thing I tell them is that the Pythagorean theorem deals with triangles. The reason for why I don’t give them the theorem is because they



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Figure 9.10.   What it says on the back: Chinese Pythagorean Theorem proof.

will discover it with this primary document self-discovery activity I’ve prepared for them.” REFLECTION BRIDGE The one area of concern I’ve seen in regards to having students create a set of primary documents is the couple of students who simply go to, say, Google Images and print out a few blurry black-and-white images and turn them in. I’ve found that to make this assignment really work that they need a rubric of what is expected of them. I mentioned earlier the six requirements I created so that the assignment is well framed, the last of which is, “Be sure to make

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a copy of your work for yourself as you’ll be donating the set you hand in ‘to the cause.’” This last part—donating a set “to the cause”—has been integral in growing this strategy to be more than I could have ever dreamed it might be. For one, over the course of several years of doing this, I have students pick the same topics over-and-over again, resulting in me having dozens of primary documents on a single topic, say Pythagorean’s Theory. One student will do a document in such a creative way that I replace that one item in my collection with that best example and, over the course of years I have collected a large, outstanding group of primary documents on many topics. It’s much better and more creative than I would have done myself. These “best practices” examples become the models that students work towards or, in many cases, try to best! This past year has seen something new again when, suddenly, students started making 3D models instead of paper documents. One student used clay to make an original set of fossils. Another student used Q-Tips as bones to make elaborate skeletons. I believe that this kind of assignment where students are asked to blend the rigor of their academic work with the brilliance of their aesthetic creativity has the potential to create what I refer to as “heirloom assignments.” I know this because I still have a wild rose that I drew in my sixth-grade science curriculum. It hangs in my hallway reminding me that some assignments are worth keeping. I believe that these sets of primary documents have the potential to become academic heirlooms. KEY DILEMMAS IN MATH AND SCIENCE EDUCATION The key dilemma I’ve come across centers on the question, “What is STEAM?” Many schools are just now getting STEM programs up and running and have trouble conceptualizing how art fits into STEM. Then there is the definition of art itself, which depending on whom you are speaking can mean many different things. Upon hearing me talk about STEAM on our campus, one of my dearest colleagues sent me the following email: “Can I share a pet peeve about the STEAM thing? I feel that arts questions and outcomes differ from STEM questions and outcomes (except at the highest levels), and I think that what is really being employed are visual thinking strategies, rather than the arts. I think it is great to advocate for young people to learn visual thinking in STEM, but to seemingly include the arts gives the mistaken impression that arts education is happening. I fear that this practice will allow program directors to say, ‘We’re doing the arts already’ and the little remaining support for true arts programming will disappear.” Scientists,



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technology people, engineers, mathematicians, designers, artists, educational theorists, and teachers may all have different ideas and definitions of what constitutes “art.” This merits more conversation for educational communities to form a definition of the arts in STEAM. SUMMARY The primary documents are simple and highly effective ways to use art as a way to reflect the historically rich impact of various cultures and genders on mathematics. Too often, the STEM education our students are offered is a domesticating education that gives them a functional literacy only. Infusing art, culture, and gender into STEM is one more step toward a more empowering mathematics, a kind of math literacy that is personal and relevant and allows students to see themselves situated in the grand conversation of mathematics. As feminist poet Adrienne Rich (2011) reminds us: When those who have the power to name and to socially construct reality choose not to see you or hear you, whether you are dark-skinned, old, disabled, female, or speak with a different accent or dialect than theirs, when someone with the authority of a teacher, say, describes the world and you are not in it, there is a moment of psychic disequilibrium, as if you looked into a mirror and saw nothing. (p. 218)

REFERENCES Buber, M. (1971). I and thou. New York, NY: Touchstone. Burkhardt, F. (1994). The correspondence of Charles Darwin: Volume 9, 1861. Cambridge, UK: Cambridge University Press. Gay, G. (2004). Beyond Brown: Promoting equality through multicultural education. Educational Leadership, 19(3), 192–216. Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465–91. McMullen, R. (1968). Art, affluence, and alienation: The fine arts today. New York, NY: Praeger. Moll, L. C. (2005). Funds of knowledge: Theorizing practices in households, communities, and classrooms. New York, NY: Routledge. Rich, A. (2011). Invisibility in the academe. In L. Buzzard, J. Gaunce, D. LePan, M. Moser, & T. Roberts (Eds.), The Broadview anthology of expository prose (pp. 217–19), Ontario, CA: The Broadview Press.

Part IV

ENGINEERING

Chapter Ten

Effective Engineering Models for Multicultural Curriculum Transformation in STEM Engineering for All Laura Luna, Twanelle Walker Majors, and Jennifer Meadows

INTRODUCTION In the field of STEM education, numerous challenges related to effective curriculum design need to be transformed in order to address the needs of a multicultural society. This chapter focuses on the E, or engineering in STEM, with a particular emphasis on an elementary-level curriculum transformation. To be clear, this chapter does not explicitly document a transformation completed by the authors. Rather, the search for the transformation of STEM education to be inclusive of elementary students led the authors to the Museum of Science, Boston’s Engineering is Elementary (EiE) curriculum. Not only does this curriculum address needs for elementary grade-level engineering education, EiE serves as an excellent model of a transformed curriculum that seeks to be inclusive of all. “From the beginning, EiE has designed materials to engage marginalized and ‘at risk’ populations, such as girls, minorities, youngsters with disabilities, and children from low socioeconomic backgrounds” (Cunningham, 2009). In our experiences using the curriculum in settings that include classroom, after-school, summer camp, and weekend workshops, we believe that EiE conforms to the constructs and dimensions of multicultural education. James Banks (2004), a leading scholar in the field of multicultural education, developed five specific dimensions of multicultural education. The first dimension of content integration is not integration of content areas, but rather integrating into the curriculum many of the possible cultural identities that we find in the faces and personalities of our students (Banks, 2004). In relation to 195

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EiE curriculum materials, it may be difficult to make assumptions about the cultural audience for whom the curriculum is intended; however, the materials provide inclusive images, scenarios, and activities for all students despite the demographics by which the students might be described. During the knowledge of construction process, students are involved in understanding and reviewing the way that knowledge is presented, perhaps traditionally found to be grounded in a Eurocentric viewpoint (Banks, 2004). EiE presents a child protagonist in each story, rather than an adult, as the lead problem solver. This child is mentored by an adult engineer to engage in problem solving with the implication that the child is also capable of coming to conclusions and contributing to the discipline. Students in the classroom then use the story as a model for a similar challenge problem with the assumption that children can contribute effectively to solutions, even solutions to tasks often addressed by adult engineers. Banks’s (2004) third dimension of multicultural education is prejudice reduction, which refers to the inclusion of specific activities to assert positive images of ethnic groups. EiE storybooks include all at-risk, marginalized groups through positive imagery and support of inter- and intragroup relations. Students are intentionally exposed to male and female engineers with a wide variety of ethnic and racial backgrounds. Implementing equity pedagogy requires the modification of teaching styles to support differentiated learning to allow all students to achieve (Banks, 2004). EiE training materials provide specific support for a minds-on, handsin collaborative environment where differences are seen as an addition to the team’s skill set. All ideas are to be heard and considered, and failure is seen as an essential part of being an engineer. Additionally, the design worksheets are academically leveled or differentiated to allow access for all students. Although the curriculum itself does not particularly call for a change in institutional practices in schools defined as empowering school culture (Banks, 2004), the implementation of the curriculum allows for application across grade levels, content areas, and tiers of ability. STORY OF SUCCESS Serena, a Latina first-grade student, attended a summer STEAM (science, technology, engineering, arts, and mathematics) academy, where she studied pollination, and participated in an EiE unit called Best of Bugs. Her teacher taught the class the Engineering Design Process: Ask, Imagine, Plan, Create, Improve. After learning the process, Serena told her teacher that she is going to be an engineer one day! Four months after the summer STEAM



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Academy, Serena opted to participate in an engineering class offered by her after-school program, and to this day she continues to apply the Engineering Design Process. Serena, as a female Latina, does not fit the typical demographic of an engineer, but she is part of a generation that can break the barriers, both perceived and actual, when it comes to her choice of career. In 2011, only 2% of engineering degrees were awarded to Hispanic females (National Center for Science and Engineering Statistics) [NCSES], (2015). Additionally, only 11.7% of employed engineers in 2013 were women, and 1.1% were Hispanic women. (NCSES, 2015). There have been numerous other instances where students from diverse populations have improved their self-efficacy as a result of the EiE curriculum and most of these observations occurred during formal learning environments when EiE curriculum was being shared with children. After reflecting on this notion, we wondered about bringing the ideas from EiE to a broader community. After much consideration, we decided that it would be more advantageous and potentially have a far-reaching impact on students and parents to model problem based STEM and engineering tasks in an informal learning environment. We were delighted that over eighty participants engaged in an EiE mini-lesson along with other STEM tasks during our informal teaching event. The purpose of the evening was to model how young people can share ideas and solve problems with the adults around them, and the participants were sent home with additional supports to continue the problem-solving process. CRITICAL CONSIDERATIONS From 2002 to 2012, gender trends within the United States in engineering remained fairly stagnant, with approximately one female to every four males (NSF, 2015). Furthermore, the number of undergraduate students of color awarded engineering degrees continued to be disproportionate to the general population (Howden & Meyer, 2011). According to the National Center for Science and Engineering Statistics (NCSES, 2015), the percent of bachelor degrees awarded to Hispanic American students increased during the same time period, while the percent of bachelor degrees awarded to African American and Asian students decreased. Katehi, Pearson, and Feder (2009) suggest that traditional engineering curricula fails to interest diverse students and much work is required of educators to increase their access and overall participation in the field. However, with implementation of transformed curriculum such as EiE, which serve to increase relevancy to the student body, as

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well as increase classroom exposure, integration, and collaboration, students from various cultural and ethnic backgrounds may in time show greater interest in engineering careers (Katehi, et al., 2009; National Academy of Engineering, 2004). Stereotypes create a division among people, and even people of the same race are sometimes guilty of stereotyping each other. From our perspective, students who are considering engineering, or other careers in the area of STEM, may experience spoken and unspoken “rules” regarding their likelihood to succeed in such a career. One theory that combats this idea is Contact Theory. This theory suggests that although there are inequalities and clear stereotypical perceptions of majority and minority groups “by exposing majority group members to new information about minority groups, contact helps majority group members disconfirm negative stereotypes and develop more favorable views of minority groups” (Dixon & Rosenbaum, 2004, p. 260). This is also supported by Banks’s (2004) theory of prejudice reduction. The transformation of engineering education puts students in contact with engineers of all demographics so that they begin to see themselves, at their current age, gender, ethnicity, and so forth as an engineer. For a successful transformation of the engineering curriculum through the multicultural education lens, PK-12 students must be able to visualize themselves as engineering professionals. Social cognitive theory explains that long-term decisions and career self-efficacy are underpinned by perceptions of personal capacity to achieve milestones necessary to approach the goal (Tang & Russ, 2007). Self-efficacy beliefs affect decision making by the development of warped ideas about one’s inadequate ability to overcome the milestones of a career goal (Tang & Russ, 2007; Soldner, Rowan-Kenyon, Inkelas, Garvey, & Robbins, 2012). Also called equity pedagogy by Banks (2004), the methods and contexts chosen by the teacher may be somewhat of a gatekeeper to the self-efficacy development—a basic need of all children. After much anecdotal evidence about the efficacy of EiE in schools, a survey was conducted in 2011 to examine the impact of the EiE curriculum on student engagement, interest, and performance. The survey specifically asked teachers questions about females and other historically underrepresented groups in STEM fields, such as students of color, English language learners, and students with an individualized education plan (IEP). While the sample size was small (i.e., forty-six teachers), results indicated that for each respective group, student engagement was rated higher for EiE than for traditional science education. Furthermore, students with low socioeconomic status and students from underrepresented groups of color were rated by their teachers as more engaged in EiE than compared to school overall (Moffett, Weis, & Banilower, 2011).



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Concrete Example of Multicultural Curriculum Transformation in Engineering Education In 2003, Engineering is Elementary (EiE) was developed at the Museum of Science in Boston, Massachusetts, with support from the National Center for Technological Literacy, through grant funding provided by the NSF. In an effort to “take advantage of the natural curiosity of all children,” EiE was designed as a research- and standards-based, classroom-tested curriculum, to “cultivate . . . understanding and problem-solving in engineering and technology” (Cunningham, 2009, p.11). “EiE has four primary goals: (a) increase children’s technological literacy; (b) increase elementary educators’ abilities to teach engineering and technology; (c) increase the number of schools in the United States that include engineering in their curricula; (d) conduct research and assessments to further the first three goals, and to develop a knowledge base on the teaching and learning of engineering at the elementary school level” (Cunningham, 2009, p. 12). Curriculum Overview Currently in the EiE program there are twenty units that are designed to integrate engineering with elementary science topics including connections to literacy, social studies, and mathematics. Each unit begins with an introductory lesson using a storybook to set the context for the engineering challenge. In the story, there is a child who seeks the assistance of a specific engineer. From a multicultural education perspective, the storybooks are equally divided by gender and represent cultures from six continents that include rural, suburban, and urban settings. Through relevant applications, students learn the engineering design process in order to creatively solve real-world problems, and more important, begin to view the field of engineering as not only applicable to their lives, but also as a possible career path (Cunningham & Lachapelle, 2011). STEM content area. The STEM content area is engineering. STEM grade level. The STEM content grade level is K-5. Standards. EiE considers NGSS, ITEEA Standards for Technology Literacy, and K-5 Science Standards for all fifty states and Washington, D.C. Educational context. The structure of each unit in EiE is divided into four main lessons with the goals of introducing a contextual challenge through the storybook focusing on connections to literacy and social studies, exploration of the engineering type discussed in the storybooks, exploration of materials, and then the final engineering challenge. These units are designed to be used in a variety of educational settings. Relationships with and among students and their families. The EIE units begin with a letter for families to explain the connections to engineering.

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Within the storybooks, a variety of family structures are portrayed. Students work with peers and adults, which may include family, neighbors, or members of the extended community to solve problems. Civic engagement. Each EiE unit is set within a larger context of a community challenge such as a school fundraiser, a family business, or transportation need in a remote village. Additionally, students explore aspects of particular engineering fields beyond the scope of the storybook settings. Engineering is presented as a problem-solving mind-set as well as a possible career goal; with this approach, students see that engineering helps people. Additional considerations. Core value six of the EiE theoretical underpinnings states that effective engineering activities are scaffolded in a way that allows children to work and think independently. Flexibility and simplicity of the EiE program allows for ease in differentiation for students with various learning needs ranging from the gifted and talented to special needs including bilingual. Content linked to pedagogy, including evaluation particulars. EiE curriculum units include pre- and postassessments designed to evaluate changes in student thinking in the context of engineering and technology rather than specific content knowledge. Integrated use of technology. EiE defines technology as any product or process that is human designed to meet a need or want. Technology then is integral to the EiE process. Other educational technology such as interactive whiteboards is nice to have but is not necessary to effective implementation of EiE. Notes to teachers. Training is available online. Curriculum/teacher guides are easy to follow in layout. Most of the materials are easy to access. All teachers will need to know that the first one will take longer to implement. REFLECTION BRIDGE Simply following the teacher’s guide for an engineering curriculum such as Engineering is Elementary will not transform your classroom. It is the educator’s responsibility to set up a classroom environment that is conducive to the transformed multicultural education curriculum. Whether you use a curriculum that is already transformed or you are transforming your own, the climate formed in your classroom through specific collaborative assignments is essential to the full multicultural STEM experience. In our personal perspective, we come from the position of three mothers who have raised combined total of eight children through a cumulative eighty-one years of education in public and private K-12 schools. Not once



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were our children expected to solve an engineering-like problem other than that of an informal learning environment that we were privileged enough to seek out, know about, and gain access to for our children. On the few occasions that it looked like something that exciting was going to happen for our children, it morphed into a take-home project rather than a true think tank exercise in schools. In those instances, the activity often consisted of worksheets sent home with our children that were perceived to be “participation” only with no true opportunity for exploration of the Engineering Design Process, with the unwritten expectation that a parent or an adult would actually complete the project. Additionally, at no time were our children ever in a school setting that actively encouraged them to perceive themselves as engineers and capable of solving real-world problems potentially supporting false stereotypes of engineers. It is for these reasons that we seek innovative curriculum that begins to address STEM, and in particular, engineering through a multicultural lens. SUMMARY The search for a transformed STEM curriculum for elementary students through the lens of multicultural education led us to EiE. While we did not transform an existing curriculum, we believe that EiE stands out as a true exemplar of a transformed curriculum by addressing multicultural education elements such as prejudice reduction, equity pedagogy, and content integration. Students such as Serena and her peers can and should have access to engineering experiences. EiE supports the development of self-efficacy in students of all backgrounds and ability levels. Increased access allows teachers to address the stereotypes in STEM fields. Teachers can rest assured that because EiE is well-researched and has been implemented in diverse settings over time, they are choosing and putting into action a pedagogical package well aligned with strong engineering connections, excellent context, and significantly, the tenants of multicultural education. REFERENCES Banks, J. (2004). Multicultural education: Historical development, dimensions, and practices. In J. A. Banks & C.A. McGee Banks (Eds.), Handbook of research on multicultural education (second edition, pp. 3–29). San Francisco, CA: JosseyBass. Cunningham, C. (2009). Engineering is elementary. The Bridge, 30(3), 11–17.

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Cunningham, C. M., & Lachapelle, C. P. (2011). Research and evaluation results for the Engineering is Elementary project: An executive summary of the first six years. Boston, MA: Museum of Science. Dixon, J. C., & Rosenbaum, M. S. (2004). Nice to know you? Testing contact, cultural, and group threat theories of anti-Black and anti-Hispanic stereotypes. Social Science Quarterly, 85(2), 257–80. Howden, L., & Meyer, J. (2011). Age and sex composition: 2010. Washington D.C.: U.S. Census Bureau. Retrieved from http://www.census.gov/prod/cen2010/briefs/ c2010br-03.pdf Katehi, L., Pearson, G., & Feder, M. (2009). The status and nature of K-12 engineering education in the United States. The Bridge, 39(3), 5–10. Moffett, G., Weis, A., & Banilower, E. (2011). Engineering is elementary: Impacts on students historically-underrepresented in STEM fields. Chapel Hill, NC: Horizon Research. National Academy of Engineering. (2004). The engineer of 2020: Visions of engineering in the new century. Washington, DC: National Academies Press. National Center for Science and Engineering Statistics (NCSES) (2015). Women, Minorities, and Persons with Disabilities in Science and Engineering: 2015 Special Report National Science Foundation (NSF) Number 15–311. Arlington, VA: National Science Foundation. Soldner, M., Rowan-Kenyon, H. T., Inkelas, K., Garvey, J., & Robbins, C. C. (2012). Supporting students’ intentions to persist in STEM disciplines: The role of livinglearning programs among other social-cognitive factors. The Journal of Higher Education, 83(3), 311–36. Tang, M., & Russ, K. (2007). Understanding and facilitating career development of people of Appalachian culture: An integrated approach. The Career Development Quarterly, 56(1), 34–46.

