Integrated Approaches to STEM Education: An International Perspective 9783030522292, 3030522296

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Advances in STEM Education Series Editor: Yeping Li

Judy Anderson Yeping Li   Editors

Integrated Approaches to STEM Education An International Perspective

Advances in STEM Education Series Editor Yeping Li Texas A&M University College Station, TX, USA

Advances in STEM Education is a book series focusing on cutting-edge research and knowledge development in science, technology, engineering and mathematics (STEM) education from pre-college through continuing education around the world. It is open to all topics in STEM education, both in and outside of classrooms, including innovative approaches and perspectives in promoting and improving STEM education, and the processes of STEM instruction and teacher education. This series values original contributions that view STEM education either in terms of traditionally defined subject-based education or as an educational undertaking involving inter-connected STEM fields. The series is open to new topics identified and proposed by researchers internationally, and also features volumes from invited contributors and editors. It works closely with the International Journal of STEM Education and Journal for STEM Education Research to publish volumes on topics of interest identified from the journal publications that call for extensive and in-depth scholarly pursuit. Researchers interested in submitting a book proposal should contact the Series Editor: Yeping Li ([email protected]) or the Publishing Editor: Melissa James ([email protected]) for further information. Series editor Yeping Li, Texas A&M University, College Station, Texas, USA International Advisory Board Spencer A. Benson, University of Macau, Macau, China Richard A. Duschl, Pennsylvania State University, USA Dirk Ifenthaler, University of Mannheim, Germany Kenneth Ruthven, University of Cambridge, UK Karan L. Watson, Texas A&M University, USA

More information about this series at http://www.springer.com/series/13546

Judy Anderson  •  Yeping Li Editors

Integrated Approaches to STEM Education An International Perspective

Editors Judy Anderson Sydney School of Education and Social Work The University of Sydney Camperdown, NSW, Australia

Yeping Li Texas A&M University College Station, TX, USA

ISSN 2520-8616     ISSN 2520-8624 (electronic) Advances in STEM Education ISBN 978-3-030-52228-5    ISBN 978-3-030-52229-2 (eBook) https://doi.org/10.1007/978-3-030-52229-2 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

1 Investigating the Potential of Integrated STEM Education from an International Perspective����������������������������������������������������������    1 Judy Anderson and Yeping Li Part I Approaches to STEM Integration 2 STEM Integration: Diverse Approaches to Meet Diverse Needs��������   15 Yeping Li and Judy Anderson 3 STEM Education for the Twenty-First Century ����������������������������������   21 Russell Tytler 4 Facilitating STEM Integration Through Design����������������������������������   45 Lyn D. English 5 A Review of Conceptions of Secondary Mathematics in Integrated STEM Education: Returning Voice to the Silent M������������������������������   67 Erin E. Baldinger, Susan Staats, Lesa M. Covington Clarkson, Elena Contreras Gullickson, Fawnda Norman, and Bismark Akoto 6 What Is the Role of Statistics in Integrating STEM Education?��������   91 Jane Watson, Noleine Fitzallen, and Helen Chick 7 Numeracy Across the Curriculum as a Model of Integrating Mathematics and Science������������������������������������������������������������������������  117 Anne Bennison and Vince Geiger 8 Investigating the Epistemic Nature of STEM: Analysis of Science Curriculum Documents from the USA Using the Family Resemblance Approach��������������������������������������������������������  137 Wonyong Park, Jen-Yi Wu, and Sibel Erduran 9 Approaches to Effecting an iSTEM Education in Southern Africa: The Role of Indigenous Knowledges ����������������������������������������  157 Judah Makonye and Reuben Dlamini v

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Part II Designing Integrated STEM Approaches for Students 10 Focusing on Students and Their Experiences in and Through Integrated STEM Education������������������������������������������������������������������  177 Yeping Li and Judy Anderson 11 Connecting Computational Thinking and Science in a US Elementary Classroom ��������������������������������������������������������������  185 Emily C. Miller, Samuel Severance, and Joe Krajcik 12 Developing US Elementary Students’ STEM Practices and Concepts in an Afterschool Integrated STEM Project�����������������  205 Sasha Wang, Yu-hui Ching, Dazhi Yang, Steve Swanson, Youngkyun Baek, and Bhaskar Chittoori 13 What Can Integrated STEAM Education Achieve? A South Korean Case������������������������������������������������������������������������������  227 Nam-Hwa Kang 14 Student STEM Beliefs and Engagement in the UK: How They Shift and Are Shaped Through Integrated Projects����������  251 Karen Skilling 15 Climate Change and Students’ Critical Competencies: A Norwegian Study����������������������������������������������������������������������������������  271 Lisa Steffensen 16 Examining a Technology and Design Course in Middle School in Turkey: Its Potential to Contribute to STEM Education����������������  295 Behiye Ubuz 17 Incorporating Mathematical Thinking and Engineering Design into High School STEM Physics: A Case Study ����������������������  313 Israel Touitou, Barbara Schneider, and Joe Krajcik 18 STEM Skill Assessment: An Application of Adaptive Comparative Judgment ��������������������������������������������������������������������������  331 Scott R. Bartholomew and P. John Williams Part III Implementing Integrated STEM Approaches in Teacher Education 19 Developing Teachers, Teaching, and Teacher Education for Integrated STEM Education������������������������������������������������������������  353 Yeping Li and Judy Anderson 20 Missing Coherence in STEM Education: Creating Design-Based Pedagogical Content Knowledge in a Teacher Education Program����������������������������������������������������������������������������������  361 Ibrahim Delen, Consuelo J. Morales, and Joe Krajcik

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21 Promoting a Learning Scenario for an Integrated Approach to STEM: Prospective Teachers’ Perspectives in Portugal������������������  385 Ana Henriques, Hélia Oliveira, and Mónica Baptista 22 Designing and Evaluating an Integrated STEM Professional Development Program for Secondary and Primary School Teachers in Australia ������������������������������������������������������������������  403 Judy Anderson and Deborah Tully 23 Argumentation in Primary Grades STEM Instruction: Examining Teachers’ Beliefs and Practices in the USA ����������������������  427 AnnaMarie Conner, Barbara A. Crawford, Timothy Foutz, Roger B. Hill, David F. Jackson, ChanMin Kim, and Sidney A. Thompson 24 Integrated STEM Education in Virginia: CodeVA Elementary Coaches Academy����������������������������������������������������������������  447 Anita Crowder, Rebecca Dovi, and David Naff 25 Integrated STEM in Australian Public Schools: Opening Up Possibilities for Effective Teacher Professional Learning��������������  469 Jane Hunter 26 Teachers’ Responses to an Integrated STEM Module: Collaborative Curriculum Design in Taiwan, Thailand, and Vietnam����������������������������������������������������������������������������������������������  491 Pei-Ling Lin, Yu-Ta Chien, and Chun-Yen Chang 27 Promoting Integrated STEM Tasks in the Framework of Teachers’ Professional Development in Portugal�����������������������������  511 Maria Cristina Costa, António Domingos, and Vítor Teodoro Part IV Reflections and Future Directions 28 Reflections of an Engineering Education Scholar on Integrated Approaches to STEM Education������������������������������������  535 Jeffrey E. Froyd 29 Reflections on Integrated Approaches to STEM Education: An International Perspective��������������������������������������������������������������������  543 Mei-Hung Chiu and Joe Krajcik Index������������������������������������������������������������������������������������������������������������������  561

About the Editors

Judy  Anderson  is an Associate Professor in Mathematics Education at the University of Sydney, Australia, with extensive experience working with undergraduate and postgraduate students. With publications on problem-solving in the school curriculum and teachers’ problem-solving beliefs and practices, she has also worked with colleagues from the University of Sydney to investigate middle school students’ motivation and engagement. Judy is currently the Director of the STEM Teacher Enrichment Academy, an innovative professional learning program for STEM teachers that was established in 2014 by a collaborative team of academics from the faculties of Education and Social Work, Science, and Engineering. A team of 12 academics deliver the program and to date, the Academy has reached over 1250 teachers from more than 240 primary and secondary school settings in NSW, Australia. With her colleagues, Judy has been conducting research into the impact of the STEM Academy program on teachers, school leaders, students, parents, and local communities. Over her career, she has been an active member of several professional teaching associations in which she has held leadership roles including president of the Australian Association of Mathematics Teachers (AAMT) and of the Australian Curriculum Studies Association (ACSA). She is currently the Secretary of the International Group for the Psychology of Mathematics Education (IGPME). Yeping Li  is Professor at the Department of Teaching, Learning & Culture in the College of Education and Human Development, Texas A&M University, USA. His research focuses on curriculum studies in school mathematics, STEM education, international education, and teacher education. He is the founding editor-in-chief of the International Journal of STEM Education and Journal for STEM Education Research, both published by Springer, and is also the editor of several monograph series including, Advances in STEM Education also published by Springer. In addition to publishing over 15 books and special journal issues in recent years, he has published more than 100 articles in topic areas that he is interested in. He has also organized and chaired many group sessions at various national and international professional conferences, such as International Congress on Mathematical Education (ICME)-10 (2004), ICME-11 (2008), ICME-12 (2012), and American Educational Research Association (AERA). He received his Ph.D. in Cognitive Studies in Education from the University of Pittsburgh, USA. ix

Contributors

Bismark Akoto  University of Minnesota, Minneapolis, MN, USA Judy Anderson  Sydney School of Education and Social Work, The University of Sydney, Camperdown, NSW, Australia Youngkyun Baek  Boise State University, Boise, ID, USA Erin E. Baldinger  University of Minnesota, Minneapolis, MN, USA Mónica Baptista  Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal Scott R. Bartholomew  Brigham Young University, Provo, UT, USA Anne Bennison  University of the Sunshine Coast, Sunshine Coast, QLD, Australia Chun-Yen Chang  National Taiwan Normal University, Taipei City, Taiwan Helen Chick  University of Tasmania, Hobart, TAS, Australia Yu-Ta Chien  National Taiwan Normal University, Taipei City, Taiwan Yu-Hui Ching  Boise State University, Boise, ID, USA Bhaskar Chittoori  Boise State University, Boise, ID, USA Mei-Hung Chiu  National Taiwan Normal University, Taipei City, Taiwan AnnaMarie Conner  University of Georgia, Athens, GA, USA Maria Cristina Costa  Instituto Politécnico de Tomar, Tomar, Portugal Lesa M. Covington Clarkson  University of Minnesota, Minneapolis, MN, USA Barbara A. Crawford  University of Georgia, Athens, GA, USA Anita Crowder  Virginia Commonwealth University, Richmond, VA, USA Ibrahim Delen  Usak University, Faculty of Education, Usak, Turkey Reuben Dlamini  University of the Witwatersrand, Johannesburg, South Africa xi

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Antonio Domingos  Universidade Nova De Lisboa, Lisbon, Portugal Rebecca Dovi  CodeVA, Richmond, VA, USA Lyn D. English  Queensland University of Technology, Brisbane, QLD, Australia Sibel Erduran  University of Oxford, Oxford, UK Noleine Fitzallen  La Trobe University, Melbourne, VIC, Australia Timothy Foutz  University of Georgia, Athens, GA, USA Jeffrey E. Froyd  Ohio State University, Columbus, OH, USA Vince Geiger  Institute for Learning Sciences and Teacher Education, Australian Catholic University, Brisbane, QLD, Australia Elena Contreras Gullickson  University of Minnesota, Minneapolis, MN, USA Ana Henriques  Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal Roger B. Hill  University of Georgia, Athens, GA, USA Jane Hunter  The University of Technology, Sydney, Australia David F. Jackson  University of Georgia, Athens, GA, USA Nam-Hwa Kang  Korea National University of Education, Cheongju, South Korea ChanMin Kim  Pennsylvania State University, University Park, PA, USA Joe Krajcik  Michigan State University, East Lansing, MI, USA Yeping Li  Texas A&M University, College Station, TX, USA Pei-Ling Lin  National Taiwan Normal University, Taipei City, Taiwan Judah Makonye  University of the Witwatersrand, Johannesburg, South Africa Emily C. Miller  University of Wisconsin—Madison, Madison, WI, USA Consuelo  J.  Morales  Michigan State University, CREATE for STEM Institute, East Lansing, MI, USA David Naff  Virginia Commonwealth University, Richmond, VA, USA Fawnda Norman  University of Minnesota, Minneapolis, MN, USA Hélia Oliveira  Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal Wonyong Park  University of Oxford, Oxford, UK Barbara Schneider  Michigan State University, East Lansing, MI, USA Samuel Severance  University of California, Santa Cruz, CA, USA Karen Skilling  University of Oxford, Oxford, UK