Part V

TECHNOLOGY

Chapter Eleven

Multicultural Technology Education The Need to Teach Digital Technologies to All Students Janessa Schilmoeller, Lori Griswold, and Neal Strudler

In our teaching settings we are working to use technology to bridge so-called cultural divides not just in response to experiences that we have with our diverse students, but proactively, to teach about complex sociopolitical issues that exist in classrooms, schools, homes, neighborhoods, and more broadly. We also use technology to cultivate diverse student interest in and prowess with technology broadly considered. What follows in this chapter are two stories that describe our technology-related teaching experiences and then discussion of the implications of those experiences for multicultural curriculum transformation in technology education. In this latter regard, this chapter is unlike all of the other chapters in this volume. This is because the field of technology operates somewhat differently where multicultural educational issues are concerned. Technology use across the curriculum can be used in manners that support or inhibit all student’s academic engagement and learning outcomes, and access to technology education can advance or impede educational and professional successes for all students. In both instances, the stakes are highest for those already underserved. This chapter engages both of these challenges by offering teaching examples, but it goes further in discussing the crucial role that transformative technology education can play in schools and society. JANESSA’S TEACHING STORY: A STEP TOWARD SUCCESS A fourth grade teacher colleague at my small private elementary school approached me to ask a favor: Could I help her students type letters to their pen205

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pals in Japan during my technology class? Of course, I agreed. The pen pals were students in an elementary school one of her students had attended before moving to the United States. After typing the letters, students used the Internet to translate their letters into Japanese. As I walked around the computer lab, I overheard a few white American students laughing about the way their Chinese words looked on the screen. Upon hearing the comments, a Japanese American student in the class caught my attention with an uncomfortable look. I walked over to the white American students and asked what they were laughing about. One of the white American students said, “Look how crazy this Chinese writing looks!” I looked at his work; he was indeed using the correct Japanese tool for translating. I asked the boy, “Which language are you using to translate?” He looked up at the screen and replied “Japanese.” So, I asked, “Why did you say Chinese before?” He chuckled and said he forgot. I asked the boy to double check his translation website to make sure he was using the correct language. As I continued to observe translation exercise, I heard the same white American students commenting about the Chinese characters again. This time, the Japanese American student who previously caught my attention called me over and asked, with a sense of urgency in her voice, “Are they using the wrong site? Please make sure they use the correct language for their letters!” To the same white American boy with whom I had spoken previously I said, “I heard you talking about Chinese characters again. Did you check to make sure you are using the correct translation page?” The boy replied, “Oh yeah, it’s Japanese. They’re basically the same thing.” So, I asked, “Why do you think they are the same?” He said, “Because they look the same.” While there were only a few minutes left in class, I did not want to let students leave without addressing this incident. I knew if I let it go I would be, at least inadvertently, reinforcing the beliefs the white American boy at focus in the incident expressed about Chinese and Japanese characters being “the same.” This would, again at least inadvertently, send a message to the Japanese American student that these beliefs—cultural stereotypes—are not recognized or contested in my classroom. Accordingly, during the last ten minutes of class, I asked all of the students in the classroom to look at the board so that, as a group, we could view some of the other languages available for translation. By displaying multiple translations of the same sentence, I was able to engage all of the students, including the white American students and boy referenced previously, in comparing and contrasting the visual representations of various languages. When several students weighed in on the differences they noticed in Chinese and Japanese characters, the Japanese American student visibly relaxed in the classroom; her body language became more open and she began sharing, unprompted, her own observations of the differences in each language’s characters. As the class came to a close,



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I encouraged the students to include their contrasting language observations in their letters to their pen pals and ask for more information about Japanese uniquenesses. In the classes following this relatively short discussion about language differences, the Japanese American student’s behavior in class stayed more relaxed and open, and she continued being more engaged in class discussions; in sum she became more motivated in her school work. Though this discussion may not have been the only catalyst for this student’s behavioral change, it was clearly a factor in this change. After that day she remained more engaged with classroom activities, and more committed to learning in a way that I had not previously seen. As a result, she was recognized as the “Technology Student of the Month” at our school-wide awards ceremony. This brief language discussion also prompted the Japanese American student’s mother to reach out to thank my fourth grade teacher colleague and me for helping with the pen-pal letter writing project, and to offer to review the Japanese translations before the letters were sent. Had I let the linguistic and related cultural stereotyping of Chinese and Japanese go unaddressed, the classroom environment in which my Japanese American student was able to thrive would, likely, not have emerged. Though time limitations, as well as limitations in my linguistic background knowledge prevented me from providing a more thorough, thus potentially more transformative lesson to my students on the grammatical, historical, and structural differences between various Asian languages, I was at least able to lean-in to the majoritized students’ comments in a way that made a marginalized student feel supported. This example illustrates that it does not take a multicultural educational expert to create room for and then actualize thoughtful classroom conversation about biases; rather, it simply takes an educator who is willing to ask questions that will prompt students to think critically about their own limited and erroneous assumptions about others and the world beyond their own experiences. Many teachers stop, avoid, or ignore stereotypical, biased, prejudicial, or other problematic statements in the classroom; however, by leaning-in to the discomfort, challenge, and/or controversies these statements bring with then—in whatever way they know or can imagine will interrupt the discriminatory impact of such statements and affirm the cultural and linguistic diversity of their students—teachers become multicultural allies. LORI’S TEACHING STORY: WHERE ARE THEY? When I look at the students in my classroom, I see an almost even ratio of female and male students, a majority of Latina/Latino students, fairly equal numbers of African American, white American, and Asian and Asian

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American students, and smaller numbers of students from other ethnic backgrounds. I teach computer literacy at the middle school level, and I often wonder what career paths these students of mine will choose. Will they choose a technical career? Will digital technologies encourage them to pursue a technical career? It is my job to make sure that they have the knowledge and skills they need to pursue a technology-related field. Prior to becoming a teacher, I was a software engineer for over two decades. I found my technical path while I was in college, at a time when digital literacy was only for those who chose to pursue a career in a technical field. My path involved computers, computer science specifically, which, at the time, involved learning computers, how to program them to do or perform specific tasks for specific reasons. Since then, the world has gone digital, and everything in our lives has been affected by digitization. As a result, I know I must prepare my students for postsecondary studies or the workforce when they graduate high school and that, either way, the digital world figures prominently in their preparation. Depending on their teachers and/or their high schools, students across the country may or may not have the opportunity to learn about many of the digital technologies that are prevalent today. In my school district, one of the largest and persistently low performing in the United States, the only technology requirement for high school graduation is computer literacy (i.e., touch typing, word processing, spreadsheet use, database interface, and Internet use). Of course, some schools in the district offer more in-depth digital technology courses (i.e., computer programming, computer aided drafting and design [CAD], and graphic arts), these are usually (though not always) specialty (magnet, career and technical education) schools which only select students may attend. While computer technology courses are taught at some of the “regular” high schools in my district, there seems to be little interest among the student population at large in enrolling in them. Even knowing that there is and will continue to be a high demand in the workforce for employees who possess these technological skills, most students seem not to want to enroll. In Stuck in the Shallow End: Education, Race, and Computing (2011), Margolis examines the typical profile of the software engineer (white, male, upper middle class, etc.), and how that profile may be a deterrent to many students entering this field. Research in multicultural education reinforces this deterrent—it is hard to choose a career in which you don’t see anyone who looks like you (Nieto & Bode, 2012). When I look back on my career as a white female software engineer, I recognize that I am a bit of an outlier. Though I was surrounded by white male engineers, I did not think much about it. There were other female en-



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gineers, but we were certainly the minority. I recall only African American male engineers, and two engineers, one female and one male, with Spanish surnames, but who were monolingual English speakers. I do not recall any Asian American engineers, which could be a function of geopolitics at the time given that I worked in an area of computer engineering having to do with security concerns. Margolis explains the underrepresentation of people of color in software engineering in a number of ways, the most significant of which is them being inadvertently or, worse, purposefully left out of programs. This structural discrimination caught my attention, which is why I am a teacher today—I can make sure that the computer science programs of which I am a part in my district, intentionally and actively recruit and retain students of color. CONNECTING TECHNOLOGY AND MULTICULTURAL EDUCATION Both Janessa’s and Lori’s stories connect technology with multicultural education through an emerging multicultural curriculum transformation process. At a basic level, multicultural education centers the cultural, ethnic, and other identities of all students into the curriculum in ways that: 1) affirms their identities; 2) connects their identities to systems of power, privilege, oppression, and discrimination; and, 3) works to bring about equity for all measure in terms of access and outcomes. Accordingly, “affirming” students’ identities does not mean hosting an international potluck or a cultural dance night, but rather engaging “students’ culture as a bridge to the dominant culture” via culturally responsive pedagogy (Nieto & Bode, 2012, p. 173). Though this largely additive approach to multicultural education is still narrow in scope, it provides tangible opportunities for teachers to make connections between the curriculum and the experiences of culturally and linguistically diverse students. Referred to by Sleeter (1996) as a “Teaching the Culturally Different” approach to multicultural education, the focus is on raising the achievement of students of color through “culturally compatible education programs” (p. 6). While making cultural connections is important in affirming all students, especially students of color, this basic approach illustrated in Janessa’s and Lori’s stories fails to recognize multicultural education as a “complex educational reform movement” rather than a “prescribed script” (Nieto, 1994, p. 1). With this more comprehensive understanding of multicultural education, in addition to affirming the strengths of all students and providing all students with culturally relevant and responsive educational experiences, a truly

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transformative approach to multicultural education in the technology must confront structural inequality, promote critical thinking, and support students as agents of social change (Nieto & Bode, 2012, p. 12). MULTICULTURAL EDUCATION AND DIFFERENTIATION: REACHING ALL STUDENTS AND AFFIRMING CULTURAL AND LINGUISTIC DIVERSITY Web 2.0 enables nontechnically trained Internet users to generate and use their own web-based content with most other content, and to interact, including collaboratively, with all other users through social media. The constant evolution of Web 2.0 provides robust opportunities to bridge gaps in experiences of students from structurally advantaged and structurally disadvantaged communities in the classroom, in increasing the quality of learning for all students across the curriculum. “Imagine trying to have students grasp complex ideas about racism, sexism, or culture by simply reading a textbook. . . . Now imagine using a “textbook” that blends reading, video, music, and pictures” (Sleeter & Tettegah, 2002, p. 4). Online blogs, videos, discussion boards, podcasts, video conferencing, and other multimedia resources can be used to help students grasp complex concepts through a critical lens. For instance, a unit on technological advancements in aviation history might assume that all students in the classroom have seen or flown on an airplane and include images that reveal this assumption (e.g., of a white male pilot and largely white middle class passengers on a commercial airplane). Students from communities historically barred from the aviation industry, who have experienced discrimination when flying, and/or for whom flying is cost prohibitive may not be able to connect with images represented in the aviation history lessons. Accordingly, a teacher could use recorded oral histories and accompanying multimedia artifacts to provide this broader aviation history in order to ensure all students can engage the curriculum from the outset with a similar understanding of air travel; this precludes those who have previously traveled on an airplane from having an uncontested curricular advantage. Teachers may also use technology to provide a more accurate representation of the roles that diverse racial, ethnic, and gender groups played in aviation history. WebQuests can be useful tools in guiding students to identify important events in aviation history through the lenses of various groups’ experiences with aviation over time. Technology can also serve as an important tool for students who speak English as a second language (Sleeter & Tettegah, 2002). Through technology, students can translate documents (as happened in Janessa’s story), view



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historical films in various languages, process sentences in multiple languages, and even research the role of various languages in the evolution of any given topic. For example, a linguistically diverse student may be able to connect with a particular unit on aviation history by researching the ways in which different airlines accommodate diverse language speakers on both domestic and international flights around the world. The tendency in US education is to frame students whose first language is not English as the students who are language learners, often in ways that render their first languages invisible. In fact, all students are language learners, and those who are monolingual speakers of English may be the ones who most need to learn the value of language and bi- and multilingualism in expressing and receiving ideas in myriad ways, and especially with heightened critical acumen (e.g., being able to interpret the same sound in more than one way). In beginning to differentiate curriculum, teachers must keep in mind that to meet the needs of all students, all students must be supported to “learn at their own rate, navigate according to their own questions, and make connections among ideas” that are situated in their own cultural and linguistic contexts (Sleeter & Tettegah, 2002, p. 5). Accordingly, technology can also be used in the classroom to bridge cultural divides by providing white students with alternative narratives about complex sociopolitical issues. For example, fifth graders in a private school might typically spend several weeks on pre-packaged unit about the rain forest in which they study animal habitats and the effects of deforestation. Atypically, these fifth graders might engage age-appropriate e-books, online videos, and teacher-guided WebQuests to compare and contrast the home and school lives of children who live in the rain forest with their own lives. Further, these fifth graders could learn to facilitate themselves in a critical discussion about how the Internet is used by indigenous communities in the Amazon to fight illegal logging. In this atypical example, students develop 21st century technology skills, while simultaneously learning to challenge stereotypes about people who live in rain forest communities, and to think more critically about themselves and people like them. At the end of the unit, students could create an educational video to teach friends and families about what they had learned, the presentation of which could serve as an effective assessment tool. CLOSING THE DIGITAL DIVIDE: TOWARDs A MORE INCLUSIVE TECH WORLD While instructional technology can be an important equalizer the classroom, solely relying on useful websites, software programs, wikis, blogs, and mul-

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timedia fails to address the greater issues of inequity plaguing technology education (Gorski, 2009). Tech-giant Google released, for the first time in May 2014, the demographic makeup of its workforce. The numbers are clear: Google’s workforce is white or Asian and male. Seventy percent of the workforce is male, while an overwhelming majority, 91%, of employees identify as White or Asian (para. 2). When the statistics are broken down by sector, the inequities become even more clear: 83 percent of Google’s tech workers are male, and 94% are White (60%) or Asian (34%) (para. 2). Unequal access to technology fields begins at the classroom level. According to the National Center for Education Statistics, some 97%t of teachers have one or more computers located in the classroom, while only 40% report using computers often in the classroom during instructional time (p. 5). Teachers reported only 29% of their students use computers often during instructional time (NCES, 2010, p. 6). Though schools across the country have launched “one-to-one” iPad initiatives, teachers must be thoughtful about how technologies are being used, by whom, and for what ends. In fact, Gorski (2009) argues that “these technologies, as they are being employed, appear to be contributing to inequalities more than disrupting them” (p. 349). The point of concern for educators to consider is whether initiatives to improve access to technology is being implemented in a meaningful way. Noncritical technology integration threatens to exacerbate the digital divide; that is, the gap created by the disconnect between technology use and application by members of various social and ethnic groups, particularly in terms of racism, language discrimination, classism, sexism, ableism in technology (Brown, 2004). Though providing access to computers and other technological tools to members of marginalized communities is a core step in closing the digital divide, merely providing students from these communities with such equipment does not change the fact that the curriculum being taught through these digital devices does not represent the diverse identities and needs of these students. As Gorski (2001) explains, it is not enough to critically analyze the individual technology resources we use to promote inclusivity, rather how the resources being used must likewise be interrogated. “Are [the technologies] contributing to education equity or supporting current systems of control and domination of those groups already historically privileged in the United States education system (such as White people, boys and men, first language English speakers, and able-bodied people)?” (Gorski, 2001, p. 1). Research on socioeconomic status and technology use reveals that “students in high-poverty schools are more likely to use computers and the Internet for rote learning whereas their peers in low-poverty schools use them for higher-order thinking activities” (Becker, 2000; Judge, Puckett, & Cabuk, 2004). Controlling for factors such as education and income, Mossberger,



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Tolbert, and Stansbury (2003) found that African American and Latinx technology users are less likely to possess the same computer and Internet skills as their white counterparts (Gorski, 2009). Technology integration without meaningful multicultural curriculum transformation may only contribute to the unequal power structures within the tech industry. TOWARD A TRANSFORMATIVE CURRICULUM At the heart of multicultural education lies a commitment to justice, equality, and dignity of all individuals (Nieto & Bode, 2012). Originally grounded in the Civil Rights struggle for equality, multicultural educators mobilize students in this struggle and actively resist the oppressive social relationships present within education (Sleeter, 1996). Unfortunately, the meaning of multicultural education as a tool of social activism has been depoliticized over the years through the “holidays and heroes” approach to multiculturalism. When technology and multicultural education are used in an additive way, students develop simplistic relationships with content that fail to address larger issues of student disengagement (Brown, 2004). Effective multicultural technology education engages students in abstract and complex problem solving, where students develop competencies to transform institutions and communities (Brown, 2004; Nieto, 2000). Turning the tide on digital inequity starts with a critical multicultural education framework that repoliticizes the field of technology education (Gorski, 2009). THE CODE.ORG MOVEMENT The Code.org (2015) movement teaches students not only how to consume technology, but how to create technology. Code.org teaches critical problem solving, sequencing, and teamwork skills. Google, DropBox, Twitter, Microsoft, Apple, and many other big-name tech companies have joined the movement: 1) to prevent the expected million job shortage in the tech industry; and, 2) to diversity the ranks in light of recent criticism of its predominately white male workforce. Code.org offers free curriculum and professional development to K-12 teachers, and works with universities, including the Massachusetts Institute of Technology, Stanford, and Harvard, to offer free online courses in computer programming, as well as with Google to offer other free online programs, some of which are grant supported for teachers who teach online computer programming based on the number of students who pass.

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One of the goals of the Code.org movement is to increase diversity in computer science based on dissemination of information about the profession and who can be successful in it. Posted on its website is research documenting that, for example, female and black and Latina/Latino students who take Advanced Placement (AP) computer science courses in high school are from 7-10 times more likely to major in it in college (Morgan & Klaric, 2007, p. 9). If Code.org and other followers of the movement are truly committed to closing the opportunity gap in computer science, they will need to 1) increase access to technology in schools and 2) implement a multicultural code curriculum for the increasingly diverse student population that appears to be participating in these programs. Learning to code can help students, particularly students of color, transform their lives through the development of real world technology applications pertinent to their communities (i.e., Black Girls Code). Instead of relying on software programs and mobile applications designed largely by and for the dominant culture, students from marginalized backgrounds are starting to see their role in changing the future of technology. For example, the code.org curriculum on “exploring computer science” utilizes real-world connections that motivate students to see the purpose of their work and how technology matches up with their natural strengths, talents, and interests while promoting technology as a tool for democracy and democratic participation through communication and open access. The “Hour of Code” curriculum provides easy entrance points to technology, in 60 minutes, that has been used in over 180 countries and has been accessed by over 110,000,000 users and engaged by over 15,000,000 children from both overrepresented and underrepresented populations. Over 80 million people worldwide participated in the code.org second annual “Hour of Code” in December 2014, during which YouTube senior vice president, Susan Wojcicki spoke what has become the Code.org movement philosophy: “If you can create technology, you can change the world” (n.a., 2015, para. 1–3). Through a process of demystifying code and access to technology, all students have the ability, from their start in school, to value their role as a creator of knowledge in an ever-increasingly technological and glocal world (Brenner, 1998; Wellman, 2004). UNDERSTANDING AND ELIMINATING THE DIGITAL DIVIDE The digital divide can be understood as both inequality and inequity in access to technology, and to information embedded in technology, where access and information are leveraged disproportionately across social classes to favor



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the wealthy (Selwyn, 2004). Today, while computers have infiltrated almost every occupation, and technology is ever present in the lives of most citizens, inequity in access, content, and, thus, use, continues to create new, and widen existing, gulfs in technology-related learning and career opportunities. While the trend toward everything technological gives students no real choice but to learn the technology necessary for them to perform their current or future jobs, issues of access and equity remain persistent obstacles to providing all students with the proper training needed to optimize their use of technologies. Instead of being seen as a right of students and a responsibility of educators to bridge gaps in access, content, and use, technology in schools with historically underrepresented students (race, class, ethnicity, for example) is often used as a reward for “good” (conforming) behavior and punishment for “bad” (nonconforming) behavior, despite the fact that technology industries thrive on divergent thinking. Instead, all students should be required to use technology in complex ways so that they are prepared for careers beyond high school that demand understanding of technology as well as the information embedded into the technology. If schools can use technology to test students, they can use it to teach them. According to the US Bureau of Labor Statistics (2013), the need for software developers, for example, will increase as much as 30% by the year 2020 (para. 1). Software developers create applications for almost everything we use in our daily lives, such as cellular telephones, messaging programs, automobiles, medical equipment, alarm monitoring systems, among many other things. However, the United States currently outsources most of its software development needs to developers in other countries because the domestic software development workforce is woefully inadequate. The digital divide contributes to the shortage in this workforce. For exactly this reason, the Code.org movement, discussed previously, emerges as a way to alleviate the enormous void in the software developer pool in the United States. Gorski (2001) articulates a multistep process for eliminating the digital divide through multicultural curricular transformation in technology education and in the use of technology across the curriculum: Teachers who choose to engage this process must critique technology-related inequities in the context of larger educational and societal inequities, keeping in mind that those groups most disenfranchised by the digital divide are the same groups historically disenfranchised by other mainstream curricular and pedagogical practices. Teachers must critically examine not only who has access to computers and the Internet, but how these technologies are being used by various people and identity groups or by those teaching these people and groups. Teachers must also broaden the significance of “access” beyond that of physical access to computers and the Internet to include access to non-hostile,

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inclusive software and Internet content, and to support and encouragement to pursue and value technology-related fields. Teachers must consider the larger sociopolitical ramifications of, and socio-economic motivations for, the expanding significance of information technology, not only in schools, but in society at large, and how the growing merger of cyber-culture with wider U.S. culture privileges those who already have access in the broadest sense. Likewise, teachers must confront propaganda, like commercials portraying children from around the world using state-of-the-art technologies, that lead people to believe that these technologies are available to everyone, everywhere, under any conditions. Further, teachers must reject as inadequate any program that purports to “close” the divide only by providing more computers and more, or faster, Internet access, to a school, library, or other public place, and any solution that aims to “close” and not “eliminate” the divide. Finally, teachers must also conceptualize the elimination of the digital divide as those actions that lead to, and maintain, a present and future in which all people enjoy: 1) equitable access to information technology including software, computers, the and Internet; educational pursuits in technology-related fields including mathematics, science, computer science, and engineering; and, career pursuits in technology-related fields including mathematics, science, computer science, engineering, and information technology; and, 2) an equitable role in determining and monitoring the sociocultural significance of computers and the Internet and the overall social and cultural value of these technologies. (para. 9–23)

Increasingly, the digital divide presents itself more as gulf or canyon relative to students’ equitable access to, use of, and advanced engagement with technology. Teachers who engage Gorski’s process can play and important role in moving technology education forward in ways that eliminate the divide. CONCLUSIONS There are successful programs designed to introduce digital technologies to students in secondary education. For example, the Exploring Computer Science (2013) program developed by the University of California, Los Angeles School of Education and Information Studies is designed to introduce computer science to traditionally underserved high school students (i.e., African American, Latina/Latino, female) in the Los Angeles Unified School District. The success of this program is evidenced in these students increased enrollments in these courses. If students, especially students of color, can be introduced to digital technologies even earlier in their education, they will be more like to pursue a career in this area.



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In order to teach the latest digital technologies, updated computers, software and networks need to be in place, serviced, and refreshed regularly in an environment centered on universal access and equity. Instructors for the digital technologies are hard to come by, as instructor remuneration is not as high as it would be outside of educational contexts. As a result, sometimes instructors are self-taught and are only one step ahead of their students. Additionally, students’ study of digital technologies must be centered in their own experiences; for example, related to their educational and economic realities. Today, most school districts are financially drained because they are putting their monies toward endeavors like high-stakes testing, special education, and other special population curricula, and sports programs. The irony is that those efforts are often marketed as an attempt to reform a system in crisis in order to provide more equitable education to all students. However, the costs of so-called educational reform leave few resources for the actual engagement with rigor education, in this case rigorous technology education, meaning in universally accessible manners, that would actually eliminate the gaps that the testing and educational reform industrial complexes have created (Fasching-Varner, Mitchell, Martin, & Bennett-Haron, 2014). Using these educational and economic realities as the point of reference for students to learn how to use technology to investigate how these realities impact their own experiences, including the quality of their own technology education, might be a provocative place to chart a different path forward. REFERENCES Becker, H. (2000). Who’s wired and who’s not: Children’s access to and use of computer technology. The Future of Children: Children and Computer Technology, 10(2), 44–75. Brenner, N. (1998). Global cities, glocal states: Global city formation and state territorial restructuring in contemporary Europe. Review of International Political Economy, 5(1), 1–37. Brown, E. L. (2004). Overcoming the challenges of stand-alone multicultural courses: The possibilities of technology integration. Journal of Technology and Teacher Education, 12(4), 535–59. Code.org. (2015). [Graphic illustration of computer science statistics]. Computer science: America’s untapped opportunity. Retrieved from http://code.org/stats Exploring Computer Science. (2013). Our partnership history. Retrieved from http:// www.exploringcs.org Fasching-Varner, K.J., Mitchell, R.W., Martin, L.L., & Bennett-Haron, K.P. (2014). Beyond school-to-prison pipeline and toward an educational and penal realism. Equity & Excellence in Education, 47(4), 410–29.