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Susan Staats  University of Minnesota, Minneapolis, MN, USA Lisa Steffensen  Western Norway University of Applied Sciences, Bergen, Norway Steve Swanson  Boise State University, Boise, ID, USA Vitor Teodoro  Universidade Nova De Lisboa, Lisbon, Portugal Sidney A. Thompson  University of Georgia, Athens, GA, USA Israel  Touitou  CREATE for STEM Institute, Michigan State University, East Lansing, MI, USA Deborah Tully  The University of Sydney, Camperdown, NSW, Australia Russell Tytler  Deakin University, Melbourne, VIC, Australia Behiye Ubuz  Middle East Technical University, Ankara, Turkey Sasha Wang  Boise State University, Boise, ID, USA Jane Watson  University of Tasmania, Hobart, TAS, Australia P. John Williams  Curtin University, Perth, Australia Jen-Yi Wu  University of Oxford, Oxford, UK Dazhi Yang  Boise State University, Boise, ID, USA

Chapter 1

Investigating the Potential of Integrated STEM Education from an International Perspective Judy Anderson and Yeping Li

Contents 1.1  B  ackground: Sharing Common Interests in STEM Education 1.2  Inviting International Perspectives on Integrated STEM Education 1.3  Structuring and Organising the Volume 1.3.1  Reviewing Approaches to STEM Integration 1.3.2  Designing Integrated STEM Approaches for Students 1.3.3  Implementing Integrated STEM Approaches in Teacher Education 1.3.4  Identifying Future Directions 1.4  STEM Education: Now More than Ever? References

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1.1  B  ackground: Sharing Common Interests in STEM Education We are both mathematics educators by training with a keen interest in curriculum and the ways teachers use innovative curriculum to transform students’ experiences in classrooms. Having written about mathematics curriculum and conducted research into the ways teachers use the curriculum to design lessons and tasks to meet their students’ needs (e.g., Anderson, 2014; Li & Lappan, 2014), we independently developed an interest in integrated curriculum and the ways the mathematics curriculum connects with the other STEM subjects: science, technology, and engineering. We have published in the field of science, technology, engineering, and mathematics (STEM) education, but we agree this is still a contested space and we J. Anderson (*) Sydney School of Education and Social Work, The University of Sydney, Camperdown, NSW, Australia e-mail: [email protected] Y. Li Texas A&M University, College Station, TX, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_1

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need to encourage our colleagues to take a more critical stance about the role of STEM education in the broader school curriculum (Li & Schoenfeld, 2019; Tytler, Williams, Hobbs, & Anderson, 2019). To pursue the goal of encouraging debate about integrated STEM education, we sought opportunities to discuss the challenges with colleagues at international conferences. As members of the International Group for the Psychology of Mathematics Education (IGPME), we facilitated a Working Group at the Singapore conference in 2017, followed by a Discussion Group at the Umea, Sweden conference in 2018. Each session was well attended with 25–30 participants from more than 15 countries at each. As participants shared their knowledge and experiences of STEM education, it became apparent many of our colleagues were similarly interested in integrated STEM curriculum and the role of mathematics in connecting the STEM subjects. At each session, we proposed the development of a volume to share our experiences, critique current practices, and propose new approaches to STEM curriculum and instruction. Not wanting to limit the contributions to mathematics educators, we also circulated a call for chapters to a broad audience of STEM educators and this volume is the outcome of this joint effort. The objective of Integrated Approaches to STEM Education: An International Perspective was to showcase international contributions to STEM research and practice with recommendations for researchers, policymakers, and teachers about the future of integrated STEM education. The book aimed to evaluate the efficacy of integrated STEM education as it is currently practised and identify opportunities for further research and potential collaborations in the STEM education research community.

1.2  I nviting International Perspectives on Integrated STEM Education Researching STEM education has been gaining momentum with increased calls for strategies to improve student engagement and to increase participation in senior schooling in countries where mathematics and science are not compulsory (Freeman, Marginson, & Tytler, 2015; Roth, 2018). At the same time, the diversity of perspectives and approaches (from curricular to pedagogical) challenges the collection of evidence to establish a research base which justifies the funds currently being invested in STEM education (Honey, Pearson, & Schweingruber, 2014). In the USA, STEM education has been extensively supported over the years with national policy and substantial Federal Government funding to develop a STEM focus (Li, 2014; Li, Wang, Xiao, Froyd, & Nite, 2020). Bybee (2013) argues the lack of a common understanding or definition of STEM education has led to a diversity of approaches with scant evidence for the success of many of the initiatives adopted by schools and school systems. In recent reports in Australia, there has been a strong recognition of the importance of STEM thinking and skills for all students and an advocacy of the need to bring school science and mathematics closer to the way

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science and mathematics are practiced in contemporary settings across the STEM disciplines (Office of the Chief Scientist, 2016; Tytler, Swanson, & Appelbaum, 2015). Integrated Approaches to STEM Education: An International Perspective provides a platform for international scholars to share evidence for effective practices in integrated STEM education and contribute to the theoretical and practical knowledge gained from the diversity of approaches. Many publications on STEM education focus on one or two of the separate STEM disciplines without considering the potential for delivering STEM curriculum as an interdisciplinary approach (Anderson, English, Fitzallen, & Symons, 2020)—this publication seeks to debate the efficacy of an integrated STEM curriculum and instruction, providing evidence to examine and support various perspectives. The volume focuses on the problems seen by teachers and academics working in the fields of science, technology, engineering, and mathematics and provides a set of valued practices which have demonstrated their use and viability to improve the quality of integrated STEM education. This volume includes chapters that debate the conceptual basis of integrated STEM education, review historical developments in integrated STEM education policy and practices, describe the outcomes of effective integrated STEM education approaches, including curriculum design and pedagogical practices, and provide recommendations for ways forward for research and practice. This volume offers evidence to a range of stakeholders interested in integrated STEM education. Policymakers can benefit from access to research into integrated STEM education and its outcomes, and teachers can benefit from learning new approaches to the design and delivery of integrated STEM education. Their students can then benefit from opportunities designed and provided to solve real-world problems using knowledge from some or all the STEM subjects. Finally, we expect our readers will benefit from reading about the ways different countries and jurisdictions have approached integrated STEM education over the last few years across all grades of schooling. Our initial invitation to contribute to the volume welcomed contributions on empirical research, theoretical frameworks, or detailed case studies showing what works in classrooms and what lessons may be learned. We were interested in chapters that investigated diverse contexts and explored a broad range of STEM education issues and challenges. The original list of suggested topics or themes for the volume included: • • • • • • • • •

Perspectives on integrated STEM education Approaches to integrating the separate STEM curriculum disciplines Case studies of integrated STEM education in countries or school jurisdictions Case studies of integrated STEM education in classrooms or schools Developing teachers’ integrated STEM education knowledge and practices Assessing integrated STEM education The role of one of the disciplines in integrated STEM education The influence of context on integrated STEM practices Involvement with the wider community and other stakeholders in integrated STEM education in schools

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• The most appropriate skills and dispositions for integrated STEM education • Students’ and teachers’ reactions to integrated STEM education and, • Approaches to researching integrated STEM education. We received contributions which explored many of these topics and themes. However, organising this diversity into a coherent volume was a challenge, but we decided to structure the volume into four parts, according to the focus on approaches to STEM integration, designing integrated approaches for students, implementing integrated STEM approaches in teacher education, and future directions. The chapter contributions in each part are described in the next section of this chapter.

1.3  Structuring and Organising the Volume 1.3.1  Reviewing Approaches to STEM Integration The challenge for teachers and school leaders is to determine how they will design integrated STEM curriculum when faced with separate subject curriculum documents and, typically, separate subject assessment and reporting regimes. The design of integrated STEM curriculum is not a trivial task and requires subject expertise and experience in designing school-based curriculum which focuses not just on curriculum content but on potentially new pedagogical approaches. While designing integrated curriculum is not a new idea (see for example Beane, 1997; Dewey, 1938), focusing on the STEM subjects has meant that schools have had to rally the STEM expertise within the school and to plan ways to work together, particularly in secondary school contexts, where teachers may be located in separate staff rooms. But as Mockler (2018) states, … a renewed focus on STEM … both in Australia and elsewhere, might provide us with a new energy for curriculum innovation and curriculum integration. We might add to this the imperatives contributed by the contemporary world, where developing students’ capacity to navigate knowledge and information across disciplinary boundaries is increasingly important (p. 229).

In designing integrated STEM curriculum, some describe the level of integration or a continuum of integration suggesting a hierarchy from disciplinary, to multidisciplinary, to interdisciplinary, and finally to transdisciplinary (Beane, 1997; Vasquez, 2015). Like Vasquez’s “inclined plan of STEM integration” (p.  13), Gresnigt, Taconis, van Keulen, Gravemeijer, and Baartman (2014) proposed a ‘staircase’ model of curriculum integration, but they added isolated, connected, and nested levels before multidisciplinary, interdisciplinary, and transdisciplinary. Rennie, Venville, and Wallace (2018) argued against these hierarchical approaches to STEM integration because they imply one end of the continuum is of greater value than the other. Instead, they used categorisations of the kinds of approaches schools adopted

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based on their extensive experience working with teachers and identified six approaches which they referred to as synchronised, thematic, project based, cross-­ curricular, school specialised, and community-focused. Regardless of the level of integration of the STEM subjects, or the approach adopted by schools to design integrated curriculum, curriculum integration is challenging and requires time, effort, collaboration, and commitment by teachers and school leaders. Mockler (2018) described enablers and constraints to designing integrated curriculum when reflecting on the development of the first national curriculum in Australia. She suggested enablers include having broader goals for education than just learning content knowledge, focusing on understanding ‘big ideas’, and learners ready access to real-world information through digital technologies. Whereas constraints might include a backlash against learner-centred approaches, a desire for standardisation and increased focus on core subjects, and greater accountability particularly through high-stakes testing. While the constraints might dampen the potential for integrated curriculum work, teachers and school leaders continue to seek ways to design more effective learning opportunities for their students and this is particularly evident in the international STEM movement (Anderson, Wilson, Tully, & Way, 2019; English, 2019; Tytler et al., 2019). The chapters in this first part of the volume consider some of the challenges described here, as well as discipline integrity and policy agendas. Tytler describes the growth of STEM education, particularly from the policy perspective and through a framework of competencies associated with the STEM disciplines; he examines interdisciplinarity in greater depth, particularly as it impacts on the integrity of mathematics. The chapter by Baldinger and her colleagues addresses the concern about the role of mathematics in integrated STEM curriculum by conducting a literature review of recent publications to identify themes from “mathematically-rich integrated STEM studies”. Themes include communication, task authenticity, the centrality of inquiry, and the importance of informal learning spaces. Park, Wu, and Erduran analyse science curriculum documents to identify evidence of types of STEM discipline knowledge and understandings. An integrated STEM framework for developing countries is investigated in the chapter by Makonye and Diamini. Chapters examining the process of, or potential models for, curriculum integration include those by English, Watson, Fitzallen and Chick, and Bennison and Geiger. In her chapter, English explores the role of design in curriculum innovation and integration, presenting evidence from students’ design project work. Watson and colleagues propose the potential of statistics to facilitate integration of the STEM subjects and describe several approaches through students’ activities. While Bennison and Geiger investigate the potential of numeracy across the curriculum as a new model for STEM curriculum integration with outcomes presented from teachers’ lessons. The second part of the volume examines integrated STEM projects developed to support student learning.

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1.3.2  Designing Integrated STEM Approaches for Students While Dewey (1938) and Beane (1997) promoted experiential and connected learning approaches to enhance students’ understanding of their world, most countries have separate curriculum documents for each of the STEM subjects. Consequently, most schools present the curriculum as separate learning experiences, particularly in secondary schools, although science, technology, and mathematics teachers may use ‘project work’ to engage students and provide them with opportunities to tackle real-world problems (Tytler et  al., 2019). However, most real-world problems require the use of knowledge from more than one of the STEM subjects. While primary school teachers are better placed to connect knowledge for their students, it seems a wasted opportunity for secondary school STEM teachers not to connect with each other when such projects are offered to the students they teach (Anderson et al., 2020). Research into the efficacy of integrated STEM education, particularly regarding long-term benefits to students, is still an emerging field. However, evidence is gradually building that an integrated, interdisciplinary approach to teaching science, technology, and mathematics (including engineering-like design practices) supports improved problem-solving skills, increased learning-engagement, and improved science and mathematics outcomes (Becker & Park, 2011; Tytler et  al., 2019). Combining inquiry-based learning with an integrated STEM approach provides rich opportunities for students to develop a range of general capabilities, such as critical thinking, self-direction, creativity, and communication (Rosicka, 2016). When the inquiry focuses on a real-world problem that is meaningful to the students, their engagement has been found to extend beyond their immediate learning, to increased interest in further study in the component disciplines of STEM, and in future STEM-­ related careers (Holmes, Gore, Smith, & Lloyd, 2018). The chapters in this part of the volume present case studies of integrated STEM program experiences for students, with evidence of impact on student learning and engagement. At the primary school level, Miller, Severance, and Krajcik describe a fifth-grade unit connecting the particle nature of matter with computational thinking. Evidence from students reveals how identifying and using patterns helps students explain and predict the phenomenon of taste. Wang and her colleagues explore the use of robotics in an afterschool setting to identify primary school students’ use of scientific language to communicate thinking. Kang presents evidence of impact of a large-scale integrated STEAM education approach in South Korea, which used project-based learning to deliver programs across most levels of schooling. Compared to a control group of students who were not taught the integrated approach, the STEAM students had variable outcomes, depending on the expertise of the curriculum designers. Several chapters have focused on integrated STEM approaches in secondary school contexts. Skilling uses a transdisciplinary STEM project to investigate students’ beliefs and engagement as they build electro-mechanical robots. Steffensen used tenth grade students’ discussions and debates about climate change to explore

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their use of mathematics to argue and critically analyse information. From a different perspective, Ubuz conducted research into teachers’ views about whether a Technology and Design course had the potential to contribute to students’ STEM capability development. Touitou, Schneider, and Krajcik report on the assessment of students’ performance on integrated STEM tasks designed to invoke mathematical and design thinking in a high school physics unit of work. Bartholomew and Williams examine an approach to STEM skill assessment aimed at improving reliability and validity of assessing open-ended STEM projects. Designing effective integrated STEM experiences for students requires substantial support for teachers in both preservice and in-service education. Studies into student engagement and motivation suggest students begin to disengage from the STEM subjects as early as primary school, although the main shifts appear to occur in early secondary school (Martin, Anderson, Bobis, Way, & Vellar, 2012). Addressing engagement and achievement in the STEM subjects in schools requires support for teachers to design curriculum which enthuses students, challenges their beliefs about the role of the STEM subjects in solving real-world problems, and inspires them to continue to study these subjects into the future (Moore, Johnson, Peters-Burton, & Guzey, 2016). Support for teachers through professional learning is a necessary component for successful implementation of innovative programs.

1.3.3  I mplementing Integrated STEM Approaches in Teacher Education Professional learning programs for primary and secondary school STEM teachers have been designed and implemented in many contexts to support teacher co-­ construction of integrated STEM curriculum and inquiry-based learning approaches (Nadelson & Seifert, 2017). Informed by research into high-quality, high-impact professional development design principles, effective programs should involve teams of teachers, working collaboratively to design programs suitable for their students (Darling-Hammond, Hyler, Gardner, & Espinoza, 2017; Voogt, Pieters, & Handelzalts, 2016). Designing real-world STEM problems or STEM project-based learning tasks also involves designing assessment rubrics to provide feedback to students on discipline knowledge as well as the key skills of critical thinking, creativity, collaboration, and communication (Care & Kim, 2018). Some of the contributions in this part of the volume examined the development of STEM knowledge in preservice teacher education. Delen, Morales, and Krajcik develop a Design-based Pedagogical Content Knowledge (DPCK) framework to support teachers using engineering design processes to connect scientific knowledge with pedagogy. Henriques, Oliveira, and Baptista investigate prospective mathematics and physics teachers’ development of integrated STEM projects using an authentic integration model.

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Other chapters examine the professional learning of practicing teachers, using a variety of approaches. Anderson and Tully evaluate a year-long program for both primary and secondary school teachers as school teams worked together to design, implement, and evaluate a school-based approach to integrated STEM education. Connor and her colleagues present results from a computer programming professional learning program for primary school teachers, using an innovative model to teach coding and collective argumentation. Crowder, Dovi, and Naff also investigate a coding professional development program for elementary school coaches with evidence of the effectiveness of the collaborative, inquiry-based design of the program. Hunter’s high possibility classroom model was used in three elementary schools to demonstrate how teachers collaborated in school-based teams to implement new pedagogies to promote integrated STEM.  Through a collaboration between researchers in Taiwan, Thailand, and Vietnam, Lin, Chien, and Chang describe an approach to the development of an integrated STEM module, followed by teachers’ reactions to a workshop demonstrating the use of the module, while Costa and her colleagues report how coaching by university educators supports elementary teachers’ implementation of integrated STEM tasks in classrooms. All the teacher education programs presented here provide evidence of the potential to impact teachers’ knowledge and understanding of STEM and their capacity to implement integrated STEM approaches in their classrooms. However, questions of scalability and sustainability for each of these programs remain. So, what of future directions for research in integrated STEM education?

1.3.4  Identifying Future Directions Two commentary chapters are contained in this volume from experienced STEM education scholars. We asked them to provide a commentary on the work published in this volume and to offer their suggestions for future directions. Froyd’s perspective, from an engineering education scholar, suggests the need for further investigation of the impact of computational thinking on STEM project work, the continued focus on teacher professional learning, and further consideration of the types of assessment approaches appropriate for STEM project work. In their reflections on the volume, Chiu and Krajcik focused on the notion of an iSTEM-plus curriculum, highlighting the opportunities afforded through an integrated STEM curriculum, but also describing the challenges and threats. They present strategies to support the further development of iSTEM-plus environments, concluding with a call for greater international collaboration and sharing of resources and expertise. While the chapters in this volume provide evidence of the potential of integrated STEM education, many authors also raise questions and possibilities for further research. Some suggestions for further research raised by authors include, but are not limited to:

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1. Investigating what models of interdisciplinarty and in what topics lead to engagement of students for particular learning outcomes (Tytler in Chap. 3) 2. Developing programs of assessment that support such curriculum innovations (Bartholomew & Williams in Chap. 18; Tytler  in Chap. 3; Wang et  al. in Chap. 12.) 3. Exploring the development and cognitive components of systems thinking (English in Chap. 4) 4. Understanding teachers’ and students’ reasoning strategies in integrated STEM environments (Baldinger et al. in Chap. 5) 5. Comparing longitudinal research on student outcomes focusing on data analysis aspects of integrated STEM activities (Watson et al. in Chap. 6) 6. Researching how teachers can provide greater emphasis on mathematics to promote critical aspects of STEM learning (Bennison & Geiger in Chap. 7) 7. Investigating how mathematics, as a discipline, operates in a wider enterprise of STEM and how it relates to the other three disciplines (Park, Wu & Erduran in Chap. 8) 8. Conducting international comparative studies about diverse and effective ways of developing twenty-first century competencies (Wang et al. in Chap. 12), 9. Exploring issues of subject integrity and inequitable subject representation in STEM project work (English in Chap. 4; Skilling in Chap. 14), 10. Considering issues of teacher implementation of integrated STEM curriculum in diverse contexts (Ubuz in Chap. 16), 11. Researching student transferability of STEM skills beyond the task or unit within which they were demonstrated (Touitou et al. in Chap. 17), 12. Following PSTs into classrooms to examine whether their STEM knowledge is transferred into their classrooms (Delen et al. in Chap. 20; Henriques et al. in Chap. 21) 13. Connecting learning in teacher professional learning about integrated STEM with improved student learning outcomes (Anderson & Tully in Chap. 22). With these research ideas in mind, we hope readers will continue to explore integrated STEM approaches and contribute to our knowledge of the field. While the STEM movement has continued for some time now, researchers still have a way to go to identify the most effective ways to design and deliver integrated STEM curriculum in schools. Given Bybee’s 2020 vision for STEM education published in 2010, it is clear we still have many questions to investigate (Bybee, 2010).

1.4  STEM Education: Now More than Ever? The title for the final section of this chapter is from a book recently published by Rodger Bybee (2018). Bybee has been a regular contributor to debates about STEM education, with several well-known and highly cited publications in the field. In 2010, he published Advancing STEM Education: A 2020 Vision, calling for a

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ten-year strategic plan to “move beyond the slogan and make STEM literacy for all students an educational priority” (p. 30). The plan recommended developing model STEM units with professional development for teachers and “exemplary assessment at the elementary, middle, and high school levels” (p. 34). He recommended this would need to be followed by systemic changes in policies, programs, and practices at local, state, and national levels, with strategies to evaluate and refine approaches over several years. Even though the contributions in this volume provide examples of model STEM units, successful professional development programs, suggestions for approaches to assessment of STEM project work, and research into national and even international collaborative efforts, there is little evidence that Bybee’s 2020 vision has been realised. While some countries appear to have committed substantial funds to STEM programs, many STEM education efforts are still piecemeal, and conducted at the local or regional levels of school education. Without STEM education becoming an integral component of the mandated curriculum, it is unlikely this will change (Lowrie, Downes, & Leonard, 2017). It seems a major challenge or hurdle which has yet to be overcome is the relationship between learning knowledge, skills, and understandings of the separate STEM subjects versus the benefits of an integrated curriculum that allows students to tackle bigger problems. Efforts to create integrated curriculum experiences in the past have not necessarily been sustained, as was the case with the middle school movement in the 1990s (Beane 1997). There are many reasons why implementing integrated curriculum is challenging, including curriculum structures, assessment practices, teachers’ knowledge and beliefs, as well as school structures and historical practices (Wallace, Sheffield, Rennie, & Venville, 2007). But is it time to seriously rethink the purpose of schooling and the knowledge students need to meet the challenges of today’s society? Returning to Bybee’s recent book STEM Education Now More than Ever (2018). He describes initial concerns about the lack of a clear definition for STEM and the need for citizens to address twenty-first century challenges such as. … economic growth, climate change, a reduction in biodiversity, vulnerabilities of the internet, energy efficiency, emerging and re-emerging infectious diseases, clean water, space exploration, and healthy oceans among others—depend on solutions that look at least somewhat to science, technology, engineering and mathematics (p. 6).

He argues “STEM provides opportunities to introduce issues beyond the traditional disciplines, such as citizenship” (p.  7). Given that politicians frequently ignore the advice of scientists, Bybee calls for education to provide increased opportunities for students to develop STEM competencies such as: • Understanding the nature of science • Cultivating an understanding and ability to use evidence and form reasonable arguments • Engaging in civil discourse and, • Developing twenty-first century workforce skills (p. 146).