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Google. (2014). [Graphic illustration of workforce demographics]. Making Google a workplace for everyone. Retrieved from https://diversity.google/commitments/ Gorski, P. C. (2009). Insisting on digital equity: reframing the dominant discourse on multicultural education and technology. Urban Education 44(3), 348–64. Thousand Oaks, CA: Corwin Press. Gorski, P. C. (2001). Multicultural education and the digital divide. EdChange.org. Retrieved from http://www.edchange.org/multicultural/papers/edchange_divide. html Judge, S., Puckett, K., & Cabuk, B. (2004). Digital equity: New findings from the early childhood longitudinal study. Journal of Research on Technology in Education (36)4, 383–96. Margolis, J. (2011). Stuck in the shallow end: Education, race, and computing. Cambridge, MA: MIT Press. Morgan, R., & Klaric, J. (2007). AP students in college: An analysis of five-year academic careers (research report no. 2007–4). New York, NY: The College Board. N. A. (2015). If you can create technology, you can change the world. Praesidium. Retrieved from http://www.praesidium.it/Articoli/The-Hour-of-Code. aspx?feed=articles Nieto, S. (2000). Placing equity front and center some thoughts on transforming teacher education for a new century. Journal of Teacher Education, 51(3), 180–87. Nieto, S. (1994). Lessons from students on creating a chance to dream. Harvard Educational Review, 64(4), 392–427. Nieto, S. & Bode, P. (2012). Affirming diversity: The sociopolitical context of multicultural Education, (sixth Ed.). Boston, MA: Pearson. Selwyn, N. (2004). Reconsidering political and popular understandings of the digital divide. New Media & Society, 6(3), 341–62. Sleeter, C. E. (1996). Multicultural education as social activism. Albany, NY: SUNY Press. Sleeter, C., & Tettegah, S. (2002). Technology as a tool in multicultural teaching. Multicultural Education, 10(2), 3–9. National Center for Education Statistics (NCES). (2010). Teachers’ use of educational technology in U.S. public schools: 2009 (NCES 2010–040). Washington, DC: Institute for Education Sciences (IES), U.S. Department of Education. U.S. Bureau of Labor Statistics. (2013). Occupational outlook handbook. Retrieved from http://www.bls.gov Wellman, B. (2004). The glocal village: Internet and community. Ideas: The Arts & Science Review, 1, 26–29.

Part VI

MATHEMATICS, SCIENCE, ENGINEERING, AND TECHNOLOGY

Chapter Twelve

Coming Out of the Lab Closet Queering STEM Education for Student Success and Well-Being Allison Mattheis, Jeremy B. Yoder, and Dixon Perey

INTRODUCTION On average, about 3.5% of people in the United States identify as lesbian, gay, bisexual, or transgender, a percentage that varies by state but not significantly by region (Gates & Newport, 2013). Furthermore, approximately 8 million people in the nation’s workforce identify as lesbian, gay, bisexual, transgender, and/or queer (LGBTQ) (Pizer, Sears, Mallory & Hunter, 2012). Undeniably, LGBTQ individuals have gained legal and social protections at an increasing rate over the last several decades and polls suggest that younger generations are increasingly knowledgeable of and tolerant toward nonbinary gender identities and a range of sexual orientations (Pew Research Center, 2013). With this being said, there is still quite a bit of work to be done in developing curriculum at all educational levels that is inclusive of the LGBTQ community. The purpose of this chapter is to share the results of a national survey that was administered to LGBTQ-identified individuals working in STEM fields as advanced graduate students, faculty members, researchers, and industry professionals. By examining the experiences of a large sample of respondents through an online survey and conducting in-depth interviews, we have identified common themes about participants’ experiences in secondary and postsecondary education that are related to the inclusion and noninclusion of multicultural curriculum transformation. In this chapter, we highlight factors that contribute to developing welcoming spaces for teaching and learning for students of multiple identities, and present cautionary messages about the 221

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impact of negative experiences early in students’ careers that contribute to underrepresentation of diverse, in particular, LGBTQ backgrounds in STEM professions. This chapter also explores the possibility of “queering” national standards that are currently influencing shifts in high school curricula in science, technology, engineering, and mathematics. Last, the importance of expanding educators’ understandings of diversity to encompass the complexity of individual students’ identities, and the benefits offered to STEM professions by a more diversified and inclusive membership, are emphasized throughout. WORKING DEFINITIONS We have used the American Psychological Association’s (2011) definitions to distinguish between the terms sex, gender, gender identity, and sexual orientation. Sex refers to a person’s biological status with regard to external characteristics and genetics. Gender refers to the attitudes, feelings, and behaviors that a given culture associates with a person’s biological sex. Gender identity refers to an individual’s sense of oneself as male, female, transgender, or somewhere along this spectrum or not identified with any particular gender. Gender expression is how individuals of any externally assigned gender or internal identity choose to display their gender through clothing or behavior. Sexual orientation references to whom a person is sexually or romantically attracted, if any. Typically, the letters in LGBTQ are defined as follows: (L) lesbian refers to people who identify as women who are romantically and/or sexually attracted to other people who identify as women; (G) gay refers to people who identify as men who are romantically and/or sexually attracted to people who identify as men, and is also sometimes used to encompass lesbians; (B) bisexual refers to people identified as women or men who are attracted to both women and men; (T) transgender (sometimes shortened to “trans”) is a term that describes a person whose assigned biological sex and gender do not match their internal identity—transgender people may identify as straight, lesbian, gay, bisexual, or any other sexual orientation; and (Q) queer is commonly used as an umbrella term to describe individuals who identify in ways that are not heterosexual or cisgender, a term that describes people whose internal gender identity is aligned with their externally assumed gender and biological sex. We chose the acronym LGBTQ for the sake of familiarity and brevity, but acknowledge that other terms exist. We do not wish to exclude any identities or imply that gender and sexuality are fixed categories. Rather, we are



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broadly referring to wide range of individual identities that are considered “other” in terms of gender identity, gender expression, sexual orientation, and biological sex characteristics. Queer, as an adjective, is a reclaimed word that has been used as a slur to denigrate LGBT communities, but is increasingly embraced by younger generations. In this chapter, we use the word queer when describing people to refer a diverse range of individual and group identities. Queer as a verb refers to a deliberate shift in understanding of what is considered “normal” or “typical” in any aspect of human behavior. The act of queering an educational space encompasses not just the deliberate inclusion of LGBTQ identities in conversation and curriculum, but challenges normative perspectives about all sorts of topics and encouraging teachers and learners to recognize how taken for granted assumptions change over time and can be disrupted. Heteronormativity is a term that refers to the way society prioritizes gender conformity and male-female romantic and sexual relationships as “normal,” thus stigmatizing and delegitimizing other types of identities or relationships. As Warner (1991) states, “Even when coupled with a toleration of minority sexualities, heteronormativity has a totalizing tendency that can only be overcome by actively imagining a necessarily and desirably queer world” (p. 8). Although different from homophobia, which refers to outright discrimination or hostility toward queer people, heteronormativity permeates social life and must be interrupted in order to create truly multicultural educational spaces. CONCRETE EXAMPLES IN STEM MULTICULTURAL TRANSFORMATION: THE PRACTICE Curricular transformation and pedagogical change are processes rather than immediate shifts, and are informed by both changes to the “what” that is taught in classrooms as well as the “how.” Approaching such efforts as longterm goals is important to achieving authentic overall changes to practice rather than adopting individual strategies as stopgap measures. A potential paradox exists in the way that science is seen as an exploration of natural phenomena, considering multiple possibilities, and pursuing new ideas but science education is often portrayed as focused on procedure rather than process, and facts rather than ideas. Reinforcing rigid expectations with little room for error in terms of experimental design and sequence can also lead to classroom environments that discipline students’ personal expression as well. Research has shown the importance of student engagement for academic success in school (Klem & Connell, 2004) and the value of in-depth collaborative experiences that challenge students to develop conceptual

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understanding of content objectives (Johnson & Johnson, 1989). Learning spaces in which different ideas and multiple problem-solving strategies are valued are also spaces that allow for acceptance more broadly, and being open to alternative explanations and viewing issues from different perspectives are qualities valued by theoreticians and research scientists. Curricular guidelines also impact classroom environment by either emphasizing regimented factual recall or fostering creative critical thinking. If implementation of the Common Core State Standards (CCSS) becomes synonymous with using scripted curricula without considering local context or connecting teaching to students’ lived experiences it will represent a missed opportunity. In contrast, a true “queering” of the CCSS in STEM subjects is aligned with the goals of multicultural education which is to create more inclusive and welcoming spaces for students from diverse backgrounds. Indeed, the cross-cutting concepts highlighted in the Next Generation Science Standards (NGSS) are rooted in inquiry—for example, asking questions, engaging in argument from evidence, obtaining, evaluating, and communicating information. By encouraging students to expand their understanding of what is normal, challenge accepted explanations for why things are the way they are, and seek alternative ways to examine the world, queered classrooms become spaces for exploration of self, community, and content. Including LGBTQ People in Curricula Including examples of LGBTQ individuals that have been successful in STEM fields is important in developing curricula, and can also send messages to students that disrupt stereotypes that students might hold about queer people. One gay engineer told us “I think it’s unfortunate, but I think it is assumed that in general, queer people are partiers who don’t take academic stuff that seriously.” The value of acknowledging queer identities exist—and exist in science and math—in a matter of fact way can be impactful in ways teachers may not realize. A lesbian biologist recalled that “nobody talked about being gay or lesbian in my high school, except [to say] that it was not considered a good thing.” Others described efforts to compensate for discomfort with their gender or sexual orientation as a teenager by overachieving as students or athletes in order to dispel suspicions that they may be gay. Such behaviors may help individuals achieve success for a period of time but can have long-term psychological costs if this behavior sacrifices acknowledging fundamental truths about one’s identity for the sake of external approval. It is important here to emphasize that when teachers do not mention LGBTQ individuals or identities, this lack of visibility is not the absence of a message. Rather, the failure to be explicitly inclusive sends a signal that LGBTQ



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people and identities are supposed to remain invisible or are unacceptable in the scholarly environment. Addressing Teacher Behaviors Expanding educators’ understandings of what a “good scientist” looks like means imagining diversity much more broadly than race, ethnicity, and language to include ability, gender identity, and sexual orientation. We also find, however, that hardly any respondents described the presence of at least one openly queer teacher or faculty member during their STEM studies. Part of this is attributable to a culture of silence about many aspects of personal identity in these fields; many participants described feeling pressure to separate their personal and professional lives. But such educational and workplace cultures reinforce white, heteronormative, Western approaches to investigation and knowledge construction, and therefore may actually stifle innovation and productivity. Efforts to create inclusive environments should take place at both the school and classroom levels. Sponsoring student groups such as Gay-Straight Alliances can also be ways for teachers to support student expression and promote acceptance within high schools. Consistent enforcement of antibullying policies across campuses can also reduce the amount of homophobic speech encountered by queer students on a daily basis. In the classroom, teachers can begin by noticing gendered and heteronormative vocabulary and introducing different terminology. For example, teachers can practice using gender neutral terms when addressing the class as a whole: “students, tenth graders, biologists-in-training, you all,” can all work just as well as “boys and girls” or “ladies and gentlemen.” More broadly, teachers can practice being less gendered in their categorization of students and instead focus on how each child communicates with the class, rather than concentrating on whether they call on boys or girls more frequently. Remembering that biological sex and gender expression are not the same and that contemporary science demonstrates the ways in which gender is a social construction that varies across context and is not tied to particular genetic makeups can be complex, but letting students tell you what names they choose to be called and terminology they assign to themselves can be more straightforward. Making a point to ask students what pronouns they use and feel most comfortable with at the beginning of the school year can signal that a classroom is a welcoming space for trans students and those with other gender identities. How teachers behave when they make a mistake with students’ names or pronouns can send an equally strong message; by apologizing, correcting oneself, and moving on with the lesson teachers can

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model how adults can change their behaviors and check their previous assumptions. Some seemingly subtle actions can have a big impact for students. One higher education instructor interviewed for the Queer in STEM study described writing “Happy National Coming Out Day” (a yearly event held in October) on the board as an opportunity to make it clear that he supported his queer students in class without interrupting his planned lesson or “making a big deal about it.” Even if students disclose a queer identity, they may not feel comfortable answering questions about their own coming-out process. Teachers should let students know they are a safe person to talk to if students want to share personal information. But teachers must also be careful not to share personal information about a student’s gender identity or sexual orientation with others unless the student has explicitly said that it is okay to do so. Addressing Student Behaviors Teachers can become more attuned to the ways in which “gender policing” occurs in student interactions and be conscientious about disrupting these moments and modeling respect for all expression of gender. When asked what he would do to improve the climate for himself as a gay scientist and make things more welcoming for people in his field, Jose said, With my magic wand I would break biases regarding gender expression and gender identity, so people can dress how they want, talk how they want, walk how they want and have it not be an issue.

Teachers must be vigilant to not let disrespectful or stereotypical language occur unchecked in their classrooms. When incidents do occur, use these as teachable moments to discuss why being an open-minded person is part of being a good scientist. A queer physicist who does outreach with high school students and educators reminds teachers that it is always better to do something and demonstrate that you are an ally than to ignore the use of homophobic slurs or discriminatory behaviors. Teachers have the ability (and responsibility) to interrupt bullying behaviors on the part of other students, and to pay attention to students who may be in need of additional supports. The Importance of Mentorship As a physical, emotional, and cognitive developmental stage, the teenage years are difficult for many people, and having additional caring adults in



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their lives at school is an essential part of many children’s safety net. For students that identify outside of gender binaries or are queer, the school context can sometimes be a source of discomfort or even a space that is physically hostile. Students who face a lack of acceptance or cannot openly express their identities at home or at school are at high risk for dropping out or engaging in risky behaviors. We urge educators to be intentional in selecting “promising” students to mentor—in order to avoid reproduction of the skewed demographics of those in upper level positions in STEM fields, mentors must be careful not to choose only those students that remind them of themselves as young people. Many high school teachers, like Brandon, work in positions where they are involved in developing pathways that specifically encourage students from underrepresented backgrounds to pursue careers in STEM. These secondary school experiences can serve as direct connections to postsecondary and professional success (GLSEN, 2015). Jon, a biologist and participant in our study, said that part of what initially drew him to science was the fact that “animals were a lot less confusing than humans” when he was in high school. The opportunity to explore summer research opportunities, however, helped him stay engaged in school and find a successful path to college. Knowing that they are supported as both scholars and individuals in high school can also help LGBTQ students deal with later challenges. Chris, an engineer and participant in our study, described his secondary and postsecondary experiences as extremely tolerant and how having developed a strong sense of self helped him confront a hostile and homophobic environment in his first job. Xavier, an additional participant in our study, completed a PhD in molecular biology and then left academia to teach high school biological and physical sciences because he wants to be an example of an out, black gay scientist because students need to see themselves mirrored in the people who present themselves as role models. Xavier believes mentorships dedicated to LGBTQ youth in STEM are important based on his own experience: I never saw another LGBTQ person reflected to me as a teacher in science until—Wow!—late college, early grad school. I didn’t see that [LGBTQ identity] in other people. Growing up I was operating as an outlier.

Along with Adam and other openly queer STEM professionals and teachers, Xavier reported that finding an authentic voice that embraced their multiple identities was key to their sense of purpose and fulfillment in their careers. High school teachers, including those that are not LGBTQ, can serve as key mentors in the development of successful young people.

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REFLECTION BRIDGE The study we completed in order to make the suggestions previous listed used an interdisciplinary, mixed methods approach to data collection, that paid particular attention to the ways that culture shapes individual and group identity development. In conceptualizing the Queer in STEM project, we drew on all our strengths and experiences as queer individuals and researchers as well as consideration of the resources available and the goals of the study. As coinvestigators we overlap in our interest in the consequences and impacts of openly identifying as LGBTQ in public spaces, but bring expertise from different fields of thought and study. Jeremy Yoder is an evolutionary ecologist studying the genetics of adaptation using field studies and genome-scale datasets, while Allison Mattheis uses ethnographically informed approaches to investigate diversity and equity issues in educational policy and practice (and is a former secondary school STEM educator). Dickson Perey, a high school guidance counselor in one of the country’s largest school districts has worked with thousands of students, joined us in applying this study to high school contexts.

CRITICAL CONSIDERATIONS IN STEM MULTICULTURAL CURRICULUM TRANSFORMATION: THE THEORY Data for the Queer in STEM project were collected in three phases. Over 1,400 responses to an online survey were received during the first phase of data collection, followed by approximately 140 open-response questionnaires completed by email and 50 one-on-one interviews conducted by phone or Skype. Figure 12.1 presents a breakdown of participants by STEM field and career types, figure 12.2 provides information about how participants identified themselves in terms of gender identity and sexual orientation, figure 12.3 shows geographic distribution of study participants, and figure 12.4 summarizes participant ages and levels of education completed in their STEM fields. The Queer in STEM study has allowed us to learn about and share stories of the hundreds of LGBTQ-identified scientists, engineers, mathematicians, and technical professionals who responded to our call for participants. We are able to document that many STEM professionals who happen to be LGBTQ have been able to earn advanced degrees and establish themselves in their fields, and some find their current workplaces welcoming and supportive places. But incredibly important to this this chapter is the finding that numerous participants in our study shared stories of overcoming experiences



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Figure 12.1.   Participants’ STEM fields.

during adolescence and secondary schooling that were less than supportive. Our study offers insight into STEM “pipeline” issues such as K-12 preparation, undergraduate completion of STEM majors, and movement through advanced degrees into practice. To complement findings from the Queer in STEM study, we collected data from seven high school teachers in the Greater Los Angeles area, a diverse

Figure 12.2.   Participant gender and sexual identities.

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Figure 12.3.   Participant ages and educational attainment.

urban educational context. Some of these teachers share identities with participants in the larger study, but all are connected by their commitment to creating LGBTQ-inclusive classrooms and improving school climate. The practices cited by the Queer in STEM study respondents and the high school teachers as promoting inclusive academic and professional workplaces are aligned with those that support difference more broadly. Table 12.1 provides

Figure 12.4.   Participant locations by U.S. region.

Race/Ethnicity

White Latino

Asian Asian Black Asian White

Name

June Adam

Brandon Lily Xavier George Mary Ellen

Straight Straight Gay Straight Lesbian

Straight Gay

Sexual Orientation

Male Female Male Male Female

Female Male

Gender Identity

Table 12.1.   Relationship of Science Standards and Suggested Curricular Approaches

 9  5  8  8  4

 4 10

Years of Experience

Math/Public High School Health and Technology/Public Adult Education Engineering/Public High School English/Public High School Science/Private High School Math/Public High School Science/Public High School

Subject/Setting

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an overview of these participants’ relevant characteristics. All names used here (and throughout this chapter) are pseudonyms. All the teachers discussed the importance of advocating for safe school environments as a whole in addition to addressing their individual practice. By building awareness about LGBTQ issues and identities and establishing school-wide norms of behavior and support, all teachers are more effectively supported in their own classrooms. A core of teachers willing to commit themselves to raising awareness among colleagues school wide is essential to the effective implementation of antibullying interventions and developing climates of respect. The teachers included here had stories of advocacy, including supporting the development of student groups on their school’s campus to building connections with other teachers to become more familiar with the needs of their school’s students. An important theme emphasized by all the teachers was a conceptualization of high-quality STEM education at the high school level as an interdisciplinary domain rather than separated fields of study. This understanding is also reflected in Clark’s (2002) emphasis that comprehensive change in curriculum content is necessary for multicultural curricular transformation. This type of approach, however, is often not the case at the higher education and professional levels, where STEM professionals have developed focused expertise and often work in highly specialized areas. The interconnectedness of academic study in high school provides an important opportunity for caring adults to support students in their social-emotional and cognitive growth in addition to developing content knowledge. Mary Ellen believes that science and math are present in all the other related disciplines in her campus, and June left a job in the corporate sector to find a job that gave her career meaning. Just as science, math, and technology teachers can work with English teachers like Lily to strengthen students’ literacy skills, other subject area teachers can work together as allies to create safe and welcoming school spaces for LGBTQ youth. By promoting differences as opportunities to better understand the world and demonstrating ways to work with others across differences, teachers can help students develop the problem-solving habits of mind of scientists early on in their STEM careers. Equally importantly, they can help students become members of communities in which diversity is considered an asset. CONCLUSION When asked how their workplace could be more inclusive of queer identities, several interviewees suggested that increasing diversity more broadly in



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terms of racial, ethnic, and linguistic backgrounds of their colleagues would create more welcoming environments. When asked about his teenage years, one gay engineer described how his school’s embrace of its international and ethnically diverse student body contributed to liberal attitudes that accepted difference. This was a contrast with his undergraduate experience, in which cultural divisions in his lab led to misunderstandings and a climate he found unsafe for openly queer individuals. Multicultural curriculum transformation is tough work, but it’s nothing compared to what it’s like to grow up a gender-nonconforming or a closeted queer child in many parts of the world, including the United States, today. Fundamentally, “queering the curriculum” means expanding one’s understanding of the world and being open to new explanations. This is a process that will make us better teachers of STEM content and problemsolving strategies; working to transform higher education and K-12 education simultaneously can promote inclusivity more broadly in educational communities. REFERENCES American Psychological Association (2011). Definition of terms: Sex, gender, gender identity, sexual orientation. Retrieved from http://www.apa.org/pi/lgbt/resources/ guidelines.aspx Brockenbrough, E. (2013). Introduction to the special issue: Queers of color and antioppressive knowledge production. Curriculum Inquiry, 43(4), 426–40. Clark, C. (2002). Effective multicultural curriculum transformation across disciplines. Multicultural Perspectives, 4(3), 37–46. Gates, G. J., & Newport, F. (2013). LGBT percentage highest in D.C., lowest in North Dakota. Retrieved from http://www.gallup.com/poll/160517/lgbt-percentage-highest-lowest-north-dakota.aspx Gay, Lesbian, & Straight Educator (GLSEN) (2015). National school climate survey. Retrieved from https://www.glsen.org/article/2015-national-school-climate-survey Johnson, D.W., & Johnson, R.T. (1989). Cooperation and competition: Theory and research. Edina, MN: Interaction Book Company. Klem, A. M., & Connell, J. P. (2004). Relationships matter: Linking teacher support to student engagement and achievement. Journal of School Health, 74(7), 262–73. McCready, L. (2013). Conclusion to the special issue: Queer of color analysis: Interruptions and pedagogic possibilities. Curriculum Inquiry, 43(4), 512–22. Pew Research Center (2013). A survey of LGBT Americans: Attitudes, experiences and values in changing times. Retrieved from http://www.pewsocialtrends. org/2013/06/13/a-survey-of-lgbt-americans Pizer, J. C., Sears, B., Mallory, C. & Hunter, N. D. (2012). Evidence of persistent and pervasive workplace discrimination against LGBT people: The need for federal

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legislation prohibiting discrimination and providing for equal employment benefits. Loyola of Los Angeles Law Review, 45, 715–80. Sumara, D., & Davis, B. (1999). Interrupting heteronormativity: Toward a queer curriculum theory. Curriculum Inquiry, 29(2), 191–208. Warner, M. (1991). Introduction: Fear of a queer planet. Social Text, 29(4), 3–17.

Chapter Thirteen

Considering Women’s Ways of Knowing in STEM Tracy Arnold, Eshani Gandhi, Schetema Nealy, and Brian Trinh

INTRODUCTION The following chapter discusses ways in which science, technology, engineering, and math (STEM) teachers can utilize the innate characteristics of young women in their classrooms (sometimes referred to as “women’s ways of knowing”) to aid in the comprehension of educational material in these content areas. In particular, this chapter explains the processes of knowledge acquisition and preferred learning styles of students who are studying STEM content, with a specific focus on how these ideas are related to mastery of content for young women. It is necessary to note that the purpose of this chapter is to reclaim women’s ways of knowing by including discussions related to emotions, relationships, and subjectivity rather than promoting essentialist assumptions regarding women and inadvertently oppressing them. The chapter begins with a brief discussion of the characteristics of middle and high school young girls who are studying STEM. Next, one of the authors shares how the inclusion of women’s ways of knowing influenced her science lessons. In an effort to provide clarity for the rest of the information provided in the chapter, working definitions of key terms are addressed, and then the authors take a close look at the current educational context, which includes an examination of teacher education programs and the education debt while at the same time relating these ideas to women’s ways of knowing. This chapter also reveals how the inclusion of women’s ways of knowing in the STEM fields could result in civic engagement, which is an essential component of multicultural curriculum transformation, as well as addresses these ideas and 235

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their connection to technology. Finally, the chapter explicitly draws connections between feminist curriculum, STEM, and multicultural curriculum transformation. STEM CONTENT AREA AND GRADE LEVEL Data collected by the National Center for Education Statistics (NCES) reveals a shift in young girls’ attitudes related to science, from positive to negative (2000). Moreover, this data also reported that young girls’ confidence in their abilities to complete science oriented tasks also changed from positive to negative (NCES, 2000). Girls generally attend science and math classes at the same rate as their male counterparts; however, by eighth grade, a majority of girls no longer describe themselves as liking the subjects of math and science. As women continue their education, data shows that they continue to drop out of science and STEM related fields. The 2009 U.S. Census Bureau’s American Community Survey reports that only 24% of the entire STEM workforce is comprised of women (Beede, Julian, Langdon, McKittrick, Khan, & Doms, 2011) and the majority of these women hold degrees in the physical sciences and engineering and they are likely working in education or healthcare. Knowledge of this data confirms the need for STEM teachers to develop practices that foster positive attitudes toward science for young girls as well as strengthen their confidence in studying STEM content. Some of the methods and curriculum changes being expressed within this chapter that will promote the success of young women in STEM-related classes are collaboration, positive teacher-student relationships, civic engagement and voice to all students, including girls, in the classroom. STORY OF SUCCESS While in graduate school I was intrigued by feminist educational theories that I was learning about in my multicultural education courses. Specifically, these new ideas prompted me to reflect upon how or if these theories are being incorporated into STEM curriculum or classrooms today. Without much hesitation, I concluded discussions regarding feminist theories and how they impact curriculum design for young women in STEM fields were not common practices in the middle schools where I had observed and work. However, when I began to reflect upon my own STEM education I noticed a connection among teachers who had made STEM content comprehensible. These teachers had used teaching methods and designed curriculum that was affirming to me as a person and perhaps, as a woman.



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Unfortunately, during this reflection of my own school experiences, I also remembered instances when my natural abilities and learning styles were devalued. For example, there was more than one experience when I asked questions or provided input during a class discussion and the teacher quickly dismissed my ideas. These happenings taught me not to speak or actively engage in dialogue, which may have had a negative impact on my success as a young female student. Eventually I developed survival methods for learning that aligned with my teachers’ expectations. Although this “mutual understanding” allowed for me to be successful in school, I cannot help but wonder—successful according to who? I took notes and kept my mouth shut. As a new teacher, my beliefs were greatly influenced by my own apprenticeship of observation (Lortie, 1975). In other words, the positive and negative occurrences I had encountered as a student informed many of the ideas I had about teaching. Being aware of this, I wanted to draw on my positive experiences as a student and find a way to create those same happenings for my future students. When I asked myself what made certain teachers or learning experiences superior to others, I found a few commonalities. The lessons I remember were engaging and participatory, and they related to my community and my culture. Additionally, the teacher conferred with each of the students about ideas and assignments and provided positive constructive feedback. The teachers I think fondly of created a sense of school and community pride, ownership, and understanding. Upon reflection, it became clear that my most memorable teachers affirmed and empowered the students in their classrooms while making sure STEM content was learned by all students. These were the characteristics I wanted to reflect in my own classroom. Along with the ideas from my apprenticeship of observation (Lortie, 1975), I also relied on current research I had read as part of my undergraduate and graduate work. Because the focus of my studies was related to the application of feminist theories in STEM related fields I decided to mimic some of the strategies for teaching women that were being discussed in the literature. While it may be argued these ideas could simply be referred to as good teaching practices, the discussion later in this chapter will address why these strategies specifically appeal to women’s ways of knowing. These strategies are making connections with students, forming collaborative and group work within a nurturing and supportive environment, and allowing freedom to pursue areas of interest within the parameters of the particular subject area. I established my classroom based on the set of strategies listed above. I created an environment in the classroom that was as warm and friendly as possible. I added posters of plant and flower taxonomy (catering to the naturalist learners which are often women), placed plants throughout the learning space, covered my chairs in the front, and added a coffee maker and a throw

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rug to the area. One wall was covered with a variety of pictures, photos and career paths, many taken from local projects and places. The plan was to introduce the local people and projects from the community to the students in the classroom in an effort to situate the learning and perhaps create a mentor program for the students. Every other wall in the classroom was to be covered with student created work. I vowed not to be a pencil and paper teacher but to let my students create and develop their voice on their terms. In order to make connections with my students I would spend the first several weeks focused on getting to know the students. What were their strengths? What were their weaknesses? What did they enjoy about school? How did they like to spend their free time? This wasn’t as easy as I expected. The sheer numbers of students in the class made this task seem never ending, not to mention my less than stellar classroom management skills, so I made my goal more attainable by focusing on my relationship with one or two students each day. I found it easiest to speak more informally with students when they were working in small groups so began to take advantage of this time during the day in order to make connections with my students. Although it was not nearly as personable, in order to attain general information about students, I also began using questionnaires. Although I incorporated students’ background knowledge and experiences into our curriculum, which led to improved student engagement, as a new teacher, I continued to struggle with classroom management skills. As part of my coping with classroom management problems I sometimes had to send students to other teacher’s rooms, make phone calls home to students’ guardians, and occasionally I had to send a student to the dean. This was difficult for me because I did not want to create an oppressive environment; nor did I want to neglect more silent, passive students, often girls, by not providing them with enough attention. As the semester went on, I tried to engage the students, girls in particular, in lessons that related to their home life and community. I provided them with examples of women working in science and science related fields. For example, during the unit on taxonomy, I had a local master gardener/landscape architect and an etymologist (both women) come to the classes and discuss why it’s important to classify plants and insects correctly as well as the necessity to have women in such careers. I chose to emphasize taxonomy because it caters to naturalist abilities where girls often excel. In another lesson, I had the students grow a kitchen garden of two distinctly different types of plants—one monocot and one dicot—in egg cartons. The students were to monitor their plants for several weeks, keeping a journal describing or drawing the plants characteristics. They were also given a dichotomous key to identify the plants at the end of the unit. This unit connected to



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student home life through the use of kitchen plants, catered to a naturalist ability, provided connections to discussions on photosynthesis, plant cells, and plant growth and development. It provided the students with introspection and reflection opportunities by keeping journals (graphic and written). In addition, students were able to learn from each other’s work. Students were asked to share their journals entries with their small groups. Each group would then share with the class a particular aspect from group that they found beneficial to their own learning. The unexpected outcomes that followed the kitchen garden were amazing. This lesson provided unanticipated scaffolding to later lessons in the ecology segment on invasive species (weeds growing from the soil used), as well as stimulating discussions related to herbicides and the food web. From the ideas presented regarding invasive species the students in my class begin discussing how they could protect our local community. This prompted active participation in local green ups and invasive plant removals. Their acquired knowledge and understanding of the environment enabled them to take ownership of the positive changes in their community. Of all the lessons I taught this year, I believe this one to have had the most impact on the students through their experiences and the content. The lesson also had the underlying curriculum that demonstrated to the student the impact they have on their environment, the environment of others and personal autonomy in their own learning. These underpinnings are subtle but significant. WORKING DEFINITIONS AND KEY CONCEPTS The purpose of this chapter is to examine how feminist perspectives can improve STEM education for women. One insight from feminist theory is that women may experience and understand the world differently from men. Women’s ways of knowing are best characterized as the “different perspectives from which women view reality and draw conclusions about truth, knowledge, and authority” (Belenky, Clinchy, Goldberger, & Tarule, 1986, p. 3). In essence, women’s way of knowing is how a woman derives her view of the world based upon criteria that she sees as important, and what makes that criterion important to her. We believe that these ways of knowing complement (and are not necessarily compatible) with traditional masculine ways of knowing that emphasize reason, individuality, and objective methods in understanding the world. We believe that a way of interpreting meaning or knowing the world is a kind of cultural lens that will focus very well on certain issues, but leave

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others in the periphery. For example, a feminist way of knowing unravels numerous injustices based on gender but may downplay the role of economic conditions and ignore other oppressive forces that could be better understood using Marxist methodologies. That is why it is important to be able to change perspectives. There is often the request for “what works” in education. Theories, books, and recommendations from the people we know can give us ideas to implement and evaluate “what works” in the classroom but ultimately figuring out “what works” can only be done through experience and reflection. Each classroom, teacher, and student-teacher relationship is unique, and each situation will require different interventions. Therefore, we present differing feminine ways of knowing, options for their use, and leave it to the reader to determine “what works.” CONCRETE EXAMPLES OF STEM MULTICULTURAL CURRICULUM TRANSFORMATION: THE PRACTICE The most explicable example of how to teach women and girls can be described by looking at the methods commonly used to set up book clubs. Book clubs exhibit many of the methods and strategies that align with positive outcomes when teaching women. Generally speaking, book clubs often take place in homes or restaurants that provide familiarity and comfort which correlates with women preferring a learning environment that is comfortable. Another characteristic of book clubs is they often have one or two leaders in the group. These are generally the individuals who chose the reading for the group members and keep the dialogue running during the actual discussion. Research also states women prefer a sense of democracy in their ideal learning situations which supports the idea that the group leader is often changed. Rarely are there book clubs that have a weekly speaker that takes an authoritative role tells the group what they should know about the book and instructs the participants to take notes on the reading. Instead the group discusses the information, relates it to their lives and experiences and shares with the rest of the group equally. Women view teaching as a more compassionate, nurturing relationship rather than one of “asserting dominance over less knowledgeable people” (Belenky et al., 1986, p. 194). Women like to see themselves as knowing and understanding a topic prior to learning it in an official capacity. In other words, women learn better when they feel they are building upon prior knowledge. Thus, using the book club analogy, women relate the content of the current book they are reading to their own lives or lives of someone they know, building on their



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understanding. This action encourages women to feel confident in their own intellectual abilities. Frequent and early connections to previous knowledge and understanding are important to encouraging women to gain confidence in themselves as knowers and learners (Belenky et al.,1986). Belenky et al. (1986) also introduces the concept of “connected teaching.” Connected teaching relies on a flow of ideas to and from the student and teacher. It is the opposite of what Freire (1971) refers to as “banking.” In “banking,” teachers provide information to “students by making deposits of information which the teacher considers to constitute true knowledge” (Freire, 1971, p. 63). With connected teaching, the teachers’ and students’ roles are interchangeable. They are peers rather than subordinate and superior. The teacher allows the student to see them as human, allowing them the opportunity to view the learning process themselves and see learning and creating theories as attainable (Belenky et al., 1986). Further developing this idea of connected teaching, it is also important students acquire an understanding of learning as part of a changing process where even the teacher is imperfect (Belenky et al., 1986). By conducting class where the thinking process is emphasized as much as learning the content provides opportunities for out loud thinking, where knowledge has varying perspectives and changes. This type of class provides the students with the opportunity to see and enact the thinking process with the teacher. The teacher becomes part of the conversation. As with the book club analogy, women like to be a part of a cooperative and collaborative learning community where there isn’t a dominant structure (Belenky et al., 1986). Many women feel as if figures of authority have talked down to them or treated them as intellectually inferior. This may cause women to feel as if the dominant person is in some way a better thinker and learner. This book club example shows a preference for more introspective and observational learning rather than rote learning. For women, empirical evidence does not constitute truth or fact, instead, knowledge is recursive and fluid, constantly changing with people and situations. Teaching strategies that demonstrate the idea that although the teacher may know more about a topic it does not make him or her “better” are more in keeping with womens’ preferred learning styles. This does not preclude the need for structure. In fact, women prefer organization that encourages freedom for exploration and personalization within defined boundaries. In response to any negative outside feedback, it is important to provide consistent and accurate positive responses to work. This is true at all levels of learning. As noted earlier in the chapter, one of the most important aspects of teaching girls is to develop positive relationships. Girls particularly need to feel that their teacher is human, understanding and supportive of their learning

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(Belenky et al., 1986). In classes where there are well over thirty students in each class, it is often difficult to find the time to individually develop relationships with each student. Engaging the students as a group and learning about each of them, both informally and formally, aids in developing a student-teacher relationship and building rapport. In addition, conferencing with parents and students helps to obtain valuable information on ways to cater lessons to student home life. Moll, Amanti, Neff, and Gonzalez (2001) conducted a study involving both teachers and anthropologists to gather information from families and students to develop lessons that fully engage the students in a manner that deeply incorporates their culture and home life. In the study, the authors discover a list of interconnected household and family educational assets that are integrated into the content and pedagogy of the class. The result is a richly executed series of lessons that affirm and acknowledge the students’ cultures while teaching school district content standards. While the researchers are aware that some teachers do not have the time or resources to consistently conduct home visits, Moll et al. (2001) note in their findings that it is important to utilize all tools available to assist in the process of getting to know students, particularly if you are a novice teacher. As impersonal as questionnaires can be, they are important in acquiring immediate data. They can also provide important methods for contacting students’ families. In addition, conferences with students and parents that happen early in the school year are important when getting to know the students in your classrooms. Communication between teachers and parents are also important and sharing student’s classroom achievements and progress, however small, can provide the basis for developing positive relationships with both student and their families. Both personal experience and the social sciences support the feminist claim that relationships are important. If we reminisce about the teacher that inspired us, we realize that we genuinely got to know them, and vice versa. The educational psychology literature also indicates that happiness and positive emotions are important for a receptive and engaged student, and that meaningful relationships contribute to this state of mind (Haidt, 2006; Noddings, 2003; Schutz, Pekrun, & Phye, 2007). Relationships are only meaningful to the extent which they involve genuine care about others (Noddings, 2013). This involves the recognition that students want to be cared for in different ways, and will respond differently. Treating all students the same is detrimental for relationships (see figure 13.1). One insight from feminist philosophy is the danger of intellectual objectification (Noddings, 2013, p. 35–37). Traditionally, the dangers of objectifica-



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Figure 13.1.   What is wrong with our educational system.

tion have been examined in the context of sexuality. Feminists have decried how women have been dehumanized as “mere things,” their autonomy and their individuality ignored as they become objects for the sexual gratification of men. However, individuality can be easily overlooked in the context of intellectual objectification, which the above cartoon shows well. We cannot care for other people if we see them as merely a problem to be solved. Take the example of the doctor whose concern is only treating the patient as fast as possible. They do not take the time to answer the patient’s questions or concerns, instead shuttling them through the eight-minute allotment to go to the next patient. At some level, the doctor is engaged with the patient, but only her medical problems. Similarly, teachers can fall into the same trap with their students, as the following interview excerpt show: I mean, if I go to assemblies now and every day, you always hear a teacher say “we’re here to help you.” But when we go there to ask for help, they don’t seem to have time for you and even though you do ask for help they only give a small amount of help. So I don’t like that concept. (Cullingford, 2010, p. 59)

Obviously this student feels as if the teacher says one thing, but acts in a different manner. So how can we show that we care and actually do it? Here

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we caution the mindset of using “methodologies” and “strategies” on students to get them to do what we want, even if it is to learn important material. Because each person is unique, there can be no universal formula or rule to “apply” to students in general. What teachers should focus on more is cultivating practical wisdom; this is about doing or saying the right thing, in a certain situation, with each individual person (Biesta, 2012; Schwartz, 2010). Some teachers may benefit from being better listeners, or being more assertive, or being better explainers of our subject. Some may have students who need attention but not of the negative kind; others may have students who do not like being picked on. We can only know this from a healthy relationship with our students and ourselves. The only general method we can recommend is that there are no general methods for relationships. Creating these kinds of relationships will be difficult. The system of education and accountability by administrators hinders the development of personal relationships between teachers and students because it focuses more on the mastery of content then relationships. As teachers, we sometimes feel like administrators do not care about us if they are constantly supervising and testing us, yet we must remind ourselves to minimize doing that very same thing to our students. Class structure is also an important aspect of the feminist classroom. A structure where students support the growth of other students, a nurturing atmosphere, is important for girls to learn (Belenky et al., 1986). Class structures that provide collaborative and cooperative learning environments where students feel comfortable within their groups are an essential element in the feminist classroom. Situations where students can share their work in a safe environment and offer positive and/or constructive criticism can be helpful for both students to grow in the process. This works best when there is no competition involved. For example, in a teaching methods course this was done effectively by having students review five different lesson plans for specific characteristics. The owner of the lesson plan was then allowed to make changes based on the comments provided by the other students. In addition, and perhaps most importantly, the feedback only serves to benefit the other student, it was non-competitive, and the review process itself helped increase the understanding of the content for each of the reviewers. This activity created a situation where the content was being taught collaboratively in an encouraging environment where students supported each other in their learning. Students expanded their own knowledge by absorbing information and examples provided by other students. In addition, the classroom discussions and sharing of work become part of a shared experience. Civic engagement links what students learn in the classroom to the actionable steps in the outside world. “All good education connects theory with



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reflection and action” (Nieto & Bode, 2012, p. 51). As mentioned earlier in this chapter, one teacher’s experience began with creating a kitchen garden to discuss plant characteristics. This led to an in-depth discussion related to invasive insects which in turn made the students wonder how this might effect their local community. Ultimately, the lesson created a natural opportunity for students to take action in their local community. This type of learning will carry over into the students’ postacademic lives. Students learned their contribution in the green up/plant removal project made a difference in the local environment and benefitted the community as a whole. They learned about their own connection to the local and global environment and their ability to influence change. Understanding how to be a part of social change, whether it is small or drastic, is an essential component of multicultural curriculum transformation. It allows the students to feel empowered in their learning process and ultimately encourages them to be justice-oriented, action-taking citizens. In order to promote civic engagement for girls and women it is important to provide as many examples of successful female professionals in STEM fields as possible. Further, girls often do well in stereotypically male-dominated subjects when they are with a group of other girls that are performing well. Thus, when grouping students, group at least two similarly achieving girls together to provide support. EDUCATIONAL CONTEXT Our changing and global landscape in education necessitates a change in what and how we teach students. Both the canon and pedagogy in the United States heavily caters to masculine and European epistemological frameworks (Nieto & Bode, 2012). As responsible teachers, it is important to include content that is informed by students with diverse racial, ethnic, gender, and sexual orientations. It is necessary for teachers to offer varying interpretations of the actual content being taught to the students and to provide a variety of respectful perspectives (Clark, 2010). As student demographics of schools continue to change, so must the instructional methods and content change to meet the needs of the student body. Teacher education programs must offer pre-service teachers with multiple methods and strategies for teaching an extremely diverse student population and for some pre-service teachers the methods they should be learning may be dissimilar to the methods from which they were taught. For pre-service teachers, learning multiple methods may prevent them from relying on or falling back to their apprenticeship of observation, the way they were taught