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With recent international catastrophes, including floods, fires, melting icecaps, and the Covid-19 pandemic, there are good reasons why we do need STEM education now more than ever.

References Anderson, J. (2014). Forging new opportunities for problem solving in Australian mathematics classrooms through the first national mathematics curriculum. In Y. Li & G. Lappan (Eds.), Mathematics curriculum in school education (pp.  209–229). Dordrecht, The Netherlands: Springer. Anderson, J., Wilson, K., Tully, D., & Way, J. (2019). “Can we build the wind powered car again?” Students’ and teachers’ responses to a new integrated STEM curriculum. Journal of Research in STEM Education, 5(1), 20–39. Anderson, J., English, L., Fitzallen, N., & Symons, D. (2020). The contribution of mathematics education researchers to the current STEM education agenda. In J.  Way, C.  Attard, J. Anderson, J. Bobis, K. Cartwright, & H. McMaster (Eds.), Research in mathematics education in Australasia, 2015–2019 (pp. 27–57). Singapore: Springer Nature. Beane, J. A. (1997). Curriculum integration: Designing the core of a democratic school. New York: Teachers College Press. Becker, K., & Park, K. (2011). Integrative approaches among science, technology, engineering, and mathematics (STEM) subjects on students’ learning: A meta-analysis. Journal of STEM Education, 12(5), 23–37. Bybee, R. W. (2010). Advancing STEM education: A 2020 vision. Technology and Engineering Teacher, 70(1), 30–35. Bybee, R. W. (2013). The case for STEM education: Challenges and opportunities. Arlington, VA: NSTA Press. Bybee, R. W. (2018). STEM education: Now more than ever. Arlington, VA: NSTA Press. Care, E., & Kim, H. (2018). Assessment of twenty-first century skills: The issue of authenticity. In E.  Care, P.  Griffin, & M.  Wilson (Eds.), Assessment and teaching of 21st century skills (pp. 21–40). Cham, Switzerland: Springer Nature. Darling-Hammond, L., Hyler, M., Gardner, M., & Espinoza, D. (2017). Effective teacher professional development. Palo Alto, CA: Learning Policy Institute. Dewey, J. (1938). Experience and education. New York: Macmillan. English, L.  D. (2019). Learning while designing in a fourth-grade integrated STEM problem. International Journal of Technology and Design Education, 5, 1–22. Freeman, B., Marginson, S., & Tytler, R. (2015). Widening and deepening the STEM effect. In B. Freeman, S. Marginson, & R. Tytler (Eds.), The age of STEM: Educational policy and practice across the world in science, technology, engineering and mathematics (pp. 1–21). London: Routledge Taylor and Francis Group. Gresnigt, R., Taconis, R., van Keulen, H., Gravemeijer, K., & Baartman, I. (2014). Promoting science and technology in primary education: A review of integrated curricula. Studies in Science Education, 50(1), 47–84. Holmes, K., Gore, J., Smith, M., & Lloyd, A. (2018). An integrated analysis of school students’ aspirations for STEM careers: Which student and school factors are most predictive? International Journal of Science and Mathematics Education, 16(4), 655–675. Honey, M., Pearson, G., & Schweingruber, H. (Eds.). (2014). STEM integration in K-12 education: Status, prospects, and an agenda for research. Washington, DC: National Academies Press. Li, Y. (2014). International Journal of Science Education—A platform to promote STEM education and research worldwide. International Journal of STEM Education, 1(1), 1–2.

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Li, Y., & Lappan, G. (2014). Mathematics curriculum in school education: Advancing research and practice from an international perspective. In Y. Li & G. Lappan (Eds.), Mathematics curriculum in school education (pp. 3–12). Dordrecht, The Netherlands: Springer. Li, Y., & Schoenfeld, A. H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6(44), 1–13. Li, Y., Wang, K., Xiao, Y., Froyd, J. E., & Nite, S. B. (2020). Research and trends in STEM education: A systematic analysis of publicly funded projects. International Journal of STEM Education, 7, 17. https://doi.org/10.1186/s40594-020-00213-8 Lowrie, T., Downes, N., & Leonard, S. (2017). STEM education for all young Australians: A bright spots learning hub foundation paper, for SVA, in partnership with Samsung. Canberra, Australia: University of Canberra STEM Education Research Centre. Martin, A. J., Anderson, J., Bobis, J., Way, J., & Vellar, R. (2012). Switching on and switching off in mathematics: An ecological study of future intent and disengagement among middle school students. Journal of Educational Psychology, 104(1), 1–18. Mockler, N. (2018). Curriculum integration in the 21st century: Some reflections in the light of the Australian curriculum. In A. Reid & D. Price (Eds.), The Australian curriculum: Promises, problems and possibilities (pp.  229–240). Canberra, Australia: The Australian Curriculum Studies Association. Moore, T. J., Johnson, C. C., Peters-Burton, E. E., & Guzey, S. S. (2016). The need for a STEM road map. In C. C. Johnson, E. E. Peters-Burton, & T. J. Moore (Eds.), STEM road map: A framework for integrated STEM education (pp. 3–12). New York: Routledge. Nadelson, L. S., & Seifert, A. L. (2017). Integrated STEM defined: Contexts, challenges, and the future. The Journal of Educational Research, 110(3), 221–223. Office of the Chief Scientist. (2016). Australia’s STEM workforce: Science, technology, engineering and mathematics. Canberra, Australia: Commonwealth of Australia. Rennie, L., Venville, G., & Wallace, J. (2018). Making STEM curriculum useful, relevant and motivating for students. In R.  Jorgensen & K.  Larkin (Eds.), STEM education in the junior secondary: The state of play (pp. 91–110). Singapore: Springer Nature. Rosicka, C. (2016). Translating STEM education into practice. Camberwell, Australia: Australian Council for Educational Research. Roth, W.  M. (2018). STEM and affect in adolescence: A cultural-historical approach. In R. Jorgensen & K. Larkin (Eds.), STEM education in the junior secondary: The state of play (pp. 15–36). Singapore: Springer Nature. Tytler, R., Swanson, D. M., & Appelbaum, P. (2015). Subject matters of science, technology, engineering, and mathematics. In M. F. He, B. D. Schultz, & W. H. Schubert (Eds.), The Sage guide to curriculum in education (pp. 27–35). Thousand Oaks, CA: Sage. Tytler, R., Williams, G., Hobbs, L., & Anderson, J. (2019). Challenges and opportunities for a STEM interdisciplinary agenda. In B.  Doig, J.  Williams, D.  Swanson, R.  Borromeo, & P. D. Ferri (Eds.), Interdisciplinary mathematics education: The state of the art and beyond (pp. 51–81). Cham, Switzerland: Springer. Vasquez, J. (2015). STEM: Beyond the acronym. Educational Leadership, 72(4), 10–15. Voogt, J. M., Pieters, J. M., & Handelzalts, A. (2016). Teacher collaboration in curriculum design teams: Effects, mechanisms, and conditions. Educational Research and Evaluation, 22(3–4), 121–140. Wallace, J., Sheffield, R., Rennie, L., & Venville, G. (2007). Looking back, looking forward: Re-searching the conditions for integration in the middle years of schooling. Australian Educational Researcher, 34(2), 29–49.

Part I

Approaches to STEM Integration

Chapter 2

STEM Integration: Diverse Approaches to Meet Diverse Needs Yeping Li and Judy Anderson

Contents 2.1  Brief Background 2.2  Investigating Different Approaches to STEM Integration 2.3  Considering Further Issues References

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2.1  Brief Background The importance of mathematics and science has long been recognized in school education around the world. School mathematics and science have been compulsory subjects for every student in widespread school contexts. For example, the International Association for the Evaluation of Educational Achievement (IEA) conducted a pilot 12-country study in 1960 to investigate the feasibility of undertaking a more extensive assessment of educational achievement (Foshay, Thorndike, Hotyat, Pidgeon, & Walker, 1962). The pilot study focused on five areas: mathematics, reading comprehension, geography, science, and nonverbal ability (see https:// www.iea.nl/studies/iea/earlier#section-171). The selection of these five areas represented what was commonly covered and valued in and through school education across different education systems at that time. After this pilot study, the IEA conY. Li (*) Texas A&M University, College Station, TX, USA e-mail: [email protected] J. Anderson Sydney School of Education and Social Work, The University of Sydney, Camperdown, NSW, Australia e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_2

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ducted its first international study with a focus on mathematics in 1964 (i.e., The IEA First International Mathematics Study—FIMS, Husén, 1967), and then follow-­up international studies with six specific subject foci in 1970–1971 including science (i.e., The IEA First International Science Study—FISS, Keeves & Comber, 1973). FISS focused on three fields of science: biology, chemistry, and physics. In some countries, the emphasis on school mathematics and science may start even earlier. For example, the School Science and Mathematics Association was ­established in 1901 in the United States with one of its four goals stated as “advancing knowledge through research in science and mathematics education and their integration” (see https://ssma.org). Its official journal, School Science and Mathematics, was founded, also in 1901, to showcase “research on issues, concerns, and lessons within and between the disciplines of science and mathematics in the classroom” (see https:// onlinelibrary.wiley.com/journal/19498594). In contrast, STEM education as explicated by the term does not have a long history. The interest in helping students learn across STEM fields can be traced back to 1990s when the U.S. National Science Foundation (NSF) formally included engineering and technology with science and mathematics in undergraduate and K–12 school education (e.g., National Science Foundation, 1998). It coined the acronym SMET (science, mathematics, engineering, and technology) first, and then changed to the acronym STEM in early 2000s to replace SMET (Li, Wang, Xiao, & Froyd, 2020). The emerging field of STEM (later also STEAM after adding “A” as arts, STREAM after adding “R” as reading, and STEMM after adding “M” as medicine) education is perceived as providing some fascinating opportunities for transforming school education since not only STEM is important for students’ learning now and in the future but also STEM brings new perspectives about possible foci and the value of school education (Li, 2018). Different from simply adding new school subjects in the past, the inclusion of “T” (technology) and “E” (engineering) calls for a broader focus on STEM education with an ever-increasing interest in discipline integration instead of taking each discipline as “silos.” Consistently, there have been more and more interests in exploring and understanding different perspectives and approaches to STEM integration in many education systems. It is in this spirit that this part is designated to share and learn about those different perspectives and approaches internationally.