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as students, but we know that relying more on apprenticeship rather than newly learned strategies is common for most beginning teachers (Lortie, 1975). Simply stated, teaching the way we were taught is easier and because pre-service teachers spent about ten years observing the educational system, their beliefs around education and teaching sometimes cannot be changed in the four short years of obtaining a bachelor’s degree. Also a concern related to educational context and multicultural education are teachers that complete alternative route programs in education. Often these teachers are underprepared and their brief training focuses on survival strategies such as classroom management. This often does not leave room for educating these future teachers with more philosophical and theoretical education ideas related to multicultural curriculum or feminist theory and women’s ways of knowing. Unfortunately, many of these alternatively trained teachers are placed in areas where teachers are most needed: urban schools with high populations of minority students. This practice results in perpetuating a situation where students do not receive equitable education, and instead, are stifled and at risk. The rhetoric in our current educational system focuses heavily on ideas including students’ achievement levels as well as the achievement gap, which is a term used to explain the discrepancy between how students are performing and how they should be performing. Gloria Ladson-Billings, a distinguished author in the area of multicultural education discusses in her speech From the Achievement Gap to the Education Debt: Understanding Achievement in U.S. Schools (2006) a shift in the way we think about the differences in achievement levels between races. She states that we should think of the difference in achievement as a debt not a gap. Ladson-Billings (2006) uses a metaphor that links the national debt to an educational debt for African American and Latina/Latino students and the national deficit to the achievement gap. She suggests that as with the national debt and deficit the “historical, economic, sociopolitical, and moral decisions and policies that characterize our society have created an education debt” (p. 5). In essence, she is stating that if we don’t somehow fill the education debt the achievement gap will continue to increase the same way the national deficit increases when the budgets aren’t balanced. In fact, when massive interests are considered, the deficit will increase even when the budgets are balanced. Thus, the education debt should not be simply balanced there should be an effort to decrease the education deficit. Although Ladson-Billings (2006) directs this argument more toward racial inequalities, we believe the idea can be applied towards teaching girls and women as well. Ladson-Billings (1995), describes the idea of culturally relevant pedagogy as teaching students to excel in subjects they gravitate to, to critically ques-



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tion their social environment, respect their own cultures, and work for the benefit of society. This perspective further supports the notion of women’s ways of knowing in the STEM field and encourages teachers to incorporate these themes into their learning activities. CONTENT LINKED TO PEDAGOGY AND ASSESSMENT In the context of a standards-driven school system, it is difficult to deemphasize testing. For women, standardized and high-stakes testing with grading systems serves to separate and divide students. It also places a heavily weighted emphasis on competition. Therefore, in a feminist classroom, it is important to emphasize helping others and taking action in the local and global community. INTEGRATED USE OF TECHNOLOGY There has been a long-standing debate in science and technology studies about how technology can both enhance relationships, but also detract from quality time spent (Turkle, 2011). MIT professors Sherry Turkle and Seymour Papert (1992) examined how female computer programing students who were attending Harvard were systematically discouraged from further pursuing this area of specialization because they favored a relational and personal approach to computers, rather than objectifying computers as “a tool to be used” (p. 164). Their way of personalizing programs and learning by trial-and-error was considered to be an inferior, rather than a legitimate and different way of learning. This raises important questions about how we can accommodate for different ways of knowing (concrete, personal, related ways) as opposed to abstract, detached, and objective ways of knowing. CRITICAL CONSIDERATIONS IN STEM MULTICULTURAL EDUCATION Discussing women’s ways of knowing will understandably prompt concerns about the dangers of essentialism and stereotyping. Essentialism is the idea that there are inherent, natural differences between men and women. Claims like “women are by nature more caring then men,” or that “men are by nature more systematic thinkers” are examples of essentialist thinking. Mentions of essentialism tend to stir up controversy and anger in feminist circles, because

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in the past, essentialist arguments have been made to oppress women and other minority groups. In short, essentialism can lead to a malicious form of stereotyping. However, we still believe it can be important and useful to make some comments about women’s ways of knowing without appealing to essentialist assumptions and inadvertently oppressing women. The prominent Stanford philosopher of education and feminist Nel Noddings (2013) has argued that “centuries of experience have left their mark on women’s ways of thinking and on the values they espouse, and not all of these ways and values are to be rejected as part of the legacy of oppression” (p. 224). We do not want avoid discussions of emotions, relationships, and subjectivity, which would implicitly reduce their importance. These are ways of knowing that feminists want to reclaim. We recognize that there may be overlap of these characteristics and individual women and men may not match these particular generalizations. A core tenet however of multicultural education is that anyone can benefit from diverse values, perspectives, and ways of knowing, including women’s way of knowing. Accordingly, we believe that both male and female students can benefit from the recommendations we give in this chapter. The world can be a better place if everyone had better interpersonal skills, emotional intelligence, and are able to critically think and debate with others without denigrating them. EVIDENCE Ways of knowing are important for education, because presumably, education should increase knowledge and wisdom for students (whether it is in their personal or professional pursuits). Feminists often call attention to how private and personal life has been undervalued compared to public and professional life. We see this regularly on the news, where low test scores, failing schools, and competitive rankings are lamented on a daily basis, but problems about strained relationships between students and teachers are overlooked. One possible explanation for this is that it is difficult to measure relationships or quantify them, while it is easier to define standards and progress in terms of test scores. As teachers, we must keep in mind that not everything that matters can be easily measured, and not all things that can be easily measured matter. Therefore, when thinking of multicultural curriculum for girls, it is important to consider the attitudes, self-esteem, and lifelong learning—the process of becoming mature, active citizens—over the quest to outscore their neighbor in a standardized test.



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REFERENCES Beede, D., Julian, T., Langdon, D., McKittrick, G., Khan, B., & Doms, M. (2011). Women in STEM: A gender gap to innovation. Washington, D.C.: U. S. Department of Commerce. Belenky, M. F., Clinchy, B. M., Goldberger, N. R., & Tarule, J. M. (1986). Women’s ways of knowing: The development of self, voice, and mind. New York, NY: Basic Books. Biesta, G. (2012). The future of teacher education: Evidence, competence, or wisdom? Research on Steiner Education, 3(1), 8–21. Clark, C. (2002). Effective multicultural curriculum transformation across disciplines. Multicultural Perspectives, 4(3), 37–46. Cullingford, C. (2010). The art of teaching: Experiences of schools. New York, NY: Routledge. Freire, P. (1971). Pedagogy of the oppressed. New York, NY: Seaview. Haidt, J. (2006). The happiness hypothesis: Putting ancient wisdom and philosophy to modern science. London, UK: Arrow Books. Lortie, D. C. (1975). Schoolteacher (second edition). Chicago, IL: University of Chicago Press. Ladson-Billings, G. (2006). From the achievement gap to the education debt: Understanding achievement in U.S. schools. Educational Researcher, 35(7), 3–12. Moll, L., Amanti, C., Neff, D., & Gonzalez, N. (2001). Funds of knowledge for teaching: Using qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132–41. National Center for Education Statistics (2000). Trends in education equity for girls and women. Washington, D.C.: National Center for Education Statistics, Institute of Education Sciences, U.S. Dept. of Education. Retrieved from http://nces.ed.gov/ pubs2000/2000030.pdf Nieto, S., & Bode, P. (2012). Affirming diversity: The sociopolitical context of multicultural education (sixth edition). Boston: Allyn & Bacon. Noddings, N. (2013). Caring: A relational approach to ethics and moral education (second education). Los Angeles, CA: University of California Press. Noddings, N. (2003). Happiness and education. Cambridge, UK: Cambridge University Press. Schutz, P., Pekrun, R., & Phye, G. (2007). Emotion in education. Burlington, MA: Academic Press. Schwartz, B. (2010). Practical wisdom: The right way to do the right thing. New York, NY: Riverhead Books. Turkle, S. (2011). Alone together: Why we expect more from technology and less from each other. New York, NY: Basic Books. Turkle, S., & Papert, S. (1992). Epistemological pluralism and the revaluation of the concrete. Journal of Mathematical Behavior, 11(1), 3–33.

Coda Christine Clark, Amanda VandeHei, Kenneth J. Fasching-Varner, and Zaid M. Haddad

In 1993, James A. Banks, arguably the father of multicultural education, described Gibson’s (1976) work in, “Approaches to Multicultural Education in the United States: Some Concepts and Assumptions,” as the first review of research in multicultural education. Reading that work today, it is easy to see progress in multicultural educational research and the multicultural educational practice deriving therefrom; it is also easy to see the lack of progress in both arenas. Gibson identifies four “conceptualizations” of multicultural education, all of which are imbued with some degree of deficit thinking about students of color, poor students, and students who are identified as “different” (i.e., not normative or “the norm”) along other identify dimensions. While asset thinking about these students has always existed, especially within their communities, it remains a “hard sell” in higher education because the majority of educational researchers and teacher education faculty are white and from at least middle class communities. As a result, these researchers and faculty study and teach about students of color, poor students, and students who are identified as “different” from the outside, relative to their own experiences which they codify as “typical” and therefore the standard against which these “other” students’ experiences are measured as less than. As a result, disconnects exist between PK-12 teachers and their meaningful engagement with evidence-based multicultural education praxis. Additional disconnects exist between especially the recent and regular experiences of teacher preparation faculty and the “real world” of PK-12 teaching. Many teacher education faculty haven’t spent much, if any, time in the PK-12 schools, much less recent and regular time, in which they are 251

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purportedly preparing their students to teach or teach better, thus many preand in-service PK-12 teachers have chosen to teach for a living based largely upon false narratives about what the work of teaching is. It should come as no surprise, then, that most teachers leave the profession within eighteen months to three years of joining it (Sutcher, Darling-Hammond, & Carver-Thomas, 2016, p. 22). Further disconnects, manifest as contempt, exist between and among educators and education stakeholders, and for education, the work of teachers, HMMS, and students’ families. The result of these disconnects and contempt is that students, especially HMMS, and their families continue to suffer lack of access to excellent educators and education; this is especially the case in highly racially and ethnically diverse, typically also the most poorly resourced, public school communities. Through MCT, teacher educators and teachers, can begin to bridge these disconnects and alleviate this contempt. Following Gibson’s lead, articulated forty-two years ago: We may now define multicultural education as the process whereby a person develops competencies in multiple systems of standards for perceiving, evaluating, believing, and doing. . . . the possibility, and indeed likelihood, that education (both in and out of school) promotes awareness of and competence in multiple cultures leads us away from the notion of . . . dichotomies between [minority] and [majority] culture. Such dichotomies are restrictive and deny individuals the freedom for full expression of cultural diversity. The fifth conceptualization [of multicultural education] brings instead an increased awareness of multiculturalism as “the normal human experience” (Goodenough, 1976, p. 1, emphasis added). Such an awareness, I believe, has the potential for leading . . . away from divisive dichotomies and toward a fuller appreciation of the range of cultural competencies available to all students. (pp. 15–16)

Building on Gibson’s work, Moll, Amanti, Neff, and González (1992, 2005) and Yosso (2005) describe multicultural educational praxis as centering HMMS’ assets characterized as funds of knowledge and community cultural wealth, respectively. Though PK-12 education policy and educational administration too often work against teacher preparedness to enact discipline-specific and grade-level appropriate MCT in ways that intentionally acknowledge and fully engage all students’ funds of knowledge and community cultural wealth, working together, teacher educators and teachers can begin to realize this enactment, simultaneously pushing back against educational inequity and injustice, and working to further educational equity and justice. In the school district in which our focus group teacher work, whether new or veteran, some teachers enter classrooms with no curricular guidance, while others are tethered to teaching scripts that are time monitored line by line. As defined and, hopefully, adequately illustrated herein, sociopolitically located



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MCT provides scaffolding for all teachers working in all schools with all students to develop their own framework for teaching in their content areas and at their grade levels, regardless of the so-called guidance or lack thereof they are getting in their school communities. Teachers can always do what is required when they are being surveilled, and then close their doors and do what they have learned works for their students; in most instances, their HMMS and these students’ families have already had to learn to do this, so having teachers who share this understanding creates additional opportunities for transformative teaching and learning. Of course, if the actual guidance teachers get in their school communities is already transformative, MCT scaffolding can be integrated to amplify the transformative impact. But teacher educators and teachers need not wait for education policymakers and administrators to become transformative educational leaders, we can become those leaders ourselves, with and for each other, and with and for our students (Walls, 2017). If we lead transformatively, perhaps our leaders will become transformed as well. While it may seem counterintuitive, even at the most elite educational and professional levels the STEM fields are embracing MCT more than they are resisting it. National Science Foundation-funded cell biologist and molecular geneticists, Robert Yuan and Spencer Benson, Emeriti Professors of the University of Maryland, College Park, have long articulated, and repeatedly so, that MCT and science share the common goal of seeking to improve the human condition, thus that STEM-focused MCT work should drive all research, teaching, learning, and praxis in STEM. It is toward these ends that this volume is dedicated. REFERENCES Banks, J. A. (1993). Multicultural education: Historical development, dimensions, and practice. Review of Research in Education, 19(1), 3–49. Gibson, M. (1976). Approaches to multicultural education in the United States: Some concepts and assumptions. Anthropology & Education Quarterly, 7(4), 7–18. Goodenough, W. H. (1976). Multiculturalism as the normal human experience. Anthropology & Education Quarterly, 7(4), 4–7. González, N., Moll, L., & Amanti, C. (2005). Funds of knowledge: Theorizing practices in households and classrooms. Mahwah, NJ: Lawrence Erlbaum Associates. Moll, L., Amanti, C., Neff, D., & González, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132–41. Sutcher, L., Darling-Hammond, L., & Carver-Thomas, D. (2016). A coming crisis in teaching? Teacher supply, demand, and shortages in the U.S. Washington, DC: Learning Policy Institute.

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Walls, T. (2017). Race, resilience, and resistance: A culturally relevant qualitative examination of how black women school leaders advance racial equity and social justice in U.S. schools (Unpublished doctoral dissertation). University of Nevada, Las Vegas. Yosso, T. (2005). Whose culture has capital? A critical race theory discussion of community cultural wealth. Race, Ethnicity and Education, 8(1), 69–91.

Resources

HISTORICAL SEMINAL WORKS Banks, J. (2008). Teaching strategies for ethnic studies (eighth edition). Boston, MA: Allyn & Bacon. Council on Interracial Books for Children (CIBC) (1980). Guidelines for selecting bias-free textbooks and storybooks. New York, NY: Author. Hilliard, A. G. (1982–Present). Multicultural/multiethnic education baseline essay project. Portland Public Schools. Retrieved from: http://www.pps.k12.or.us/departments/curriculum/5024.htm

COMPREHENSIVE APPROACH Lee, E., Menkart, D., & Okazawa-Rey (2002). Beyond heroes and holidays: A practical guide to K-12 anti-racist, multicultural education and staff development (second edition). Washington, DC: Teaching for Change. Mack, T., & Picower, B. (Eds). (2012). Planning to change the world: A plan book for social justice teachers. New York, NY: New York Collective of Radical Educators (NYCoRE) and the Education for Liberation Network. 

GENERAL MULTICULTURAL EDUCATION Banks, J. (1993). Approaches to multicultural curriculum reform. In J. Banks and C. M. Banks (Eds.), Multicultural education: Issues and perspectives. Boston, MA: Allyn & Bacon. 255

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Nieto, S., & Bode, P. (2011). Affirming diversity: The sociopolitical context of multicultural education (sixth edition). Boston, MA: Allyn & Bacon. Nieto, S. (2010). The light in their eyes: Creating multicultural learning communities (tenth anniversary edition). New York, NY: Teachers College Press.

STANDARDS FOCUSED Karno, D. (2008). NCLB, standardized curriculum, & privatization: Where does democratic education fit in? (Unpublished paper). Annual Meeting of the Midwest Political Science Association (MPSA), Palmer House Hotel, Chicago, IL. 3 April 2008. Sleeter, C. (2005). Un-standardizing curriculum: Multicultural teaching in the standards-based classroom. New York, NY: Teachers College Press.

SUBJECT OR CONTENT-AREA SPECIFIC Science, Technology, Engineering, and Mathematics Clark, C. (Fall/Winter 2002). Effective multicultural curriculum transformation in “advanced” mathematics and “hard” sciences. Diversity Digest, 6(12), 18–19. Clark, C., & Gorski, P. (2002). Multicultural education and the digital divide: Focus on class. Multicultural Perspectives, 4(3), 25–36. Clark C., & Gorski, P. (2002). Multicultural education and the digital divide: Focus on gender. Multicultural Perspectives, 4(1), 30–40. Clark, C., & Gorski, P. & (2001). Multicultural education and the digital divide: Focus on race, language, socioeconomic class, gender, and disability. Multicultural Perspectives, 3(3), 39–44. Clark, C., & Robinson, T. (1999). Multiculturalism as a concept in nursing. Journal of the National Black Nurses’ Association, 11(2), 39–43. Gorski, P., & Clark, C. (2003). Turning the tide of the digital divide: Multicultural education and the politics of surfing. Multicultural Perspectives, 5(1), 29–32. Gorski, P., & Clark, C. (2002). Multicultural education and the digital divide: Focus on disability. Multicultural Perspectives, 4(4), 28–36. Gorski, P., & Clark, C. (2002). Multicultural education and the digital divide: Focus on language. Multicultural Perspectives, 4(2), 30–34. Gorski, P., & Clark, C. (2001). Multicultural education and the digital divide: Focus on race. Multicultural Perspectives, 3(4), 15–25. Gutstein, E., & Peterson, B. (2005). Rethinking mathematics: Teaching social justice by the numbers. Milwaukee, WI: Rethinking Schools. Moses, R. (2002). Radical equations: Civil Rights from Mississippi to the Algebra Project. Boston, MA: Beacon Press. Settlage, J., & Southerland, S. (2012). Teaching science to every child: Using culture as a starting point (second edition). New York, NY: Routledge.



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Language Arts Cogorno Radencich, M. (1998). Multicultural education for literacy in the year 2000: Traversing comfort zones and transforming knowledge and action. Peabody Journal of Education, 73(3), 178–201. Colarusso, D. M. (2010). Teaching English in a multicultural society: Three models of reform. Canadian Journal of Education, 33(2), 432–58. Dutro, E. (2009). Children writing “hard times:” Lived experiences of poverty and the class-privileged assumptions of a mandated curriculum. Language Arts, 87(2), 89–98. Egan-Robertson, A. (1998). Learning about culture, language, and power: Understanding relationships among personhood, literacy practices, and intertextuality. Journal of Literacy Research, 30(4), 449–87. Ladson-Billings, G. (2005). Reading, writing, and race: Literacy practices of teachers in diverse classrooms. In T. L. McCarty (Ed.), Language, literacy, and power in schooling (pp. 133–50). Mahwah, NJ: Lawrence Erlbaum Associates (LEA). Ladson-Billings, G. (1995). But that’s just good teaching! The case for culturally relevant pedagogy. Theory Into Practice, 34(3), 159–65. Ladson-Billings, G. (1992). Reading between the lines and beyond the pages: A culturally relevant approach to literacy teaching. Theory Into Practice, 31(4), 312–20. McCarthey, S. J. (1998). Constructing multiple subjectivities in classroom literacy contexts. Research in the Teaching of English, 32(2), 126–60. Rogers, R. & Mosley, M. (2006). Racial literacy in a second-grade classroom: Critical race theory, whiteness studies, and literacy research. Reading Research Quarterly, 41(4), 462–85. Schieble, M. (2012). Critical conversations on whiteness with young adult literature. Journal of Adolescent and Adult Literacy, 56(3), 212–21. Vásquez, V. (2004). Negotiating critical literacies with young children. Mahwah, NJ: Lawrence Erlbaum Associates (LEA).

Social Studies, History, and Geography Bigelow, B. (2006). The line between us: Teaching about the border and Mexican immigration. Milwaukee, WI: Rethinking Schools. Bigelow, B. (2008). A people’s history for the classroom. Milwaukee, WI: Rethinking Schools. Bigelow, B., & Peterson, B. (Eds.). (1998). Rethinking Columbus: The next 500 years (second edition). Milwaukee, WI: Rethinking Schools. Ladson-Billings, G. (Ed.) (2003). Critical race theory perspectives on the social studies: The profession, policies, and curriculum. Greenwich, CT: Information Age Publishers. Loewen, J. (2007). Lies my teacher told me: Everything your American history textbook got wrong (second edition). New York, NY: Touchstone. Takaki, R. (2008) A different mirror: A history of multicultural America (revised edition). New York, NY: Back Bay Books.

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View, J., Menkart, D., & Murray, A. (Eds.). (2004). Putting the movement back into Civil Rights teaching: A resource guide for classrooms and communities. Washington, DC: Teaching for Change. Zinn, H. (2010). A people’s history of the United States. New York, NY: Harper Collins.

Fine Arts Bode, P., Fenner, D., & El Halwagy, B. (2011). Incarcerated youth and arts education: Unlocking the light through youth arts and teacher development. In M. Hanley, T. Barone, & G. Noblit (Eds.), A way out of no way: The arts as social justice in education. Cresskill, NJ: Hampton Press. Bode, P. (2009). The circulatory system of oil contamination, visual culture, and Amazon Indigenous life. In E. Delacrúz, A. Arnold, A. Kuo, & M. Parsons (Eds.), Globalization, art, and education (pp. 269–77). Reston, VA: NAEA. Bode, P. (2008). Radicalizing the reading of the world through art. In S. Nieto (Ed.), Dear Paulo: Letters from the those who dare to teach (pp. 74–77). Boulder, CO: Paradigm. Bode, P. (2008). Puerto Rican arts in social context. In S. Nieto (Ed.), What keeps teachers going? (pp. 82–85). New York, NY: Teachers College Press. Bode, P. (2002, Fall). The Puerto Rican vejigante: The importance of teaching art in its social context. Rethinking Schools, 17(1), 8–9.

Physical Education, Health, Human Growth and Development, and Human Sexuality Adelman, L. (2008). Unnatural causes: Is inequality making us sick? San Francisco, CA: California Newsreel. Barnard, I. (1994, Winter). Anti-homophobic pedagogy: Some suggestions for teachers. Radical Teacher, 45, 26-8. Sexuality Information and Education Council of the United States (SIECUS) (2004). Guidelines for comprehensive sexuality education (third edition). New York, NY: Author. Centers for Disease Control and Prevention (CDC). (n.d.) Adolescent and school health. Retrieved from: http://www.cdc.gov/healthyyouth/ Centers for Disease Control and Prevention (CDC) (n.d.). National Health Education Curriculum Analysis Tool (HECAT). Retrieved from: http://www.cdc.gov/ healthyyouth/hecat/index.htm Centers for Disease Control and Prevention (CDC) (n.d.). National Health Education Curriculum Analysis Tool (HECAT) for Sexual Health Education (SHECAT). Retrieved from: http://www.cdc.gov/healthyyouth/hecat/pdf/HECAT_Module_ SH.pdf Drolet, J. C., & Cline, K. (1994). The sexuality education challenge: Promoting healthy sexuality in young people. Santa Cruz, CA: ETR Associates.