2.2  Investigating Different Approaches to STEM Integration A total of seven chapters (excluding this chapter) are included in this part. Two chapters are literature reviews of STEM education in general (Chap. 3) and the inclusion of mathematics in integrated STEM education (Chap. 5). Three chapters (Chaps. 4, 6, and 7) present and discuss specific approaches to STEM integration from a curriculum perspective. One chapter (Chap. 8) illustrates the use of a specific approach for analyzing curriculum documents to examine their epistemic nature of

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STEM. The final chapter (Chap. 9) discusses a pedagogical framework for implementing integrated STEM education in Southern Africa. Instead of focusing on a specific STEM integration effort, Tytler (2020) provides a historical overview of STEM education as originated in the United States and then expanded internationally. The chapter summarizes various forms of STEM education that have been developed including, promoting the integration of engineering with science and mathematics in curricula, the inclusion of digital technology in school education, and/or connections between school education and STEM professional work in the real world. In accounting for possible reasons (i.e., “why”) that led to the dramatic development of STEM education, Tytler discusses several drivers that are commonly perceived and highlighted in various documents: the need for improving a nation state’s economic productivity, the need for advancing a nation’s science and technology research and development, and the need for preparing a workforce with STEM competencies. Building upon the discussion about STEM-­ competent workforce preparation, Tytler discusses a framework of STEM competencies needed in the future (i.e., “what”). The framework includes four types of knowledge (disciplinary knowledge, epistemic knowledge, interdisciplinary knowledge, and procedural knowledge) and three types of skills (cognitive/metacognitive, social/emotional, and physical/practical), attitudes, and values. To develop students’ STEM competencies, Tytler discusses the ongoing movement of developing and using interdisciplinary approaches in STEM teaching and learning (i.e., “how”), with an extended review of possibilities and challenges associated with interdisciplinary mathematics education. As mathematics is commonly perceived as a discipline that has received the least attention in integrated STEM education, Baldinger et al. (2020) conducted a literature review of articles published in 19 journals from 2013 to 2018. They found that only 32 out of 4072 articles in 12 journals demonstrated mathematically rich integrated STEM at the secondary level. The finding provides empirical support to the common perception and it is also consistent with what has been reported recently by looking at publications in the International Journal of STEM Education (Li & Schoenfeld, 2019). The three chapters on a specific STEM integration from a curriculum perspective are contributed by English (Chap. 4), Watson and colleagues (Chap. 6), and Bennison and Geiger (Chap. 7). English (2020) highlights the use of engineering design as an important approach for STEM integration, with special benefits of engaging students and providing opportunities for them to apply disciplinary knowledge and make knowledge connections across disciplines. Watson, Fitzallen, and Chick (2020) argue that statistics, as part of mathematics, is well positioned for integrating STEM around the fundamental nature of variation across STEM contexts. Bennison and Geiger (2020) present and discuss the use of numeracy, the capability of using mathematics to solve real-world problems, as a rich cross-­ curricular model for integrating mathematics and science in Australia. In Chap. 8, Park, Wu, and Erduran (2020) demonstrate the feasibility of using the framework of the Family Resemblance Approach to examine the epistemic nature of STEM disciplines as represented in curriculum documents. As illustrations, they

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present an analysis of the two science-based curriculum documents from the United States. Makonye and Dlamini (2020) discuss in Chap. 9 special challenges educators and teachers in developing countries, especially in Africa, are facing to begin to develop and implement integrated STEM education. Based on a literature review and interviews with selected teacher educators, they proposed a pedagogical ­framework that calls for the infusion of local context and culture in STEM education together with political support and professional development for teachers.

2.3  Considering Further Issues These seven chapters, as discussed above, provide a wide spectrum of what we can learn, ranging from a broad picture related to integrated STEM education based on literature reviews, specific approaches to STEM integration, to specific approaches for curriculum analysis and implementing integrated STEM education. The three chapters with a focus on specific approaches present different curriculum models for STEM integration. They share a common feature of developing STEM integration with a primary discipline base: design in engineering and technology (Chap. 4), statistics (Chap. 6), and numeracy in mathematics (Chap. 7). These chapters inspire us to think about the possibility of developing other curriculum models of STEM integration with a selection of different disciplines as a primary discipline base, which may be used to serve different educational purposes. STEM integration is not the end, but a means of developing students’ competencies needed in the future. At the same time, these approaches tend to be discipline-­centric that emphasize knowledge acquisition and application. Thus, further considerations are needed to discuss different types of knowledge (including epistemic knowledge and interdisciplinary knowledge) and skills in these integrated STEM curriculum models, as Tytler discusses in his chapter. There can be some other perspectives in thinking about STEM integration. As Tytler quotes (Chap. 3), Andreas Schleicher, OECD (Organization for Economic Co-operation and Development) Director of Education and Skills, argued in the 2017 OECD forum: What is required is the capacity to think across disciplines, connect ideas and ‘construct information’: these ‘global competencies’ will shape our world and the way we work and live together.

An emphasis on the development of thinking is a very important aspect of competencies for the future workforce and STEM education is well positioned to develop students’ thinking (Li et al., 2019a). Li et al. (2019a) proposed that thinking needs to be reconceptualized as plural and can be differentiated as multiple models with levels. Specifically, as examples of models of thinking, Li and colleagues further discussed design thinking (Li et  al., 2019b) and computational thinking (Li, Schoenfeld, et al., 2020), without subject fixation, that are important for every student to develop and apply in the twenty-first century. STEM integration can be

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developed and used to help develop students’ transdisciplinary models of thinking, such as design thinking and computational thinking. This perspective should provide another direction for developing various approaches, different from discipline-­ centric approaches, for integrated STEM education. With a primary focus on integrated STEM curriculum models in this part, readers can certainly want to learn more from reading this book. There are many other important aspects of STEM education beyond curricular issues. We invite readers to read our introductory chapters (Chaps. 10 and 19) for the follow-up parts with specific considerations about students and their experiences (Part 2, see Li & Anderson, 2020a) and teachers and their practices (Part 3, see Li & Anderson, 2020b).

References Baldinger, E.  E., Staats, S., Covington-Clarkson, L., Gullickson, E., Norman, F., & Akoto, B. (2020). A review of conceptions of mathematics in integrated STEM education: Returning voice to the silent M. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Bennison, A., & Geiger, V. (2020). STEM and numeracy in the Australian curriculum. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. English, L. (2020). Facilitating STEM integration through design. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Foshay, A. W., Thorndike, R. L., Hotyat, F., Pidgeon, D. A., & Walker, D. A. (1962). Educational achievements of thirteen-year-olds in twelve countries. Hamburg, Germany: UNESCO Institute for Education. Husén, T. (1967). International study of achievement in mathematics: A comparison of twelve countries (Vol. 1-2). Stockholm: Almqvist and Wiksell. Keeves, J.  P., & Comber, L.  C. (1973). Science education in nineteen countries: An empirical study. Stockholm: Almqvist and Wiksell. Li, Y. (2018). Journal for STEM education research—Promoting the development of interdisciplinary research in STEM education. Journal for STEM Education Research, 1(1–2), 1–6. https://doi.org/10.1007/s41979-018-0009-z Li, Y., & Anderson, J. (2020a). Focusing on students and their experiences in and through integrated STEM education. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Li, Y., & Anderson, J. (2020b). Developing teachers, teaching, and teacher education for integrated STEM education. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Li, Y., & Schoenfeld, A. H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6, 44. https://doi.org/10.1186/ s40594-019-0197-9 Li, Y., Schoenfeld, A. H., diSessa, A. A., Grasser, A. C., Benson, L. C., English, L. D., et al. (2019a). On thinking and STEM education. Journal for STEM Education Research, 2(1), 1–13. https://doi.org/10.1007/s41979-019-00014-x Li, Y., Schoenfeld, A. H., diSessa, A. A., Grasser, A. C., Benson, L. C., English, L. D., et  al. (2019b). Design and design thinking in STEM education. Journal for STEM Education Research, 2(2), 93–104. https://doi.org/10.1007/s41979-019-00020-z

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Li, Y., Schoenfeld, A. H., diSessa, A. A., Grasser, A. C., Benson, L. C., English, L. D., et al. (2020). Computational thinking is more about thinking than computing. Journal for STEM Education Research, 3(1), 1–18. https://doi.org/10.1007/s41979-020-00030-2 Li, Y., Wang, K., Xiao, Y., & Froyd, J. E. (2020). Research and trends in STEM education: A systematic review of journal publications. International Journal of STEM Education, 7, 11. https:// doi.org/10.1186/s40594-020-00207-6 Makonye, J., & Dlamini, R. (2020). Approaches to effecting an integrated STEM education in Southern Africa. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. National Science Foundation. (1998). Information technology: Its impact on undergraduate education in science, mathematics, engineering, and technology. (NSF 98-82), April 18–20, 1996. Retrieved January 16, 2018, from http://www.nsf.gov/cgi-bin/getpub?nsf9882 Park, W., Wu, J.-Y., & Erduran, S. (2020). Investigating the epistemic nature of STEM: Analysis of curriculum documents from the USA using the Family Resemblance Approach. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Tytler, R. (2020). STEM education for the 21st century. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Watson, J., Fitzallen, N., & Chick, H. (2020). What is the role of statistics in integrating STEM education? In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer.

Chapter 3

STEM Education for the Twenty-First Century Russell Tytler

Contents 3.1  W  hat Is STEM? 3.2  Drivers for the Contemporary Focus on STEM Education 3.2.1  The STEM Workforce 3.3  Work Futures and STEM Competencies 3.4  The Move Towards Interdisciplinarity 3.4.1  Findings from Australian Case Studies 3.4.2  Learning Progression Through Interdisciplinary Mathematics 3.5  Conclusion References

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3.1  What Is STEM? The acronym STEM (Science, Technology, Engineering, and Mathematics) has become increasingly important in policy advocacy across the world, in relation to industry and research, to higher education participation, and to school curricula (Marginson, Tytler, Freeman, & Roberts, 2013). STEM education and research are increasingly recognized as fundamental drivers of national development, economic productivity, and societal well-being. Yet, the particular juxtaposition of these subjects is only recent, is not universal, and is in many respects contested. The acronym was coined by Dr Judith Ramaley in 2001, then assistant director of the human resources directorate at the US National Science Foundation. She is quoted as saying (Chute, 2009): It is impossible to make wise personal decisions or to exercise good citizenship or compete in an increasingly global economy or to begin to address the enormous challenges we face in exercising our stewardship of our environment without knowledge of science and the ability to apply that knowledge thoughtfully and appropriately.

R. Tytler (*) Deakin University, Melbourne, VIC, Australia e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_3

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This quote picks up some of the key constructs underpinning STEM advocacy: that of the need for STEM knowledge and skills in a contemporary world, the demands of a global economy, and the challenges of an increasingly threatened environment. Underpinning the acronym is the notion that these four disciplines together constitute a coherent package of subjects that cover the knowledge and skills around the sciences, applied sciences, and the digital world that constitute the driving force towards a post-industrial global future and the future wealth of countries. Yet, the term is not precise in its meaning. The original acronym was SMET, with science and mathematics taking pride of place, but Ramaley’s conception was of a more meaningful connection amongst these disciplines. Thus, we see early on the introduction of the suggestion that STEM amounts to more than the sum of its disciplinary parts. The US STEM School Education Strategy report (Education Council, 2015) argues that the four elements work together as a united concept by virtue of their intersecting use. For instance, the engineering design process is informed by scientific empirical evidence (Honey, Pearson, & Schweingruber, 2014). The American National Science Foundation (NSF) also reports STEM as a way to encompass a new “meta-discipline” that combines the four subject areas. Nevertheless, as we will explore below, questions are raised about the epistemic viability of the STEM construct. There is imprecision in the disciplinary makeup of STEM (Marginson et  al., 2013). For instance, in reporting on STEM participation or economic figures, the term sometimes includes the health sciences and medicine, and sometimes agriculture (some have advocated an extension of the acronym to STEMM, or STEAM, on this basis) and sometimes not. In Germany, the acronym is MINT (Mathematik, Informatik, Naturwissenschaft und Technik), which makes apparent the inclusion of information technologies, whereas in the English-speaking versions, in schools, Technology ambiguously encompasses both design and information technology. In school curricula, the acronym has largely focused on mathematics and science, these being the major high-status disciplinary subjects, with engineering education in academic streams struggling to achieve the attention implied by the acronym (English, 2016). Historically, there has been longstanding advocacy of the inclusion of technology within school science (namely, in the Science-Technology-­ Society movement: Fensham, 1981, 1985; Yager, 1996), yet the T in STEM is increasingly associated with digital technologies as the fourth industrial revolution, built on artificial intelligence, machine learning, and big data processes, takes hold of both industrial organization, work realities, and personal lives. Correspondingly, the meaning of STEM in education has a variety of forms internationally, including: • An emphasis on promotion of mathematics and science as a response to perceptions that these subjects are attracting less student interest and participation (Marginson et al., 2013) • Promotion of engineering design curricula allied with mathematics and science, for instance, as part of the Crosscutting Concepts in the US Next Generation Science Standards (NRC, 2012)