Resources 259

Future of Sex Education Initiative. (2012). National sexuality education standards: Core content and skills, K-12. Retrieved from: http://www.futureofsexeducation. org/documents/josh-fose-standards-web.pdf Hedgepeth, E., & Helmich, J. (1996). Teaching about sexuality and HIV: Principles and methods for effective education. New York, NY: New York University Press. Irvine, J. M. (1995). Sexuality education across cultures: Working with differences. San Francisco, CA: Jossey Bass. Johnson, W. R. (1975). Sex education and counseling of special groups. Springfield, IL: Charles Thomas Publishing. Kempton, W. (1988). Sex education for persons with disabilities that hinder learning. Santa Barbara, CA: James Stanfield Company. Douglas, K., Laris, B. A., & Rolleri, L. (2006). Sex and HIV education programs for youth: Their impact and important characteristics. Scotts Valley, CA: Family Health International. Krueger, M. M. (1993). Everyone is an exception: Assumptions to avoid in the sex education classroom. Phi Delta Kappa, 74(7), 569–72. Ooms, T. (1981). Teenage pregnancy in a family context: implications for policy. Philadelphia, PA: Temple University Press. Sears, J. T. (1992). Sexuality and the curriculum: The politics and practices of sexuality education. New York, NY: Teachers College Press. Stigler, J. W., & Hiebert, J. (1998). Teaching is a cultural activity. American Educator, 22(4), 4–11. Temple, M. (2001). Creating awareness of the relationship between racial and ethnic stereotypes and health. Journal of School Health, 71(1), 42–43. Thorne, B. (1994). Gender play: Girls and boys in school. Piscataway Township, NJ: Rutgers University Press. Ward, J. V., & McLean Taylor, J. (1991). Sexuality education in a multicultural society. Educational Leadership, 49(1), 62–64.

GRADE-LEVEL SPECIFIC Cowhey, M. (2006). Black ants and Buddhists: Thinking critically and teaching differently in the primary grades. Portland, ME: Stenhouse Publishers. Derman-Sparks, L. (1989). Anti-bias curriculum: Tools for empowering young children. Washington, DC: National Association for the Education of Young Children (NAEYC). Derman-Sparks, L., & Ramsey, P. (2011). What if all the kids are white? Anti-bias multicultural education with young children and families (second edition). New York, NY: Teachers College Press. Derman-Sparks, L., & Edwards, J. O. (2009). Anti-bias education for young children and ourselves. Washington, DC: National Association for the Education of Young Children (NAEYC). York, S. (2005). Roots and wings: Affirming culture in early childhood education programs (third edition). Upper Saddle River, NJ: Prentice Hall.

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TEACHER EDUCATION CONTEXT Gay, G. (1988). Designing relevant curriculum for diverse learners. Education & Urban Society, 20(4), 327–40. Gay, G. (1990). Achieving educational equality through curriculum desegregation. Phi Delta Kappan, 72(1), 56–62. Gay, G. (2000). Culturally responsive teaching: Theory, research, and practice. New York, NY: Teachers College Press. Howard, G. (2006). We can’t teach what we don’t know: White teachers, multiracial schools (second edition). New York, NY: Teachers College Press. Milner, R. (2010). Start where you are, but don’t stay there: Understanding diversity, opportunity gaps, and teaching in today’s classrooms. Boston, MA: Harvard University Press. Thompson, A., & Cuseo, J. (2012). Infusing diversity and cultural competence into teacher education. Dubuque, IA: Kendall Hunt. Vavrus, M., & Ozcan, M. (1995). Multicultural content infusion by student teachers: Perceptions and beliefs of cooperating teachers. Unpublished paper. Eric Document Number ED 384 609. Retrieved from: http://www.eric.ed.gov/PDFS/ ED384609.pdf

HIGHER EDUCATION CONTEXT Duster, T. (1993). The diversity of California at Berkeley: An emerging reformulation of “competence” in an increasingly multicultural world. In R. Thompson and S. Tyagi, (Eds.), Beyond a dream deferred: Multicultural education and the politics of excellence (pp. 231–56). Minneapolis: University of Minnesota Press. Hedges, E. (1997). Getting started: Planning curriculum transformation. Towson, MD: National Center for Curriculum Transformation Resources on Women (NCCTRW). Monk, J., & Rosenfelt, D. (2000). Internationalizing the study of women and gender. Towson, MD: National Center for Curriculum Transformation Resources on Women (NCCTRW). Reviere, R. (2003). Race, gender and science. Towson, MD: National Center for Curriculum Transformation Resources on Women (NCCTRW). Schmitz, B. (1992) Core curriculum and cultural pluralism: A guide for campus planners. Association of American Colleges and Universities: Washington DC.

ACADEMIC AND PROFESSIONAL ASSOCIATIONS Representative, not exhaustive, list of general, multicultural, group-specific, subjectspecific, and grade-level specific educational organizations. AACTE: American Association of Colleges of Teacher Education



Resources 261

AAEE: Asian American Educators Association AAHE: American Association for Health Education AAHPERD: American Alliance for Health, Physical Education, Recreation, and Dance AASA: American Association of School Administrators ACEI: Association for Childhood Education International ACFTL: American Council on the Teaching of Foreign Languages AERA: American Educational Research Association AESA: American Educational Studies Association AFT: American Federation of Teachers ALA: American Library Association AISES: American Indian Science and Engineering Society AMLE: Association for Middle Level Education APATA: Asian Pacific American Teachers Association ASCD: Association for Supervision and Curriculum Development ASPIRA ATE: Association of Teacher Educators CAHSEE: Center for the Advancement of Hispanics in Science and Engineering Education CEC: Council for Exceptional Children CCSSO: Council of Chief State School Officers IRA: International Reading Association ISTE: International Society for Technology in Education ITEEA: International Technology And Engineering Educators Association LRA: Literacy Research Association MALDEF: Mexican American Legal Defense and Education Fund NAACP: National Association for the Advancement of Colored People NAAEE: North American Association for Environmental Education NAAPAE: National Association for Asian and Pacific American Education NABE: National Association for Bilingual Education NADOHE: National Association of Diversity Officers in Higher Education NAGC: National Association for Gifted Children NAESP: National Association of Elementary School Principals NAEYC: National Association for the Education of Young Children NAES: National Association of Ethnic Studies NAESP: National Association of Elementary School Principals NAME: National Association for Multicultural Education NAMSP: National Association of Middle School Principals NASBE: National Alliance of Black School Educators NASBE: National Association of State Boards of Education NASDME: National Association of State Directors of Migrant Education NASDTEC: National Association of State Directors of Teacher Education and Certification NASP: National Association of School Psychologists NASSP: National Association of Secondary School Principals

262

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NBPTS: National Board for Professional Teaching Standards NCATE: National Council for the Accreditation of Teacher Education NCLA: National Council of La Raza NCORE: National Conference on Race and Ethnicity NCSS: National Council for the Social Studies NCTE: National Council of Teachers of English NCTM: National Council of Teachers of Mathematics NEA: National Education Association NEASP: National Education Association Student Program NHEC: National Hispanic Education Coalition NIEA: National Indian Education Association NMSA: National Middle School Association NMSHA: National Migrant and Seasonal Headstart Association NSBA National School Boards Association NSDC: National Staff Development Council NSTA: National Science Teachers Association NWSA: National Women’s Studies Association STEM Education Coalition: Science, Technology, Engineering, and Mathematics Education Coalition TEAC: Teacher Education Accreditation Council TESOL: Teachers of English to Speakers of Other Languages

SELECTED WEBSITES Critical Race Studies in Education Association (CRSEA): http://www.crseassoc.org Dr. Pedro Albízu Campos Puerto Rican High School (PACHS): http://www.pedroalbizucamposhs.org Engineer Girl: http://www.engineeryourlife.org/ Engineering by Design: http://www.iteea.org/EbD/ebd.htm Engineering Go For It! (eGFI): http://www.egfi-k12.org/ Engineering is Elementary: http://www.eie.org/ Exploratorium: http://www.exploratorium.edu/http://www.exploratorium.edu/ Facing History and Ourselves: https://www.facinghistory.org Free Minds, Free People (FMFP): http://fmfp.org Gay, Lesbian, & Straight Education Network (GLSEN: http://glsen.org/educate/ resources Highlander Research and Education Center: http://highlandercenter.org I³ Project: Invention-Innovation and Inquiry: http://www.iteea.org/i3/index.htm Innovation Portal: https://innovationportal.org/ Kinetic City: http://www.kineticcity.com/ LGBT+ Physicists: http://lgbtphysicists.org/resources.html National Association for Multicultural Education (NAME): http://www.nameorg.org National Conference on Dialogue and Deliberation (NCDD): http://ncdd.org National Girls Collaborative Project: http://www.ngcproject.org/



Resources 263

National STEM Video Game Challenge: http://www.stemchallenge.org/ Pedagogy and Theatre of the Oppressed (PTO): http://ptoweb.org/aboutpto/ Project Lead the Way (PLTW): http://www.pltw.org/ Public Broadcasting Service: http://www.pbs.org/teachers/stem/http://www.pbs.org/ teachers/stem/ Queer in STEM: http://www.queerstem.org Rethinking Schools: http://www.rethinkingschools.org/index.shtml SciGirlsConnect: http://scigirlsconnect.org/ Social Justice Mediation Institute: http://people.umass.edu/lwing/ Teaching for Change: https://www.teachingforchange.org Teaching Tolerance: http://www.tolerance.org Trevor Project Education and Resources for Adults: http://www.thetrevorproject.org/ section/education-training-for-adults Twenty (Self-)Critical Things I Will Do to Be a Better Multicultural Educator: http:// www.edchange.org/handouts/20things.doc Words, Beats, and Life, Inc. (WBL): http://www.wblinc.org Zinn Education Project: http://zinnedproject.org

Index

Page references for figures are italicized. accountability, of teachers, 95 achievement gap, 246 adaptation, earthquakes/tsunami related to, 148, 152 Adequate Yearly Progress (AYP), 142 administrators, 244 Affirming Diversity: The Sociopolitical Context of Multicultural Education (Nieto & Bode), 70 algorithm: in math education, 20–21; in math education, MCT example, 27–28, 28, 37 alternative route training, of teachers, 246 Amanti, C., 242, 252 animal diversity and behavior, 131 Antonio Casillas, Jose, 179, 182, 183 applet, 20, 26 apprenticeship, of pre-service teachers, 245–46 argumentation: assessment and, 103, 108–10, 136–39; for life science, 135–38, 136, 137 art, 175–76, 176; in STEAM, 190–91, 196–97. See also math-science art; math-science art examples

assessment: argumentation and, 103, 108–10, 136–39; in dual language meteorology, 168; in ELLs, 82; as evidence, 109; of family math night, 3–4, 15; in multicultural curriculum example, 74; in NGSS, 103, 108–10, 136–39; qualitative data, 103–4, 111; quality of, 120; WIDA, 75, 77–79. See also content linked to pedagogy and assessment autobiography, 48–49, 53 aviation history, 210 AYP. See Adequate Yearly Progress Babylonian Pythagorean Theorem, 187 Banks, J. A., 85, 118, 150, 195–96, 198, 251 “behavioral schools,” xvii behaviors: animal diversity and, 123; life science and, 125, 125 Belenky, M. F., 241 Benson, Spencer, 253 Best of Bugs, 196–97 bias, 129–130, 198, 206–7 Biegel, S., 134 bilingual communication, 48–49, 51, 62. See also English as a Second Language

265

266

Index

biology, cellular and molecular, 123 biology course apprenticeship, 96–98 bisexual (B), 222. See also lesbian, gay, bisexual, and transgender Bits and Pieces II (Lappan, Fey, Fitzgerald, Friel, & Philips), 22, 33 Bode, P., 70, 73 book clubs, women’s ways of knowing related to, 240–41 borders, 63. See also crossing borders MCT example Brownie Station Representation, 23, 24, 25, 25–29 Bruner, J., 41 Bureau of Labor Statistics, U.S., 215

Cobb, C. E., 32 Code.org movement, 213–14 Codex Conciliorum Albeldense, 61 collaboration, 244; for ELLs, 68–71, 79–80, 82; in multicultural curriculum example, 77–80, 81, 82–83 collaborative emergence, 150–51 collaborative science, 150–53 Coltrane, B., 72 Common Core State Standards (CCSS), xxii, 224; family math night and, 3, 13; math education and, 5–6 communication, 60, 120; bilingual, 48–49, 51, 62; borders related to, 63; in division MCT example, 58–59, 61–63; in math education, MCT, Cajete, G., 150 9–10. See also language Call for Chapters, xxv communities: disaster resilience of, Camero, January, 186, 187 148–49; of learners, 96; MCE car accidents, 48–49 and, 41; in NGSS, 92–93, 102; in Carter, L., 146 women’s ways of knowing, 237–38 CCSS. See Common Core State community cultural wealth, 252 Standards competition, among students, 104–5 cellular biology, 131 computer literacy, 208 CEMELA. See The Center for the connections: in technology MCE, Mathematics Education of Latinos/as 209–10; women’s ways of knowing Census, U.S., 47, 71–72, 236 related to, 238–39, 241. See also The Center for the Mathematics MCT/MCE connection Education of Latinos/as Contact Theory, 198 (CEMELA), 40 content: for ELLs, 72, 79–80, 82; linked Chinese characters, 206–7 to pedagogy, in EiE, 200 Chinese numeral system, 186 content linked to pedagogy and Chinese Pythagorean Theorem, 188, 189 assessment, xxiii; in crossing borders CIPS. See Cycle of Instructional MCT example, 46, 49–51, 50; in Planning and Support division MCT example, 46, 59; civic engagement, xxiii; in crossing earthquakes/tsunami and, 150–52, borders MCT example, 45, 47, 151; in math education, MCT 52–53; in dual language meteorology, example, 21–23, 24, 25, 25–30, 26, 168; in earthquakes/tsunami, 148–49, 27, 28; in subtraction MCT example, 157–58; in EiE, 200; math education, 46, 55–57; in women’s ways of MCT example and, 32; women’s knowing, 246–47 ways of knowing and, 235–36, 239, contest, 10 244–45 Convertino, C., 75 Clark, C., 41–42, 52, 56, 60, 127, 232 coyotes. See crossing borders MCT class, social, 73, 208, 210, 251 example



Index 267

critical thinking, 106–7 critique, 130 crossing borders MCT example, 60, 62; autobiography in, 48–49, 53; basics in, 44, 47–48; civic engagement in, 45, 47, 52–53; content linked to pedagogy and assessment in, 46, 49–51, 50; demographics of, 47; educational context in, 45, 53; map skills in, 49–51, 50; MCT/MCE connection in, 44, 53; relationships with/among students in, 45; standards in, 44, 53; success story in, 44, 53; teacher notes, 46, 48; unit conversion in, 47, 52–53 cultural relevance, in pedagogy, 246–47 cultures, 61–62; exploration of, 74–75. See also specific topics curricular integration, 149 curriculum and MCT STEM transformation, 150 “curriculum desegregation,” 177 curriculum overview: of EiE, 199–200; on math education, MCT, 7–9; in math-science art examples, 179 curriculum specifics: attendance and, 9; checklist in, 10; communication in, 9–10; family activity in, 12; family exit survey in, 9, 12–13; family information packet in, 12; language in, 9–10; math education, MCT, 9–13; relationships in, 10, 15–16; warm-up activity in, 11; whole-group activity in, 11 Cycle of Instructional Planning and Support (CIPS), 77

demographics: of crossing borders MCT example, 47; of district, xix; dual language meteorology and, 168; in earthquakes/tsunami, 148; EiE and, 197; of ELLs, 36, 71–73; at Google, 212; of LGBTQ, 221; women’s ways of knowing and, 236 digital divide, 211–16 directed observation, 97 Discovery Middle School: ELL teachers in, 142; SIP for, 142; standards in, 142–43. See also Orphan Tsunami of 1700 diversity, 123; of chapter authors, xxvii; LGBTQ related to, 232–33; technology MCE and, 210–13 Diversity and Multicultural Education in Teaching ELLs, 69 division MCT example, 45; communication in, 58–59, 61–63; content linked to pedagogy and assessment in, 46, 59; language in, 59; MCT/MCE connection in, 44, 59–60; real world in, 58–59; resistance in, 58; teacher notes in, 46, 59 documents, 177–78; of MCE, xviii dual language meteorology, 167; assessment in, 168; civic engagement in, 168; demographics and, 168; engagement in, 169–70; language in, 168; motivation in, 170–71; reflection bridge in, 170; relationships with/ among students in, 168; standards in, 170; success story in, 168–69

daily warm-up question, 93 Darwin, Charles, 177 data sources: in LGBTQ, 228–30, 229, 230, 231, 232; in NGSS, 98–99, 101, 103–4, 110–11, 114 De La Cruz, Y., 4 democracy: technology MCE related to, 214; women’s ways of knowing and, 240

earning students’ trust, 97 earthquakes/tsunami, 141–42; adaptation related to, 148, 152; causes of, 154–55; civic engagement in, 148–49, 157–58; content linked to pedagogy and assessment and, 150–52, 151; curricular integration in, 149; curriculum and MCT STEM transformation, 150;

268

Index

demographics in, 148; ecologically connective consciousness and, 147; educational context in, 148; emergency preparedness for, 144–45, 157–60; engagement about, 143, 148, 153, 158; evaluation and, 152; glocalization related to, 146; lesson sample 1, 153–58; lesson sample 2, 158–59; limitations related to, 151, 151–52; mysteries related to, 154–55, 161; Native Americans on, 154; pendulum related to, 159; plate movement and, 156–57; properties of, 155; questions about, 143; reflection bridge on, 145–46; relationships with/among students and families related to, 148; resources for, 159–62; S- and P-waves in, 155, 157; scientific exchange on, 154; seismic activity and, 155; seismographs and, 144, 145, 149, 155–59; Social Action Approaches to, 150–51, 151; social action approaches to MCT STEM, 150–51; standards in, 146–47, 147; TAG and, 149; before technology, 158–59; technology integration in, 152; triangulation and, 156; Zhang Heng on, 144, 145, 149, 158–59, 162 Earth Science, 141; relevance of, 143–44; role-playing in, 143–44 ecologically connective consciousness, 147 educational content, xxii–xxiii educational context: in crossing borders MCT example, 45, 53; in earthquakes/tsunami, 148; of math education, MCT example, 30; of women’s ways of knowing, 245–47 education policy, xvii, 91; leadership and, 252–53; national debt related to, 246 EiE. See Engineering is Elementary elementary grade level. See Engineering is Elementary ELLs. See English Language Learners

emergency preparedness, for earthquakes/tsunami, 144–45, 157–60 empowering school culture, 196 empowerment: of mothers, 57; in NGSS, 93; of students, 93, 100, 102, 105–6, 237; teachers and, 103, 237 endocrinology, 124 engagement: in dual language meteorology, 169–70; about earthquakes/tsunami, 143, 148, 153, 158. See also civic engagement engineering, xviii, xxvi, 129–130; STEAM, 190–91, 196–97 engineering design, 119 Engineering is Elementary (EiE): civic engagement in, 200; Contact Theory and, 198; content linked to pedagogy in, 200; curriculum overview of, 199–200; demographics and, 197; failure related to, 196; goals of, 199; inclusion in, 195–96, 199; as MCE, 195–96; personal perspective related to, 200–201; problem solving in, 196, 200–201; reflection bridge on, 200–201; relationships with/among students and families in, 199–201; self-efficacy related to, 197–98, 201; success story in, 196–97; survey on, 198; teacher notes in, 200; technology integration in, 200 English as a Second Language (ESL): evidence in, 76; multicultural curriculum example and, 73–74, 76; pre-service teachers in, 68–69; specialists in, 79–80; technology MCE and, 210–11 English Language Learners (ELLs), 19, 142; assessment in, 82; collaboration for, 68–71, 79–80, 82; content for, 72, 79–80, 82; demographics of, 36, 71–73; guest speakers and, 71; “human relations approach” for, 70; in-service



Index 269

programs and, 67–69; key dilemmas in, 71–73; language objectives in, 82; language proficiency of, 72–73, 75; math education, MCT example and, 21, 29–30; pre-service teachers for, 68–71; service-learning and, 70–71, 78; social justice for, 70; strategies for, 67–68, 71, 76; vocabulary of, 68 epidemiology, 124 epistemic practice, 97 equity pedagogy, 198 ESL. See English as a Second Language Espelage, D., 127 essentialism, stereotypes and, 247–48 evidence, xxiv–xxv; assessments as, 109; in ESL, 76; in NGSS, 136; in science teaching, 122; on women’s ways of knowing, 248 experimentation process, 101, 104 expository process, in NGSS, 98–100 failure: EiE related to, 196; reasons for, 94–95 family: activity, 12, 57; exit survey, 9, 12–13; information packet, 12 family math night: assessment of, 3–4, 15; CCSS and, 3, 13; SMP and, 13. See also math education, MCT Feder, M., 197 feminist theories, 244, 248; objectification in, 242–43; success story and, 236–37; in working definitions, 239–40 Fey, J. T., 22, 33 Fitzgerald, W. M., 22, 33 Flecha, R., 63 focus inquiry, in NGSS, 98–100, 106–8, 111, 114–15 four points assessment rubric, 103 A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (the Framework), 96 Freire, P., 42, 53, 241