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• Promotion of the inclusion of digital technologies either as a standalone subject or infused throughout the curriculum • Interdisciplinary project work or subjects that combine two or more of the STEM disciplines, grounded in ‘authentic’ contexts and focused on problem solving (Tytler, Swanson, & Appelbaum, 2015) • Increased curricular emphasis on the world of STEM professional work, including partnerships or links with STEM industries and professional practices in Australia (Australian Education Council, 2018) and the UK (Mann & Oldknow, 2012) or the Siemens-Siftung ‘Experimento’ in Germany • The combination of the STEM disciplines with ‘Arts’ in ‘STEAM’ initiatives that emphasize creativity and design thinking (Taylor, 2016). These initiatives are linked to an emphasis on innovation as a core industrial wealth-building practice and • Increasing curricular emphasis on ‘STEM skills’, aligned with concerns to prepare students for a fast-changing world of work in the twenty-first century (Prinsley & Baranyai, 2015; UK National Audit Office, 2018). Internationally, governments around the world are focused on enhancing their citizens’ STEM capabilities. The Australian Government funded STEM: Country Comparisons project (Freeman, Marginson, & Tytler, 2015; Marginson et al., 2013) commissioned 23 country reports that investigated, among other things, patterns of STEM provision in school and tertiary education, student uptake of STEM programs, factors affecting student performance and motivation, and strategies and programs to enhance STEM. Country and regional reports spanned Europe (Western Europe, Finland, France, Portugal, Russia), the Anglosphere (United States, Canada, New Zealand, United Kingdom, Australia), Asia (China, Taiwan, Japan, Singapore, South Korea), Latin America (Argentina, Brazil), the Middle East (Israel), and South Africa. The consensus of all the country chapters is that it is essential to foster scientific and mathematical literacy in all students to middle school level; it is desirable to persuade all students to maintain some STEM programs for as long as possible; and more students should be persuaded to aspire to STEM learning and STEM-based careers. These latter aims respond to a substantial literature in each of mathematics and science education concerning the factors that affect student attitudes and perceptions to these subjects, and intentions to continue in a ‘STEM pipeline’ to post compulsory school mathematics and science, and further tertiary STEM studies. In a comprehensive review, Tytler, Osborne, Williams, Tytler, and Cripps Clark (2008) identified a complex array of intersecting factors that differed at different points along the education pathway from primary school through to upper secondary school. These factors include experience of success or otherwise, and students’ attitudes, particularly interest and self-efficacy, determined by a range of cultural factors including socio-economic, teaching and teachers, patterns of choice and knowledge and expectations of future pathways.

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3.2  D  rivers for the Contemporary Focus on STEM Education The arguments for the global turn to STEM in education and in research and development, common across both industrialized and developing countries, are well rehearsed and widely recognized (Freeman et  al., 2015; Marginson et  al., 2013). The turn to STEM is clearly evident in government efforts worldwide to elaborate policy regarding school mathematics and science, and tertiary level education and research in the STEM disciplines. The argument for this increasing focus on STEM is based on claims of the centrality of STEM knowledge and skills, and STEM-­ based innovation, to national wealth creation. The case has been argued, for instance, in a series of major policy documents in the industrialized world (COSEPUP, 2006; HLG, 2004; Office of the Chief Scientist, 2013, 2014) and, in these cases, is accompanied by a sense of crisis concerning a perceived drop in participation of youth in the ‘STEM pipeline’ (e.g. Osborne & Dillon, 2008; Tytler, 2007; Tytler et al., 2008) towards post-compulsory STEM studies and employment, and an impending shortfall in the STEM professional workforce perceived of as central to global economic competitiveness. The focus on STEM education relates to the demonstrable links between countries’ education attainment (increasingly perceived in global terms through comparative assessment regimes such as PISA and TIMSS), science research and development programs, and economic dynamism. In governments around the world it is believed there is a relationship between, on the one hand, national investment in STEM-related skills, and the quality and quantity of the national skill base, and, on the other hand, the economic productivity of the workforce … and research-based innovations in industry. There is no contemporary nation with an economy both vigorous and well-integrated that is not also strong in STEM (Freeman et al., 2015, p. 1)

The move to centralize STEM in schools is premised on the argument that success in STEM within schools, increasingly linked to performance on national curricular assessment regimes, is a core determinant of a nation state’s future international economic competitiveness and a necessary driver for economic growth. Figure 3.1 represents the presumed interactive relationship between STEM national educational attainment, health of STEM research and development, and the economic dynamism of the nation.

Fig. 3.1  The interactive relationship between national educational attainment, health of STEM research and development, and economic dynamism

Education attainment

Science R&D

Economic dynamism

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In this way, the STEM acronym has represented more than a set of academic subjects, but as a distinctive discourse serving an agenda of globalizing economic modernization within the New Knowledge Economy. Further, the acronym serves to provide a distinction between the STEM disciplines and those of the Arts, Humanities, and Social Sciences.

3.2.1  The STEM Workforce This tight linking of STEM advocacy with national economic well-being is driven by recognition of the increasing importance of the STEM disciplines in the workforce. For example, in Australia, it is claimed that 75% of the fastest growing occupations require STEM skills (Office of the Chief Scientist, 2014). It is estimated that shifting just 1% of the workforce into STEM roles would add $57 billion to GDP over 20 years (PwC Australia, 2015). The (STEM) fields and those who work in them are critical engines of innovation and growth: according to one recent estimate, while only about five percent of the U.S. workforce is employed in STEM fields, the STEM workforce accounts for more than fifty percent of the nation’s sustained economic growth (Office of the Chief Scientist, 2014)

It is claimed (Institute of Mechanical Engineers, 2018), based on a survey of business leaders in the UK, that lack of STEM skills costs that country £1.5bn each year. Most of the fastest growing occupations in the US are predicted to be in STEM, particularly in health and computing (Lacey & Wright, 2009). In the US, it is claimed (Olson & Riordan, 2012) that the US must produce approximately 1 million more STEM professionals over the next decade than are projected to graduate at current rates (an estimated increase of about 34% annually) if the country is to retain its historical pre-eminence in science and technology. Concern with supply of engineering graduates is well established in the US, for instance, in talk of a ‘gathering storm’ in the COSEPUP (2006) report about the relative proportional number of engineers graduating from the US compared to China, which, at the time, was less than 1:8. Nevertheless, questions have been raised about the veracity of these estimates. Oleson, Hora, and Benbow (2014) point out that estimates of STEM jobs differ widely, depending on assumptions embedded in the acronym. Further, there is acknowledgement that despite these calls for more STEM graduates, many graduates from the STEM disciplines fail to get jobs in their chosen fields and end up working in professions only indirectly related to their degree. There is growing recognition of the complexity of the STEM construct in future work predictions, particularly around the distinction between STEM competencies distinct from STEM professions. It has been argued for instance with reference to the US that “STEM jobs account for about 5 percent of all jobs in the economy. STEM competencies, however, valued outside of traditional STEM jobs – account for 40 percent of all jobs” (Carnevale, quoted in Sarachan, 2013). A recent US report (National

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Science Board, 2015) has questioned presumptions of a linear link between a ‘STEM pipeline’ and STEM professions, and argued for a more nuanced consideration of STEM pathways to “foster a strong, STEM-capable workforce” (p. 2) conceived of more flexibly. Thus, recent concern has shifted from a focus on the need for STEM professionals, to a focus on the building within the workforce of STEM skills or competencies (Marginson et al., 2013).

3.3  Work Futures and STEM Competencies The world of work is undergoing dramatic change, causing significant disruption in patterns of jobs, and changing the nature of expectations of the young people currently in our schooling systems, as to what their career futures might look like. Increasingly, young people are experiencing significant change away from the settled careers expected by previous generations. A 15-year-old today will experience a portfolio career, potentially having 17 different jobs over five careers in their lifetime” (FYA, 2017, p. 3)

The major drivers for these changes are largely agreed. How we work is being impacted by mega-trends, including “globalisation, technological progress and demographic change” (OECD, 2017, p. 2). The key sites for technological progress are in “Big Data, artificial intelligence (AI), the Internet of Things and ever-­ increasing computing power” (p. 4). Added to this are the substantial natural world and social drivers of climate change, globalization, urbanization, population pressures, and changed demographic profiles, with an aging population in industrialized countries leading to substantial pressures on wealth creation and health provision. The effect of this fourth industrial revolution (Schwab, 2016) is already being felt in a shift from manufacturing and the loss of many repetitive jobs to machines. In the coming years, digitization will increasingly encroach on professional work previously presumed to be impervious to machine replacement, such as accountancy and office work generally. High status STEM professions will change due to big data processes and automation, such as diagnosis processes in medicine, or data analysis and display and virtual reality-supported design procedures in engineering. These changes will be fundamental and disruptive and may have profound implications for the conduct of schooling. Already, STEM subjects in schools are increasingly taking on digitization as a key aspect of teaching and learning. The explosion of information access and organization through the internet has posed profound questions on the position of schooled knowledge and the relationship between declarative knowledge, critical thinking, and higher-level skills. A recent and major study of work futures in Australia (Hajkowicz et al., 2016) identified ‘new skills and mindsets’ that will be needed for the future, including: increasing importance of education and training; the importance of digital literacy alongside literacy and numeracy; new capabilities to match new jobs; and, increased

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importance of STEM knowledge and skills. This latter is linked to the STEM-related sector as having the biggest increases in job numbers and wages. The current education system teaches people to be effective in a highly structured system, but Australia’s future workforce is likely to encounter much ambiguity and openness. For this reason, commentators argue that our future educational system will need to do more to encourage innovative, entrepreneurial and flexible mindsets (Hajkowicz et al., 2016, p. 87)

Writers in this area of work futures are agreed that youth, in preparing for this fast-­ changing future of work, need to develop new skills that include problem solving, fluency and active learning (Bakhshi, Downing, Osborne, & Schneider, 2017), adaptability and creativity, interpersonal skills, and transdisciplinary skills (Tytler et  al., 2019). There is increasing emphasis on the notion of twenty-first century skills as a focus for education, which will prepare students for these volatile work futures (Binkley et al., 2012). Andreas Schleicher, OECD Director of Education and Skills, argued in the 2017 OECD forum: What is required is the capacity to think across disciplines, connect ideas and construct information: these global competencies will shape our world and the way we work and live together.

These imperatives regarding the new realities of work and life are driving increasing advocacy of competency-based curriculum framing, and a corresponding framing of STEM education in terms of STEM skills, as distinct from disciplinary knowledge in the traditional sense, as a crucial component of twenty-first century skills. But, while the phrase ‘STEM skills’ is often used in public advocacy of STEM, the term is not well defined. In Australia, the Office of the Chief Scientist (Prinsley & Baranyai, 2015) reported on an investigation of the skills and attributes employers look for in STEM graduates. The top five skills were active learning (on the job), critical thinking, complex problem-solving, creative problem-solving, and interpersonal skills. Occupation-specific STEM skills came down the list at number 8. All but the last of these five was held to be more characteristic of STEM, compared to non-STEM employees. Drawing on an analysis of Carnevale and colleagues, the National Science Board (2015) talked about ‘STEM capabilities’ thus: Among the cognitive competencies associated with STEM are knowledge of math, chemistry, and other scientific and engineering fields; STEM skills, such as complex problem solving, technology design, and programming; and STEM abilities, including deductive and inductive reasoning, mathematical reasoning, and facility with numbers. Among the non-cognitive competencies associated with STEM are preferences for investigative and independent work (p. 8)

Siekmann and Korbel (2016), in a review of the STEM skills literature, argue that the term is not appropriate for many of the competencies claimed in that these refer to skills that can be developed equally through non-STEM disciplines. They argue that “current definitions of STEM skills are inconsistent and not specific enough to inform education and skill policies and initiatives” (p. 8), and put the case that the term should be restricted to specific technical skills. Their analysis draws attention to the different ways in which we can think of STEM curricula contributing to