Friel, S. N., 22, 33 funding, 7, 199 funds of knowledge, 252 games, 10–11, 39–40 García, R., 63 garden, 238–39, 245 gay (G), 222 Gay, G., 177 gender, 129, 222, 225–26. See also lesbian, gay, bisexual, and transgender genetics, 124, 131 Germain, Sophie, 181 Gibson, M., 251–52 gifted student extensions, 149 Giouroukakis, V., 84 glocalization, 146 Gobble, K.C., 186, 187 González, N., 75, 242, 252 Google, demographics at, 212 Gorski, P.C., 212, 215–16 group genius, 150–51 guest speakers, 71 guided practice, in NGSS, 100–104 Guyon, Jessica, 179, 180, 183, 185 heredity, 131 hermaphroditism, 122, 128 heteronormativity, 134, 223 Historically Marginalized and Minoritized Students (HMMS), xviii, 18, 20, 252–53 history: of aviation, 210; of science, 123–24 HMMS. See Historically Marginalized and Minoritized Students “Holidays and Heroes,” 42, 213 Hollins, E. R., 105–9 homophobia, 126, 225 Honigsfeld, A., 84 Hour of Code curriculum, 214 human relations approach, 70 human reproduction, 132 hypotheses, 99, 101, 116, 119

270

Index

identities, 125, 125–26, 209; “different” in, 251; exploration of, 74; in LGBTQ, 224–25, 224–28, 229, 230, 231 immigrants, 47. See also crossing borders MCT example Inca knot recording and numerical devices, 180 in-service programs, 67–69 in-service teachers, xix, xxi, 2, 11, 69, 85 integration, 10, 76–77, 108, 149, 152; in NGSS, 96–97, 118, 120, 147. See also technology integration integrity, 108–9 interdisciplinary chapters, xxvii interdisciplinary domain, 232 Jackson, Sheeveta, 183, 183 Japan, orphan tsunami in, 154 Japanese American, 206–7 Japanese characters, 206–7 Jennings, Kevin, 133 Kagawa, F., 149 Katehi, L., 197 Khisty, L. L., 61 Kosciw, J. G., 134 KQL. See What We Know, What We Question, and What We Learned labels, life science and, 125, 125 Ladson-Billings, G., 176, 246–47 language, 19, 168; in curriculum specifics, 9–10; in division MCT example, 59; gender related to, 225–26; life science and, 120–21; in math education, MCT example, 22–23, 29–33, 35–37; in subtraction MCT example, 44. See also dual language meteorology; English as a Second Language language objectives, in ELLs, 82 language proficiency, 72–73, 75, 81 Lappan, G., 22, 33

Latina/Latino families, 6, 196–97. See also crossing borders MCT example; math education, MCT Latinas/Latinos, 40, 47 LAUSD. See Los Angeles Unified School District leadership, education policy and, 252–53 learning, 98–99, 105; definitions of, 41–43; science, 106; service-, 70–71, 78 Lee, E., 60 lesbian (L), 222 lesbian, gay, bisexual, and transgender (LGBT), 123, 222; behaviors and, 125, 125; religion and, 132–33; research on, 133–35; teachers, 124–25, 133. See also life science lesbian, gay, bisexual, transgender, queer (LGBTQ), 126; authors in, 228; curricula inclusion of, 224–25; data sources in, 228–30, 229, 230, 231, 232; demographics of, 221; diversity related to, 232–33; equity of, 221; identities in, 224–28, 229, 230, 231; interdisciplinary domain and, 232; mentorship in, 226–27; the practice in, 223–27; reflection bridge in, 228; standards in, 224; STEM fields and, 228–29, 229, 231, 232; stereotypes and, 224–25; student behaviors and, 226; teachers related to, 225–26, 229–30, 231, 232; theory in, 228–32, 229, 230, 231; underrepresentation of, 221–22, 227; working definitions in, 222–23 Levinson, B. A., 75 LGBT. See lesbian, gay, bisexual, and transgender LGBTQ. See lesbian, gay, bisexual, transgender, queer life science: argumentation for, 135–38, 138, 139; bias and, 129–30, 198, 206–7; cautions about, 123–24, 127–28; classroom leadership and management related to, 128–29;



Index 271

gender sorting and, 129; genetics, 124, 131; hermaphroditism and, 124, 128; heteronormativity and, 134; homophobia and, 134; language and, 128–29; MCT/MCE connection related to, 126–27; nature and history of science for, 130–31; the practice related to, 127–133; reflection bridge and, 133–34; scientific and engineering practices related to, 129–30; standards and, 127; theory and, 134–37, 136, 137; transformative opportunities in, 130–32; working definitions and, 125, 125–26 liquid measurement, 52 López, Veronica, 179, 181 Los Angeles Unified School District (LAUSD), 175 map skills, 49–51, 50 Margolis, J., 208 math education, 4, 76; academic language in, 19; CCSS and, 5–6; cultures in, 61–62; disinterest in, 5–6; expectations from, 5; multicultural, 39–40; multiple competencies in, 19; parents in, 6; popcorn method in, 20; real world and, 5; resources for, 36; shared fraction multiplication problem set in, 20–21; socioculturalism of, 36; world rankings in, 5 math education, MCT: activity enhancements in, 8; appreciation in, 15; challenges for, 83–84; checklist for, 10; curriculum overview on, 7–9; family exit survey in, 9; funding for, 7; opening activities in, 7–8; parents’ math phobia and, 13–15; probability in, 8; real world and, 8, 11; standards and, 84 math education, MCT example: algorithm in, 27–28, 28, 37; civic engagement and, 32; confirmation

of, 29; content linked to pedagogy and assessment in, 21–23, 24, 25, 25–30, 26, 27, 28; educational context of, 30; ELLs and, 21, 29–30; iterative visuals in, 23, 24, 25, 25–29, 26, 27, 28; language in, 22–23, 29–33, 35–37; models related to, 31; modifications in, 22, 30, 32–33; multiple formative assessment in, 29; patterns in, 26–28, 28; popcorn method in, 20, 22–23; reading supports in, 33; reflection bridge on, 35–36; relationships with/among students in, 31–32; resources in, 37; respect in, 31–32; standards and, 30–31; student dialogue in, 21–22, 29–30; supports in, 33; teachers in, 34–36; technology integration in, 33–34, 37; virtual manipulatives in, 25–27, 27, 34–35 mathematical concepts, 11 mathematics, xxv–xxvi; bilingual communication in, 48–49, 51, 62; in middle school, 4 math night. See family math night math-science art, 175; MCT/MCE connection of, 177; success story of, 176–77 math-science art examples: anticipatory activities in, 178–79; Chinese numeral system in, 186; Chinese Pythagorean Theorem in, 188, 189; curriculum overview in, 179; extensions in, 187, 188; Inca knot recording and numerical devices, 180; Mayan numeral system, 176–77, 183, 183, 184, 185; Mayan pyramids, 182; Mayan temple-calendar, 182; Pythagorean Theorem, 183, 187, 188, 188–89, 189; reflection bridge in, 189–90; relationships with/among students and families in, 178; students’ contributions to, 189–90; women mathematicians in, 179, 181

272

Index

Mayan numeral system, 176–77, 183, 183, 184 Mayan pyramids, 182 Mayan temple-calendar, 182 MCD. See Multicultural Curriculum Development MCE. See Multicultural Education MCT. See Multicultural Curriculum Transformation MCT/MCE connection: in crossing borders MCT example, 44, 53; in division MCT example, 44, 59–60; life science related to, 126–27; of math-science art, 177; to NGSS, 93–96; in subtraction MCT example, 44, 55 measurement, millimeters, 49, 51 mentorship, 226–27 Mercer, O. R., 146 Merkle, D. G., 130 metric systems, 49, 51 middle school, 4, 6, 142–43 migration. See crossing borders MCT example molecular biology, 131 Moll, L., 242, 252 Moschkovich, J., 36 Moses, R. P., 32 Mossberger, 213 mothers, empowerment of, 57 motivation, 170–71, 208 Multicultural Curriculum Development (MCD), xviii multicultural curriculum example: assessment in, 74; CIPS in, 77; classroom observation in, 76; collaboration in, 77–80, 81, 82–83; curriculum revisions in, 78; ESL and, 73–74, 76; integrated lesson plans in, 76–77; reflection bridge and, 83; session one, 74–77; session two, 76–78; session three, 78; standards in, 74–75, 80, 81, 82–83; WTs in, 73–75

Multicultural Curriculum Transformation (MCT), xxvii, 85, 252–53; definition of, xviii; parameters for, 42; strategies for, 60. See also specific topics Multicultural Education (MCE): accuracy and, xviii; as basic education, 42; communities and, 41; definitions of, xviii, 41–42, 60; developmental phases of, 151; disconnects and, 251–52; documents of, xviii; processes from, xviii; social class and, 73, 208, 210, 251. See also specific topics multiculturalism, 252; “Holidays and Heroes” in, 42, 213 multicultural STEM, 141 National Center for Education Statistics (NCES), 236 National Library of Virtual Manipulatives, 20, 25, 33–34 National Research Council (NRC), 121–22 Native Americans, 154 Native science, 150 NCES. See National Center for Education Statistics Neff, D., 242, 252 Next Generation Science Standards (NGSS), 91–92, 224; assessment and argumentation in, 103, 108–10, 118–21; community in, 92–93, 102; curriculum organization for, 107–8; daily warm-up question in, 93; data sources in, 98–99, 101, 103–4, 110–11, 132; empowerment in, 93; essential knowledge for, 105; evidence in, 118; expository process in, 98–100; first five weeks of, 101–2; focus inquiry in, 98–100, 106–8, 111, 114–15; four points assessment rubric in, 103; guided practice in, 100–104; integration



Index 273

in, 96–97, 118, 120, 147; KQL in, 99, 102–3, 107, 116–17; MCT/ MCE connection to, 93–96; midsemester in, 102–3; observation in, 97, 99–100; organization of, 93; qualitative data of, 103–4, 111; reflection bridge and, 104–5; relationships with/among students and families in, 94; socioculturalism of, 97–100, 105–10; working definitions in, 96–98 Nieto, S., 41–42, 57, 60, 70, 73 No Child Left Behind (NLCB), xxii, 72 Noddings, Nel, 248 Nogales, Arizona, 50, 50–51 NRC. See National Research Council objectification, women’s ways of knowing and, 242–43, 243, 247 observation, 76; in NGSS, 97, 99–100; in women’s ways of knowing, 237 organizing tools: basic information, xx; civic engagement, xxiii; content linked to pedagogy and assessment, xxiii; educational content, xxii– xxiii; evidence, xxiv–xxv; practice and theory, xxi–xxii; reflection bridge, xxii; relationships with/ among students and families, xxiii; resources, xxiv; speak to teachers directly, xx–xxi; “special” populations, xxiii; standards, xxii; success stories, xxi; teacher notes, xxiii; technology, xxiii–xxiv; working definitions, xxi Orphan Tsunami of 1700, 143–44, 154, 160–61 Ortega, S., 63 Papert, Seymour, 247 parents, 4, 39–40; in math education, 6; math phobia of, 13–15 Pearson, G., 197

pedagogy, xvii–xviii; content linked to, in EiE, 200; cultural relevance in, 246–47; equity, 198; humanization of, 177; intergenerational differences in, 54–57. See also content linked to pedagogy and assessment peer-help, 102, 104. See also collaboration Philips, E. D., 22, 33 Physical Sciences, 141 plate movement, earthquakes/tsunami and, 156–57 politics, of teaching, xvii popcorn method, 20, 22–23 power, xxvii. See also empowerment the practice: in LGBTQ, 223–27; life science related to, 119–25; on women’s ways of knowing, 240–45, 243 prejudice reduction, 196 preparation, 10 pre-service teachers: apprenticeship of, 245–46; development of, 85–86; for ELLs, 68–71; in ESL, 68–69; homogeneity of, 73–75. See also multicultural curriculum example primary documents and sources, 177–78 probability, 8, 39–40 problem-solving, 91, 196, 200–201 process, xxvii–xxviii putting yourself out there, 97 qualitative data, 103–4, 111 quantitative reasoning, 120 queer (Q), 126–27, 223. See also lesbian, gay, bisexual, transgender, queer questioning (Q), 126 race, 231; technology MCE and, 214 Racionero, S., 63 Ramsey, P. G., 150 reading, 33, 39 reading guide, 103

274

Index

real world, 5; in division MCT example, 58–59; math education, MCT and, 8, 11 reflection bridge, xxii; in dual language meteorology, 170; on earthquakes/ tsunami, 145–46; on EiE, 200–201; in LGBTQ, 228; life science and, 133–34; on math education, MCT example, 35–36; in math-science art examples, 189–90; on MTC examples, 60–62; multicultural curriculum example and, 83; NGSS and, 104–5 relationships: in curriculum specifics, 10, 15–16; with families, 242; with students, in women’s ways of knowing, 241–44, 248 relationships with/among students: in crossing borders MCT example, 45; in dual language meteorology, 168; in math education, MCT example, 31–32; in subtraction MCT example, 45, 56–57 relationships with/among students and families, xxiii, 31–32; earthquakes/ tsunami related to, 148; in EiE, 199–201; in math-science art examples, 178; in NGSS, 94 religion, life science and, 132–33 research: on LBGT, 133–35; NRC, 129–30; question development, 98–99, 102 resources, xxiv; for earthquakes/tsunami, 159–62; for math education, 36; in math education, MCT example, 37 Rich, Adrienne, 191 rigor, 97–98, 111, 146, 152 Ríos, Francisco, 41 Robinson, J., 127 Rodríguez, Jazmin, 188, 188 Sawyer, R. K., 150 scale, on map, 49–50 School Improvement Plan (SIP), 142

science, xxv–xxvi; bias and, 130; collaborative, 150–53; Earth, 141, 143–44; history of, 131–32; learning, 106; literacy development, 99–100; Native, 150; science education and, 223–24; teaching, 122. See also math-science art; Next Generation Science Standards science, technology, engineering, art, mathematics (STEAM), 190–91, 196–97 science, technology, engineering, mathematics (STEM), xviii; STEAM and, 190–91, 196–97. See also specific topics science education, 91–92, 170; rigor in, 97–98, 111, 146, 152; science and, 223–24. See also Next Generation Science Standards science education MTC. See dual language meteorology scientific methods, 98–99 seismographs, earthquakes/tsunami and, 144, 145, 149, 155–59 self-efficacy, 197–98, 201, 227 Sen, A., 63 sexual orientation, xxvii, 123, 221–22, 231. See also lesbian, gay, bisexual, and transgender; lesbian, gay, bisexual, transgender, queer SIP. See School Improvement Plan Sleeter, C. E., 109 SMP. See Standards of Mathematical Practices Social Action Approaches, 150–51, 151 social activism, 213 social class, 73, 208, 210, 251 social justice, for ELLs, 70 socioculturalism: identities and, 226; of math education, 36; of NGSS, 96–100, 105–10 software developers, 215 Spanier, B., 131 specialists, in ESL, 79–80



Index 275

standards: CCSS, xxii, 3, 5–6, 13, 224; in crossing borders MCT example, 44, 53; in Discovery Middle School, 142–43; in dual language meteorology, 170; in earthquakes/ tsunami, 146–47, 147; language proficiency and, 75; in LGBTQ, 224; life science and, 127; math education, MCT and, 84; math education, MCT example and, 30–31; in multicultural curriculum example, 74–75, 80, 81, 82–83; in subtraction MCT example, 44–45, 57. See also Next Generation Science Standards Standards of Mathematical Practices (SMP), 3, 5, 8, 13, 15 Stansbury, 213 statistics, 68, 215; NCES, 236 STEAM. See science, technology, engineering, art, mathematics STEM. See science, technology, engineering, mathematics STEM-MCT theory, 36–37, 62–63 stereotypes, 198; essentialism and, 247–48; LGBTQ and, 224–25; technology MCE related to, 206–7 Sterling, S., 147 Stuck in the Shallow End: Education, Race, and Computing (Margolis), 208 student dialogue, 111; in math education, MCT example, 21–22, 29–30 students: competition among, 104–5; confusion of, 101; empowerment of, 93, 100, 102, 105–6, 237; failure of, 94–95; HMMS, xviii, 18, 20, 252; knowledge about, 35–36; peer-help for, 102, 104; skepticism of, 94–95 subtraction MCT example: content linked to pedagogy and assessment in, 46, 55–57; language in, 44; MCT/MCE connection in, 44, 55; relationship with/among students in, 45, 56–57; standards in, 44–45, 57;

success story in, 44, 56–57; teacher notes in, 46, 55–56 success stories, xxi; in crossing borders MCT example, 44, 53; in dual language meteorology, 168–69; in EiE, 196–97; of math-science art, 176–77; in subtraction MCT example, 44, 56–57; about women’s ways of knowing, 236–39 surveys, 9, 12–13, 198 talented and gifted (TAG), 149 teacher focus groups: demographics of, xix; organizing tools from, xx–xxv teacher notes, xxiii; crossing borders MCT example, 46, 48; in division MCT example, 46, 59; in EiE, 200; in subtraction MCT example, 46, 55–56 teachers: accountability of, 95; alternative route training of, 246; beliefs of, 15; consistency of, 109; directly speaking to, xx–xxi; disconnects of, 251–52; empowerment and, 103, 237; in-service, xix, xxi, 2, 11, 69, 85; LGBT, 124–25, 133; LGBTQ related to, 225–26, 229–30, 231, 232; of life science, 124–25, 133; in math education, MCT example, 34–36; pre-service, 68–71, 73–75, 85–86, 245–46; putting yourself out there as, 97; in technology MCE, 217; trust related to, 94–97, 104, 108–9; values of, 41; WT, xix–xx, 73–75 teaching, politics of, xvii technology, xxiii–xxiv, xxvi–xxvii, 46; STEAM, 190–91, 196–97; STEM, xviii, 190–91, 196–97 technology integration: in earthquakes/ tsunami, 152; in EiE, 200; in math education, MCT example, 33–34, 37; on women’s ways of knowing, 247

276

Index

technology MCE, 205; additive approach in, 209; in aviation history, 210; award in, 207; careers in, 208; classroom computers and, 212; Code.org movement and, 213–14; computer literacy in, 208; connection in, 209–10; cultural divides and, 211, 217; democracy related to, 214; digital divide in, 211–16; diversity and, 210–13; ESL and, 210–11; Google and, 212; identities in, 209; inclusivity in, 211–13; Japanese American in, 206–7; motivation in, 208; multimedia in, 210; race and, 214; social activism and, 213; socioeconomics in, 212–13, 216; software developers and, 215; stereotypes related to, 206–7; teachers in, 217; underrepresentation in, 208–9, 212–13, 215–16; Web 2.0 in, 210; WebQuests in, 210–11 test study rubric, 114–15 text study learning experience, 98–99 The Center for the Mathematics Education of Latinos/as (CEMELA), 41 theory, xxi–xxii, 198; in LGBTQ, 228–32, 229, 230, 231; life science and, 134–37, 136, 137; STEM-MCT, 36–37, 62–63 Tolbert, 213 Torres, Chris, 188, 188–89 Transformational Approach, 150 transgender (T), 222 trust, 94–97, 104, 108–9 tsunami, 160–61; earthquakes related to, 144–46, 153–58. See also earthquakes/tsunami Tucson MCT example, 47–53 Turkle, Sherry, 247 unit conversion, 47, 52–53 United States (U.S.): Bureau of Labor Statistics, 215; Census of, 47, 71–72, 236; regional participation in, 230

Valdes, G., 56 virtual manipulatives, 26–27, 27, 35; National Library of Virtual Manipulatives, 20, 25, 33–34 Vold, E., 150 volume, 52–53 warm-up activity, 11 Warner, M., 223 wealth, 212–13; art related to, 175–76, 176 Web 2.0, 210 WebQuests, 210–11 What We Know, What We Question, and What We Learned (KQL), 99, 102–3, 107, 116–17 white teachers (WT), xix–xx; in multicultural curriculum example, 73–75 whole-group activity, 11 Wicket, W., 20–37. See also math education, MCT example WIDA. See World-Class Instructional Design and Assessment Williams, L. R., 150 Wojcicki, Susan, 214 women, 57 women mathematicians, 179, 181 women’s ways of knowing: book clubs related to, 240–41; civic engagement and, 235–36, 239, 244–45; class structure and, 244; communities in, 237–38; connections related to, 238–39, 241; content linked to pedagogy and assessment in, 246–47; critical considerations on, 247–48; democracy and, 240; demographics and, 236; dismissal of, 237; educational context of, 245–47; evidence on, 248; feminist theories and, 236–37, 239–40, 242–44, 248; garden in, 238–39, 245; grade levels in, 236; key concepts on, 239–40; objectification and, 242–43, 243, 247; observation in, 237; the practice



on, 240–45, 243; relationships with families in, 242; relationships with students in, 241–44, 248; success story about, 236–39; technology integration on, 247; working definitions for, 239–40 working definitions, xxi, 44; in LGBTQ, 222–23; life science and, 125, 125–26; in NGSS, 96–98; for women’s ways of knowing, 239–40

Index 277

World-Class Instructional Design and Assessment (WIDA), 75, 77–79 world rankings, in math education, 5 WT. See white teachers Yosso, T., 252 Yuan, Robert, 253 Zhang Heng, 144, 145, 149, 158–59, 162

About the Editors and Contributors

EDITORS Christine Clark is a professor and senior scholar for multicultural education, and founding vice president for diversity and inclusion at the University of Nevada, Las Vegas. Clark was a Fulbright senior scholar in México and Guatemala, where she conducted research on school and community violence. Clark serves on the editorial board for Equity & Excellence in Education (Routledge), the journal of the University of Massachusetts, Amherst, College of Education, Multicultural Perspectives (Taylor & Francis), the journal of the National Association for Multicultural Education (NAME), and is the associate editor for the higher education section of Multicultural Education (Caddo Gap Press). In 2010 and 2013, Clark was appointed/reappointed to the National Advisory Council of the National Conference on Race and Ethnicity (NCORE). Clark’s research focuses on white antiracist identity development, dismantling the school-to-prison pipeline, sociopolitically located multicultural education, and multicultural organization development. Amanda VandeHei is an assistant professor of literacy in the School of Education at Nevada State College. VandeHei teaches various literacy courses for elementary education majors from a social justice perspective, inspiring future teachers to do the same in their PK-12 classrooms. VandeHei is committed to supporting new teachers and, thus, has been instrumental in the creation of Nevada State College’s New Educators Support and Training (NEST) program, offering teaching mentorship to recent graduates newly entering 279