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competencies for the workforce or for living, including; (a) specific STEM knowledge and skills and particular forms of reasoning; (b) competencies particularly but not exclusively associated with STEM (such as critical and creative thinking); and (c) general competencies (such as collaborative or communicative skills) that could be productively developed in STEM contexts. Table 3.1, based on the OECD Learning Framework 2030 (OECD, 2018), presents a framework for thinking about skills needed by young people to prepare them for future life and work, with descriptors that aim to articulate the contribution of STEM subjects to the development of these skills. The knowledges, skills, attitudes, and values of Table 3.1 are well aligned with findings and advocacy within the research literature in mathematics and science education, but with the exception of disciplinary knowledge, and arguably procedural knowledge, have not found their way into formulations of mainstream curriculum practice or assessment. STEM advocacy around skills for future work, however, has given them renewed prominence. These skills and attitudes can be seen in the OECD Mathematics Competencies Framework 2030, for instance, in the attention to mathematics use across multiple contexts, or in categories, such as creative problem solving, critical thinking, inquiry, resilience, design thinking. Epistemic knowledge is a category within the 2015 Scientific literacy framework, and refers to knowledge of the constructs and defining features of knowledge-­ building in science (Duschl, 2008), including the way evidence is used to test and Table 3.1  A framework of competencies associated with the STEM disciplines, based on the OECD Learning Framework 2030 Knowledge  Disciplinary knowledge  Epistemic knowledge  Interdisciplinary knowledge  Procedural knowledge Skills  Cognitive/ metacognitive  Social/  Physical/practical Attitudes

Values

Concepts such as energy, geometric relations, material and structural properties, ecosystem principles … How knowledge is built in the STEM disciplines, social and personal settings of STEM knowledge building, nature of models in maths and science, design processes, algorithmic coding processes … Interdisciplinary processes, links between mathematics and science, technology, STEM and other knowledges- societal, humanities and arts … Investigative and problem-solving approaches, design knowledge, coding knowledge … Complex and creative problem solving, design thinking, critical thinking, systems analysis, computational skills, complex, model based reasoning … Interpersonal skills, cooperation/ collaboration, … Technical skills, coding, manipulation … Productive disposition, persistence and optimism, curiosity, aesthetic preferences, open mindedness, respect for evidence, commitment to learning … Care for animals, objectivity, cooperation, responsibility … (Personal-global)

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establish claims, and the nature and role of models and representations in scientific discovery and explanatory processes. Similarly, in mathematics, epistemic knowledge includes understanding of the nature of mathematical knowledge-building, proof, and including the role of representational systems (Lehrer, 2009; Lehrer, Kim, & Schauble, 2007). Lehrer and Schauble (2012), over a decade long program of research, have worked with young children to develop and refine representational systems in response to genuine exploration of natural systems, including the construction, interrogation, and modelling of data sets. In science, such representational work underpins inquiry pedagogies focusing on multimodal representational work (Hand, McDermott, & Prain, 2016; Lehrer, 2009; Tytler, Prain, Hubber, & Waldrip, 2013), visualization (Gilbert, 2005), and metarepresentational competence (diSessa, 2004). Epistemic knowledge also underpins the literature on the nature of science (Lederman, 2014), and argumentation (Simon, Erduran, & Osborne, 2006), where it is held to be a crucial aspect of scientific literacy to understand the processes by which scientific knowledge is built on evidence, in an age, where science findings are increasingly subject to political critique. Consideration of epistemology and epistemic processes has a long history also in mathematics education (Ernest, 2003). Further, epistemic knowledge also includes knowledge of the personal and social drivers of STEM discovery and development processes, and the ways in which STEM practitioners operate in a variety of professional and practical settings. Again, this aspect of epistemic knowledge is aligned with calls for the school STEM subjects to better reflect practices in the STEM professions, to offer exposure to STEM practices, and to encourage partnerships between schools and STEM industries and STEM practitioners. This call underpins, for example, the UK STEMNET Ambassadors initiative (https://www.stem.org.uk/stem-ambassadors), the Siemens Siftung initiative (https://www.siemens-stiftung.org/en/foundation/working-areas/ education/), and the Australian STEM professionals in schools initiative (Tytler et al., 2015). For mathematics education in particular, there is a disparity between the formal curriculum and the diverse ways in which mathematics is created and used in multiple professional settings such that the link between mathematics and what is a ‘mathematician’ is much less clearly defined or understood than the link between school science and perceptions of a ‘scientist’. This represents a dual challenge for mathematics education within a STEM setting: to develop a mathematical literacy perspective that encompasses a rich view of mathematical epistemic practices and to represent the diverse professional settings in which mathematics is created and used, aligned with the need to alert students to the centrality of mathematics to multiple possible work futures. Interdisciplinary knowledge has not been an explicit focus for mathematics and science in schools. However, science, along with other subjects, utilizes mathematics as a tool for many purposes, and mathematics, in applied topics especially, uses science for context. Similarly, technology/engineering design projects draw on both mathematics and science as part of the design and evaluation process, but, typically, the science and the mathematics are not developed beyond their immediate utilitarian value. However, there is a growing argument that interdisciplinary thinking and practice is a core feature of contemporary STEM professional work, and that

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innovation occurs mostly at the intersection of disciplinary practices. This implies a need to explore ways of developing serious learning approaches in mathematics and science within interdisciplinary settings. How this might be done, and the challenges involved, will be discussed in the next section. Further to advocacy for STEM, in a number of systems around the world, the acronym STEAM, with the A being for ‘Arts’, is achieving curriculum currency as an expanded form of interdisciplinarity. In Korea, for instance, there has been major system innovation around STEAM, with an emphasis on creativity and innovation (Baek et al., 2011; Jon & Chung, 2015). In China also, there is significant curricular activity around the STEAM concept. The term originated in the U.S., but is gaining increasing currency globally around this association with creative thinking and innovation (Taylor, 2016), which has garnered support from industries who see innovation and design as central to their STEM practices. STEM teachers working with arts teachers, around more flexible pedagogies, have seen the association as powerful for increasing student engagement with mathematics and science. Cognitive/metacognitive skills. As was described above, industry and government are looking to STEM education as a principal training ground for the development of skills of complex and creative problem solving, critical thinking, and analytic and quantitative thinking, all highly valued as workforce skills. This places, therefore, a premium, for STEM curriculum framing, on these cognitive/metacognitive skills. Since the turn of the century, Scientific Literacy (Bybee, 1997) has been argued to be a core purpose of school science curricula, emphasizing the importance of preparing future citizens for being able to interpret and use scientific knowledge and processes in their everyday lives. This focus constitutes an implicit critique of the traditional purpose ascribed to science education, of preparing a core of students as future STEM professionals. As with Scientific Literacy, Mathematical Literacy has underpinned the PISA mathematics framework. Similarly, the construct of numeracy “connects the mathematics learned at school with out-of-school situations that additionally require problem solving, critical judgment, and making sense of non-mathematical context” (Goos, 2016, p. 71). The PISA framework has been structured around competencies, recognizing that what is important, as the result of an education in mathematics, science, or any discipline, is the capacity to turn discipline-­based knowledge to use in interpreting and solving questions and problems. This move towards ‘knowledge in use’ and away from declarative or lower level conceptual knowledge has been aligned both with a concern for a STEM education that prepares all citizens for future lives, but, more recently, with a concern to foster the flexible sets of skills and competencies that will be increasingly important in future workplaces. Attitudes and values are increasingly recognized as an important component of learning and are an important dimension in understanding the conditions for students’ ongoing engagement with STEM subjects. In the next section, the perceived importance of attitude and engagement responses to mathematics is identified as an important driver for schools’ interdisciplinary work. Values both frame students’ responses to STEM subjects and are promoted within these subjects (Bishop, Seah, & Chin, 2003; Schreiner & Sjøberg, 2007). Regarding attitudes in the science

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education literature, an important distinction is made between ‘attitudes towards science’ and ‘scientific attitudes’ (Tytler & Osborne, 2012). The latter are envisaged as a component of working and thinking scientifically and include such things as a commitment to evidence as the basis of belief, and a scepticism towards hypotheses and claims. The distinction also holds true for mathematics and could be applied also to ‘values’. Attitudes include broad orientations to working within a subject, such as resilience and optimism, which are important facets of deeper level mathematical learning and ways of knowing (Williams, 2002, 2014). In mathematics, productive disposition “includes the student’s habitual inclination to see mathematics as a sensible, useful, and worthwhile subject to be learned, coupled with a belief in the value of diligent work and in one’s own efficacy as a doer of mathematics” (Kilpatrick, 2001, p. 107). This competency is framed as important for the learning of mathematics (or science), but is also essential for any ongoing tendency to seek out or use school STEM knowledge in adult life or work. A particularly productive link between conceptual learning and attitudes and values was articulated by John Dewey (1996) as a continuity between conceptual learning and the aesthetic. This idea has been explored in the work of mathematicians (Netz, 2005), scientists (Wickmann, 2006), in mathematics classrooms (Sinclair, 2009), and in science classrooms (Jakobson & Wickman, 2008), where aesthetic expression is shown to intertwine with conceptual statements, as students interact with material objects and scientific practices.

3.4  The Move Towards Interdisciplinarity The STEM acronym, originally coined to represent an interrelated grouping of disciplines and school and tertiary level subjects, has shifted towards advocacy of interdisciplinary curriculum practices built around authentic problems, involving some or all of science, technology, engineering, and mathematics. This shift occurred early in the US, but, in recent years, has become a feature of global STEM curriculum advocacy (Marginson et  al., 2013). A key aspect of the argument for interdisciplinary approaches to STEM is the call for students to be engaged with authentic problems that reflect the interdisciplinary nature of much contemporary STEM work. Often, these activities involve project-based learning and, often, these are based around engineering/technology design challenges. Part of the argument for authentic problem contexts lies in the concern about lack of conceptual engagement of many students with school science and mathematics, described above, and the premise that work around authentic contexts will lead to more meaningful learning. Another part of the argument is that interdisciplinary contexts and project-based learning can more effectively provide the settings for developing the STEM skills of critical thinking, creative problem-solving, innovation, and collaborative team work, than prevailing curriculum/pedagogical traditions in school mathematics and science. Such interdisciplinary work is held to bring school STEM activities closer to the way these are practised in real world STEM.  The move towards

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interdisciplinary STEM is thus justified through arguments of authenticity, engagement, and open pedagogies supporting STEM skills. There is some confusion, however, about what interdisciplinary STEM in schools should look like. Bybee (2013) described a variety of arrangements for implementing interdisciplinary STEM curricula, pointing to a state of relative confusion as to what might prove a productive approach. There are a variety of accounts of how relations between contributing STEM subjects might be conceptualized in this work. Vasquez (2015) describes these as disciplinary, multidisciplinary, interdisciplinary, and transdisciplinary. Samuels (2009, p. 49) describes multidisciplinarity as the sharing of individual knowledge by experts, interdisciplinarity as the creation of knowledge “at the intersection of established disciplines”, and transdisciplinarity as the creation of new knowledge stemming from “the interaction of diverse people within an entirely new group”. The distinction between these terms is hard to decipher in the details of how teachers and ideas and activities might interact in a school setting, but, essentially, the difference lies in the extent to which new ‘meta-­ knowledge’ is produced that is more than the sum of the parts of the disciplinary knowledge and the extent to which members of an interdisciplinary team form a coherent group around ideas that transcend their individual disciplinary knowledges. We have argued elsewhere (Tytler, Prain, & Hobbs, 2019) that part of the problem in characterizing such interdisciplinary activity lies with the spatial metaphor through which the interactions across boundaries are described, which leaves untouched the short- and longer-term temporal relations concerning the way disciplinary knowledges are conscripted to a task. Indeed, there have been serious questions raised about the epistemic basis on which the STEM subjects are imagined to interact and about the capacity of interdisciplinary STEM activity to support significant learning in mathematics and science. Clarke (2014) points to the very different epistemic practices that constitute the four STEM disciplines, in terms of the relations between truth claims and evidence and the nature of the evidence, the discursive practices through which knowledge is built and the tools used. He characterizes interdisciplinary STEM as a possibly ‘monumental category error’. Lehrer (2016, 2017) argues that many integrated STEM projects, while engaging for students, fail to engage students in deeper disciplinary practices and fail to present a curriculum agenda that would represent a coherent knowledge progression. A major review of integrated STEM curricula in the US (Honey et al., 2014) found that, while these activities improved student attitudes, there was little evidence of improved learning, especially for mathematics. There was a general concern about the level of mathematical thinking represented in these projects. They nevertheless argue the potential of integrated approaches, alongside maintaining a focus on the individual subjects. There seem to be two related problems particular to mathematics learning through interdisciplinary design tasks. First, mathematics often plays a service role, involving already known mathematics as a tool, for instance, through calculations or graphical representation, without regard for the development of new mathematical insights through students making mathematical decisions as part of a challenging, unfamiliar problem (Barnes, 2000). Second, the highly structured nature of the