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About the Editors and Authors

school-based teaching roles. VandeHei’s research interests include teacher education and pedagogy, teacher racial identity, critical literacy, multicultural education, and recruitment and retention of teachers of color. Kenneth J. Fasching-Varner is the Shirley B. Barton and assistant professor in elementary education at Louisiana State University. His areas of expertise include educational foundations, pre-service teacher development, reflective practice, literacy, second language development, critical race theory, culturally relevant pedagogy, and multicultural education. Previously, Fasching-Varner was an assistant professor of literacy and bilingual education at Edgewood College in Madison Wisconsin, and assistant professor of literacy at St. John Fisher College in Rochester New York. Fasching-Varner has a multifaceted research agenda, centered in critical race theory, which examines white racial identity development as it relates to educator identity, culturally relevant engagement, and the development of legal literacy in judicial and educational contexts. Zaid M. Haddad is an assistant professor of interdisciplinary studies and curriculum and instruction, and a member of the Department of Interdisciplinary Learning and Teaching at the University of Texas, San Antonio (UTSA). As a teacher educator and social justice advocate, his research interest is founding the understanding of ways we negotiate our many intersecting identities as we encounter new and changing contexts. At UTSA. Haddad works as the department liaison and coordinator for the UTSA/SAISD Community Lab Schools and is the principal investigator on the UTSA CAREs Project, a collaboration with UT, Austin. Prior to joining the faculty at UTSA, Haddad was a visiting faculty member and doctoral student at the University of Nevada, Las Vegas. GUEST EDITORS Sandra Candel is a researcher and instructor, at the University of Nevada, Las Vegas, in the Department of Teaching and Learning, in the cultural studies, international education, and multicultural education (CSIEME) emphasis. Candel has a background in international education and peace education, has conducted research on peace education in teacher professional development in Saltillo, Mexico, and was invited by the Baja California Department of Education to present her research on the transformative aspect of peace education in Tijuana, Mexico. Candel served as research and editorial assistant to acclaimed multicultural educator, Gary Howard, on the third edition of his



About the Editors and Contributors 281

book, We Can’t Teach What We Don’t Know (Teachers College Press, 2016). Candel’s research interests include critical peace education, multicultural education, social healing, forced and reverse migration, intergroup dialogue, Freirian pedagogy, feminism/muxerismo, and social justice. Candel is a native of Guadalajara, Mexico. Lauren Bell is an MS student at the University of Nevada Las Vegas in the Department of Teaching and Learning with an emphasis in Multicultural Education. Previously, Bell provided wrap-around social services to women and children seeking shelter from domestic violence, and as an academic success coach to undergraduate college students, both in Las Vegas, Nevada. Bell is also an accomplished vocalist. Mónica J Hernández-Johnson is a PhD student at the University of Nevada, Las Vegas in the Department of Teaching and Learning with an emphasis in cultural studies, international education, and multicultural education (CSIEME). Hernández-Johnson is also an instructor for the Department of Gender and Sexuality Studies Program, and the vice president of a campus student organization, the Alliance of Non-Traditional Students. HernándezJohnson is the founder of a non-profit organization, Empowerment through Education, established to support underserved students and their families. Hernández-Johnson’s research primarily focuses on Latinas’ experience in higher education using standpoint theory in concert with the concepts of borderlands and minoritization. In addition, Hernández-Johnson’s research relies on the extensive use of testimonios as a way to offer new perspectives and to challenge Western epistemological frameworks which have ignored or silenced marginalized voices. Cindy Bezard is an instructor and program facilitator for the International Baccalaureate Career Programme at Basic Academy of International Studies in Las Vegas, Nevada. Bezard is also curriculum manager for the Nevada National Aeronautics and Space Administration (NASA) Space Grant Consortium, where she works to establish new and/or revised courses and materials that infuse NASA-related content with Nevada System of Higher Education (NSHE) institutional curricula. Bezard’s course for the Nevada NASA Space Grant Consortium project is titled, “How Your World Works: The Physics of Daily Life.” Since 2016, Bezard has been teaching methods and curriculum development courses focused on improving learning outcomes for students who speak English as a second language for Nevada State College. Bezard’s research focuses on the development of critical cultural competence of career and technical education instructors through transformative

282

About the Editors and Authors

learning experiences. Bezard has presented at state and regional conferences in her areas of research. AUTHORS Tracy Arnold is an eighth grade physical science teacher at Thurman White Academy of the Performing Arts in the Clark County School District in Las Vegas, Nevada. Arnold received her master’s in education in science education in the Department of Teaching and Learning, in the College of Education from the University of Nevada, Las Vegas. Yolanda De La Cruz is professor of mathematics education at Arizona State University. De La Cruz’s research focuses on the mathematics achievement among English language learners, on the role of language in theories of academic achievement differences among language minority students, and education policy related to English language learners in U.S. schools. De La Cruz is editor of the nationally acclaimed book, Volume. 4: Changing the faces of mathematics: Perspectives on Latinos, published by the National Council of Teachers of Mathematics (NCTM). De La Cruz’s work appears in Teaching Children Mathematics, Hispanic Journal of Behavioral Sciences, and in several edited collections. In 1997, De La Cruz was selected as a grant recipient of the National Science Foundation (NSF) and of the McDonnell Foundation. De La Cruz has been a visiting research scholar at Northwestern University in Evanston, Illinois, Cape Peninsula University of Technology in South Africa, and Universidad de la Habana, in Cuba. Javier Díez-Palomar is a Ramon y Cajal senior researcher in the Department of Mathematics and Science Education at the University of Barcelona. He is link convenor for Network 24 (Mathematics Education Research) at ECER (European Conference on Educational Research). Díez-Palomar was Fulbright visiting scholar at CEMELA (Center for the Mathematics Education of Latinos/as) in the Department of Mathematics at the University of Arizona, and is a member of CREA (Community of Research on Excellence for All) and INSEL (International Network for the Social Essentials of Learning), and the Spanish delegate for the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM). Diez-Palomar’s research focuses on mathematics education, curriculum inclusion, learning communities, vulnerable groups and ethnic minorities, and inclusive education, and serves as chief editor for REDIMAT—Journal of Research in Mathematics Education (Hipatia Press), and for Adults Learning Mathematics: An International Journal.



About the Editors and Contributors 283

Eshani Gandhi Lee is a PhD candidate and the President’s UNLV Foundation Graduate Research Fellow in the Department of Chemistry and Biochemistry in the College of Sciences at the University of Nevada, Las Vegas. Lee’s research focuses on making chemistry assessments more accessible and equitable to linguistic minority students, and on faculty perceptions of student success in STEM (science, technology, engineering, and mathematics). Lee has served as a Presidential Student Ambassador and departmental Graduate and Professional Student Association (GPSA) representative. Within the GPSA, Lee has served as executive board treasurer, Constitution and Bylaws Committee chair, and Government Relations Committee member. Through advocacy for STEM access, Lee aims to raise awareness about issues impacting education access and student rights in higher education. Lori Griswold is a middle school computer literacy teacher for the Clark County School District in Las Vegas, Nevada. Griswold also teaches computer science at an online charter high school. Marna Hauk is a postdoctoral scholar for Prescott College mentoring and teaching graduate educators in climate change and sustainability innovation through social and ecological justice. Hauk is a Community Climate Change Fellow of the North American Association for Environmental Education (NAAEE), the Environmental Education (EE) Capacity Project, and the U.S. Environmental Protection Agency (EPA), and a founding faculty member of the Institute for Earth Regenerative Studies (www.earthregenerative.org). Hauk leverages biomimicry, permaculture, and regenerative design to educate for socially just innovation, nurturing cognitive diversities and complex metacognition; her additional research interests include multicultural science education and collaborative ecosocial creativity, as well as intergenerational place relationship as a process in white educator antiracist identity development. Hauk serves on the board of the Journal of Sustainability Education and has more than seventy peer-reviewed presentations and publications. Previously Hauk taught in the Portland Public Schools, at the University of Oregon, and at the University of California, Irvine, as well as at the Chinese Social Service Center at which she taught Chinese language and culture, discovery science, design and construction math, and creative problem solving with elementary-aged learners. Mary Hoelscher is a program specialist for Out for Equity in the Office of Equity at Saint Paul Public Schools in Minnesota. Hoelscher’s work was central to the development and implementation of the District Gender Inclusion Policy, as well as the Gender and Sexual Diversity Parent Advisory Council.

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About the Editors and Authors

Hoelscher was a Teacher Education Redesign Initiative Fellow at the University of Minnesota, Twin Cities where she researched teacher development of pedagogical practices inclusive of gender and sexual diversity. Prior to working in education research and policy, Hoelscher taught biology and physics for five years. Hoelscher is a longtime bisexual community activist and, in 2015, was invited to the Bisexual Community Policy Briefing at the White House. Hoelscher’s transformational change approach to education research aims to bridge multicultural theories to district and classroom practices that empower lesbian, gay, bisexual, transgender, and queer students and families across racially and culturally diverse communities. Adam Masaki Joy has been a public school science teacher for fifteen years. Currently as a certificated teacher in K-8 and 4-12 physics at Discovery Middle School in Vancouver, Washington, he has taught Earth science, life science, math intervention, honors math, honors humanities, and physical education and, currently, teaches eighth-grade physical and high school credit environmental science courses. Joy is currently co-leads MESA, a science program intended to engage women and people of color in science, at Discovery Middle School, and is a member of Vancouver School District’s Science Cadre. Joy graduated with a BA in physics from Reed College and a master of arts in teaching from Lewis and Clark College with an early-childhood math and science focus. Before certification, Joy also taught at the Alberta Science for Kids multicultural science program and was a science explainer for Oregon Museum of Science and Industry. Joy has participated in geology research through the University of Portland’s Teacher’s on the Leading Edge Program, and is a member of National Science Teachers Association (NSTA). Bettibel Kreye is a clinical associate professor in mathematics education in the Department of Teaching and Learning at Virginia Polytechnic Institute and State University (Virgina Tech), in Blacksburg, Virginia. Kreye teaches advanced curriculum and instruction courses for elementary and middle school mathematics majors, works with interns and student teachers at the secondary level, and works with the mathematics specialist master’s program. She currently serves on the executive boards of the Blue Ridge Council Teachers of Mathematics and the Virginia Council Teachers of Mathematics. Betti has worked with the Virginia Department of Education on writing Teacher Resource Guides (2000), revisions of the Mathematics SOL (2001), and as a member of the Mathematics Specialist Task Force. Her interests include the education and training of mathematics specialists, providing professional development for inservice elementary, middle, and high school



About the Editors and Contributors 285

mathematics teachers, and the improvement of student learning through teacher education in best instructional strategies. Antoinette Linton is an assistant professor of science education at California State University, Fullerton. Linton’s research focuses on science teaching methodology and the improvement of academic performance for urban secondary students. She is a co-author of A Clinical Classroom Process a chapter in Rethinking Field Experiences in Preservice Teacher Preparation (Routledge). Linton champions the construction of science learning environments that facilitate mastery of the mind and empowerment of diverse and underserved students in school districts and higher education. Linton serves on the executive board of Division K, Teaching and Teacher Education, for the American Educational Research Association (AERA). As a focus group participant for the Stanford Center for Assessment, Learning and Equity’s (SCALE) EdTPA, she has helped shape the conversation on the knowledge, skills, and understandings needed to effectively demonstrate science teacher competency I clinical programs. Carlos LópezLeiva is an assistant professor in the Department of Language, Literacy, and Sociocultural Studies at the University of New Mexico. LópezLeiva was a CEMELA (Center for the Mathematics Education of Latinos) fellow at the University of Illinois at Chicago in the Program of Curriculum and Instruction with emphasis in bilingual mathematics education. LópezLeiva’s research focuses on understanding the social processes of learning and the development of mathematical and linguistic identities of culturally and linguistically diverse learners. Recent collaborative and interdisciplinary research projects include: TECLA (Teacher Education Collaborative in Language Diversity and Arts Integration) promoting the integration across subjects and arts in a bilingual/TESOL K-5 teacher preparation program, the Mathematics and Engineering Club supporting the learning of computer programming and mathematics of bilingual middle school students through an integrated curriculum (please visit: aolme.unm.edu), and Teachers’ Intercultural Exchange, promoting the intercultural and pedagogical relations between Guatemalan and U.S. K-8 mathematics teachers. Laura Luna is a data analyst for the Tennessee Department of Education in the Upper Cumberland Center of Regional Excellence in Cookeville, Tennessee. Luna previously served as the science, technology, engineering, and math (STEM) coach for Prescott South Elementary and Middle Schools under the Upper Cumberland Rural STEM Initiative as part of the Tennessee STEM Innovation Network, a unique public-private collaboration between

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the Tennessee Department of Education and regional partners with the goal of leveraging Tennessee’s rich STEM resources into opportunities for educators and students. Prior to this, Luna served seventeen years as a high school mathematics teacher and worked to provide opportunities in STEM for students in rural areas through robotics including but not limited to FIRST Robotics. Luna’s research interests include effective professional development, elementary school STEM implementation, and rural mathematics education. Twanelle Deann Walker Majors is an instructor for the College of Arts and Sciences at Tennessee Technological University in Cookeville, Tennessee. Within the Department of Chemistry, Majors teaches introductory undergraduate chemistry courses. Majors was a dissertation fellow for the Southern Regional Education Board while conducting research on quantitative methods for describing physics performance differences as a function of pedagogy. Prior to attaining a PhD in exceptional learning with a STEM education concentration, Majors served in a rural public school as chemistry, advanced placement (AP) chemistry, and scientific research teacher for eight years. Majors began her career as AP coordinator and a grades 8–12 science and mathematics teacher at a rural private school; she held these roles for seven years. Majors’s research focuses on interactive-engagement methods in the STEM lecture setting, assessment development, quantitative data analysis, powerblindness in data analysis, hegemonic practices that produce inequities for females in STEM, and rebuttal of deficit thinking. Allison Mattheis is an assistant professor of applied and advanced studies in education at California State University, Los Angeles, where she teaches courses on sociopolitical foundations of education and research methods. Before completing her PhD in educational policy and leadership at the University of Minnesota, Mattheis was a K–12 science and math teacher for eight years. Research interests include sociocultural analysis of policy and the exploration of educational cultures and climates, using ethnographic qualitative approaches as well as interdisciplinary mixed methods. Mattheis’s work as an educator is driven by a commitment to creating inclusive learning environments that value diversity and promote equity for all students. Mattheis is active in the American Educational Research Association’s (AERA) Queer Studies SIG and engages in a range of research projects with colleagues and students both locally and nationally. Jennifer Meadows is an instructor for the College of Education at Tennessee Technological University in Cookeville, Tennessee. Within the Department of Curriculum and Instruction, Meadows teaches mathematics education



About the Editors and Contributors 287

courses for middle and elementary teachers at the undergraduate and graduate levels. Prior to attaining a PhD in exceptional learning with a STEM education concentration and transitioning to teaching in higher education, Meadows served as an elementary teacher for fourteen years. Meadows’s research focuses on mathematics education, mindset and mathematics, preservice teacher education, and teacher evaluation. Schetema Nealy is a PhD candidate in the Department of Chemistry and Biochemistry in the College of Sciences at the University of Nevada, Las Vegas. Nealy was a National Aeronautics and Space Administration (NASA) Jenkins Pre-Doctoral Fellow, NASA Student Ambassador, and GEAR UP graduate student researcher while she was involved in designing, developing, and delivering professional development workshops for middle school and high school teachers. Nealy was appointed as the Department of Chemistry and Biochemistry’s Graduate and Professional Student Association (GPSA) representative and currently serves on the Board of Directors for the Learning Equipment Supply Service (LESS), a science education nonprofit organization. Nealy’s dissertation research focuses on understanding how underrepresented minority organizations on university campuses affect the science identity development of the undergraduate and graduate students that they serve who are majoring in STEM fields of study. Nealy aims to advance the field of chemistry by motivating and empowering underrepresented minority K-12 students in their scientific abilities, and encouraging them to major in a STEM field in college. Sandra Lucia Osorio is an assistant professor at Illinois State University. A former bilingual educator who worked with children from diverse, racial, ethnic and linguistic backgrounds for eight years, Osorio teaches courses in early childhood and bilingual/English as a second language endorsement. Osorio grew up bilingual and, because of her linguistic differences, had a deficient-based identity placed upon her in school; this has served as source of motivation to her to become an educator and researcher. Osorio recently published, “Que Es Deportar? Teaching from Students’ Lives” (Rethinking Schools, Fall 2015) and “One Test is Not Enough: Getting to Really Know Your Students” (2016 in Disrupting Early Childhood Education Research: Imagining New Possibilities, coedited by Parnell and Iorio, Taylor & Francis). Osorio’s research focuses on how children and pre-service teachers can develop critical consciousness. Dixon Perey is a graduate of the EdD program in educational leadership at California State University Los Angeles, and completed his dissertation on

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the intersectionality of advocacy roles among school counselors and samesex fathers. As a student, Perey presented at American Educational Research Association (AERA) and the University Council on Educational Administration (UCEA) annual meetings. Perey’s research interest include urban education, school counselor leadership, same-sex parent roles in education, antibullying efforts and safe-school climate. Perey is currently an administrator in a public school in Los Angeles. Sarah Roberts is an assistant professor of mathematics education at University of California, Santa Barbara. Roberts, a former middle school and high school math and science teacher, studies and works with inservice and preservice middle and high school mathematics teachers around issues of equity in the teaching and learning of mathematics. Roberts’s research attends to issues of equity in mathematics education focusing on two key areas: 1) working with and investigating secondary mathematics teachers’ practices in supporting English learners (ELs) in their mathematics classrooms; and 2) supporting preservice mathematics teachers to develop and grow ideas about equity in their teaching and learning. Most recently, Roberts has investigated how exemplary secondary mathematics teachers supported ELs in developing skills and tools for inclusion in mathematics (“Big D”) Discourse communities (Gee, 1996) and how these teachers provided cognitively demanding mathematics experiences for all students. Jeff Sapp is a professor of education at California State University, Dominguez Hills, in Carson, California. Sapp has been a teacher, writer, and activist for thirty-six years. Sapp was senior curriculum specialist/writer at Teaching Tolerance, a project of the Southern Poverty Law Center. Sapp is an associate editor of Multicultural Perspectives (Taylor & Francis), the journal of the National Association for Multicultural Education (NAME), and one of the editors/writers for Rethinking Schools’ newest book, Rethinking Sexism, Gender, and Sexuality. Sapp’s children’s book, Rhinos & Raspberries: Tolerance Tales for the Early Grades, won the Golden Lamp Award, the Association of Educational Publishers’ highest honor. Find out more at www.jeffsapp.com. Janessa Schilmoeller is director of Camp Rising Sun an initiative of the Louis August Jonas Foundation, headquartered in New York City. Previously, Schilmoeller was lead technology teacher at an elementary school in Las Vegas, Nevada. As lead technology teacher, Schilmoeller taught weekly technology classes, assisted with IT-related issues and advised staff members on the effective integration of multicultural education and technology in school-wide curriculum and instruction. Schilmoeller holds an MS in cur-



About the Editors and Contributors 289

riculum and instruction with an emphasis in Multicultural Education from the University of Nevada, Las Vegas. Schilmoeller’s research interests include multicultural service-learning, dismantling the school-to-prison pipeline, and critical pedagogy. Her research has been presented at conferences sponsored by the National Association of Multicultural Education (NAME), the Comparative and International Education Society (CIES), and the Ethnographic and Qualitative Research Conference (EQRC). Neal Strudler is professor emeritus in the Department of Teaching and Learning in the College of Education at the University of Nevada, Las Vegas. Previously Strudler was assistant chair, and elementary education coordinator in the Department of Curriculum and Instruction. Strudler’s research has focused on strategies for integrating technology in both teacher education and K-12 schools. Strudler has served as a member of the board of directors of the International Society for Technology in Education (ISTE), as president of ISTE’s Teacher Education Special Interest Group, as president of the American Educational Research Association’s (AERA) TACTL (Technology as an Agent of Change in Teaching and Learning) Special Interest Group (SIG), as research paper chair for the National Educational Computing Conference (NECC), and as member of the National Educational Technology Standards for Teachers’ (NETS-T) Stakeholders Advisory Committee. Gresilda Tilley-Lubbs is an associate professor of English as a Second Language/Multicultural Education in the School of Education at Virginia Polytechnic Institute and State University (Virginia Tech) in Blacksburg, Virginia. Tilley-Lubbs’s research is informed by critical pedagogy and autoethnography. Tilley-Lubbs interrogates the role of whiteness, power, and privilege in preparing teachers to teach in immigrant and refugee communities, and in conducting research with participants in vulnerable and marginalized communities. Tilley-Lubbs’s research listens to the voices of Mexican immigrants through the perspective of transnational (auto)ethnography, integrated with critical autoethnography, ultimately combining critical pedagogy and autoethnography. Tilley-Lubbs’s work has been published in both English and Spanish in the United States, Spain, and México. Tilley-Lubbs also teaches courses on critical autoethnography and multiculturalism for the Institute of Critical Pedagogy in Chihuahua, México. Brian Trinh is a researcher in the Department of Psychology at the University of Nevada, Las Vegas, where he has worked on computational models of GABAergic hippocampal networks implicated in schizophrenia. Trinh is interested in secondary education, particularly from a pedagogical, psy-

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About the Editors and Authors

chological, and philosophical perspective, that focuses on fostering creative and critical thinking in students across disciplines. Previously, Trinh taught twelfth grade religious, moral, and philosophical studies at Madras College, in St. Andrews Fife Scotland. Jeremy Yoder is an assistant professor at California State University, Northridge, studying ecology and evolutionary genetics. Yoder has conducted research on the coevolution of interacting species, the genetic basis of adaptation to different environmental conditions and biological communities, and the interaction of LGBTQ identities with scientific careers.