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school mathematics curriculum, compared to science or technology, for instance, makes it difficult to accommodate such interdisciplinary tasks as a significant contribution to the curriculum as it currently stands. Williams et  al. (2016), in their review of interdisciplinarity in Mathematics Education, argue that disciplines are defined through historically and culturally contextualized social practices supported by a variety of structures that constrain discourse and allow efficient communication in disciplinary group processes. They make the point that disciplinary thinking does not exist in pure form and that mathematicians will inevitably draw on other-than-abstracted mathematical thinking in their activity. They argue that “interdisciplinary mathematics education offers mathematics to the wider world in the form of added value (e.g. in problem solving), but on the other hand also offers to mathematics the added value of the wider world” (p. 13). By implication, therefore, school mathematics learning can be advantaged from opening up to interdisciplinary curricular practices. In a review of studies of interdisciplinary mathematics education, Williams et al. (2016) drew on a number of previous meta analyses and reviews. For instance, they refer to a 28-study meta-analysis of Becker and Park (2011) which concluded that: integration at elementary level has the largest effect, as does integrating all four S, T, E and M. They also found that the positive effects of integration were the smallest in relation to mathematics achievement, but argue that the increased student interest in the subject due to seeing its real-world connections, may lay the basis for improved achievement in the longer term (Williams et al., 2016, p. 16)

Williams et al.’s review offered a number of significant findings for interdisciplinary mathematics education. First, they make the point that, despite it having been advocated and explored in curricular practice for many years, this field of research is relatively underdeveloped in that in the existing studies there is “wide variation in who is measured (teachers or students …); the nature of the interdisciplinarity involved … ; how integrated that interdisciplinarity is; the nature and fidelity of the intervention; which outcomes are being measured; how these outcomes are measured and how they are analysed” (p. 19). Second, they concluded: “there is evidence of learning gains from integrated curricular and interdisciplinary working, mainly for learning outcomes of affect, of problem-solving processes, and of metadisciplinarity” (p. 17). Third, they point out that these gains are non-traditional and non-standard and that integration is thus likely to be rejected in systems that value only traditional measures. The history of integrated studies indicates a difficulty in their establishment within a culture of school teaching and learning strongly focused around high status discipline-based subjects (Venville, Wallace, Rennie, & Malone, 1998). Venville, Rennie, and Wallace (2012, p. 737) list a range of barriers to subject integration as envisaged in STEM, including “subject matter knowledge, pedagogical content knowledge and beliefs … instructional practices … administrative policies, curriculum and testing constraints … school traditions … school organization, classroom structure, timetable, teacher qualifications, collaborative planning time and approach to assessment”. Williams et al. (2016), in their review, argue the need for investment

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in development, support, and infrastructure, if such innovation is to succeed at the system level. They point, as an example, to the failure of a “remarkable” system-­ wide “Yutori” integrated studies intervention in Japan (Howes, Kaneva, Swanson, & Williams, 2013, p. 10) due to lack of system-wide investment.

3.4.1  Findings from Australian Case Studies In this section, findings from research into two major Australian STEM teacher development initiatives will be used to illustrate some of the challenges described above for interdisciplinary mathematics, regarding teacher motivations, and student outcomes. The STEM Teacher Enrichment Academy, run by Sydney University, and the ‘Successful Students-STEM’ program, run by Deakin University, each involved teachers of mathematics, science, and technology attending a series of workshops to innovate, with mentoring support, interdisciplinary curricula in their schools. The analysis of these programs, involving field notes, document analysis, and teacher, school leader and student interviews, provided insights into a number of dimensions of interdisciplinary curriculum innovation (Tytler, Williams, Hobbs, & Anderson, 2019). Models of interdisciplinary curriculum: Variation in approach reflected experience across a wider range of initiatives in Australia and internationally and could be grouped into the following broad models: • An inter-disciplinary project (sometimes a theme, such as ‘space exploration’, sometimes a design task, such as a sustainable house) with teachers from different subjects planning and teaching together; this was a common model, with mathematics being devised and explored in that class but with some team teaching. There was variation in the extent to which the activity was situated mainly within one subject or equally shared. Often students were assigned different mathematics tasks within the project, depending on their capabilities. • Cross disciplinary activities within a single subject. Mathematics teachers in one school incorporated science and design work aimed to make mathematics more relevant for students. One activity involved the design of a wheelchair ramp, involving experimenting with the effects of slope, and grappling with appropriate measurement, geometrical and basic trigonometric concepts. Teachers argued an advantage for students in creating and working with their own, real data, and noted the flow on effects for staff in developing more engaging pedagogies and for students in linking mathematics with wider purposes, including social purposes. These are consistent with Williams and colleagues’ findings from a case study of mathematics applied to nutrition, in Williams et al. (2016, p. 27). • Special STEM project activities; such as robotics days, competitions/challenges, or visits to local STEM facilities or industries. • A separate integrated STEM unit specifically designed to be inter-disciplinary, with teachers from different subjects contributing.

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• In some schools, the focus on STEM involved the explicit planning of digital technology tasks, and progression of skills, across the curriculum. The process of change: As teachers grew in their collaborative planning and practice, a number of features of the change process were evident, including: (1) growing experience of mathematics teachers in devising tasks and approaches that maintained the integrity of mathematics learning; (2) growing confidence with group-based, student-centred pedagogies, including exploratory tasks and open-­ ended questioning; (3) professional learning through interactions across the network of schools; and (4) increasing collaboration in planning and implementing projects: in some schools the achievement of a shared purpose was difficult, requiring strategic and sensitive planning processes and leadership support. Teacher perceptions and student outcomes: A major feature of the motivation for teachers and schools was the perception that ‘things had to change’ to increase student engagement with deeper learning. For teachers of mathematics, the process of learning to devise approaches to the mathematics involved in the task was not straightforward, but there were indications that they became more confident about this over time. The projects varied in the extent to which the mathematics was central to the task and arose naturally from it, with some tasks involving mathematics, which was somewhat arbitrary and not challenging. However, student interviews indicated students were positive about the fact the mathematics they learnt was for a purpose, and there was evidence from student and teacher interviews of improved attitudes to STEM and potential STEM careers. There were examples, from student notebooks, of significant mathematics learning, consistent with teacher perceptions. The implications for interdisciplinary mathematics curriculum practice, from analysis of these programs, included (Tytler et al., 2019): • Within the variety of approaches, the core feature of mathematics in the most compelling cases was the application of the mathematics to ‘authentic’ projects in ways that were meaningful to students, and involved developing new mathematics, or applying known mathematics in new ways. • There was no suggestion in any case that mathematics should evolve into an interdisciplinary, as distinct from a disciplinary, practice. Rather, what was involved was the re-alignment of mathematical thinking and working to real-life, complex, problem-oriented contexts. • For productive mathematics learning in these interdisciplinary settings, tasks should engage students’ interest, involve problem solving, involve students in using mathematics in unfamiliar and creative ways, and lead to fresh insights into the problem being pursued. • Teachers of mathematics found it challenging to develop productive learning opportunities from STEM tasks. This involves a different perspective and skill set and a more responsive view of mathematics learning and knowing. • There was evidence that students were generally more enthusiastic about mathematics through these interdisciplinary tasks. From students’ viewpoint, the

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development of mathematics that was immediately applicable and helpful in problems they felt invested in provided significant motivation. • In all cases, the development and sustaining of these curriculum innovations depended on high-level support from principals and discipline leaders.

3.4.2  L  earning Progression Through Interdisciplinary Mathematics Productive interdisciplinary mathematics curricula involve the authentic generation and application of mathematical knowledge relevant to a real-life project or task. While there is evidence that students find these interdisciplinary settings motivating, and that they see mathematics as more meaningful through its applied purposes, as yet no clear picture has emerged as to the ways in which such work can contribute more fundamentally to progression in mathematical ideas. Generally, interdisciplinary tasks are advocated as a minor part of a mathematics curriculum. However, there are some models of interdisciplinary curriculum practice that aim to contribute to long-term progression in student learning of foundational mathematical concepts. Richard Lehrer’s and Leona Schauble’s research, based in the theoretical perspective of model-building and model-based reasoning as a core disciplinary epistemic practice, seeks to ground mathematical learning in progressive experiences of representational invention and refinement. With regard to statistical reasoning for instance, Lehrer and English (2018) explain: we take a genetic perspective toward the development of knowledge, attempting to locate productive seeds of understandings of variability that can be cultivated during instruction in ways that expand students’ grasp of different aspects and sources of variability (p. 229).

Lehrer and Schauble (Lehrer, 2009; Lehrer & Schauble, 2012) have introduced mathematical modelling in students’ investigations of growth and ecosystem function and organization, focusing on measurement. Students explored necessary properties of units and unit iteration that anchor their interpretation of a measure as a ratio: a measured length of 4 units is 4 times as long as a unit length (e.g. Barrett & Clements, 2003). These understandings of the nature of unit and of measurement scale served as resources when students next attempted to measure qualities of natural systems, such as the rate of growth of organisms, such as plants and insects (Lehrer, Schauble, Carpenter, & Penner, 2000). Thus, students’ experiences of measure extend beyond the simple ‘application’ of mathematical principles, and involve invention, evaluation, and refinement of mathematical representational systems, as they re-describe, for instance, plant growth across pictorial, tabular, and graphical modes. Moreover, measures of natural systems are variable, and thus introduce the need for a ‘logic of approximation’ that stands in contrast to curriculum traditions focusing on mathematical necessity. Discussions of growth variability and approximation in this grade 3 class showed that, under effective guidance, primary students are capable of this deeper kind of reasoning.

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These innovative mathematical approaches unlock significant aspects of ecological and natural systems, such as interaction and growth as the determinants of system change, and the science questions that arise tend to lead, in turn, to further mathematical exploration (Lehrer & Schauble, 2012). Currently, we are conducting cross-national interdisciplinary research to explore the extension of this approach to a range of primary school topics (Tytler et  al., 2018–2020). The approach is, in principle, possible for secondary schools, although the less flexible timetabling and more scripted curricula could prove challenging.

3.5  Conclusion The global focus on STEM Education reflects a concern of nation states to build strong economies and enhance societal well-being, coupled with an assumption that the building of a STEM-skilled populace is an important key to this. Perceptions of diminishing engagement of contemporary youth with STEM subjects, and predictions of work futures that will increasingly emphasize STEM-related transportable skills, such as critical thinking, creative problem solving, design thinking, and collaborative team work, as well as STEM disciplinary knowledge in forms that are applicable in authentic settings, has led to calls for a changing emphasis in school STEM curricula. These calls amount to an argument that prevailing content and pedagogies in school mathematics and science are failing to engage students in the sorts of knowledge and skills that will best prepare them for the future. The STEM phenomenon thus represents a challenge to ‘business as usual’ in school mathematics and science. This applies to all levels of schooling, since decisions to engage or not with STEM futures can be determined at an early age. Increasingly, STEM rhetoric has been aligned with advocacy of interdisciplinary approaches to mathematics and science learning, built around authentic problem solving and cross-subject interactions. In a number of countries, STEAM, with the A representing creative art and design, has been pursued as a way of enhancing creativity in STEM school practices. For mathematics, STEM advocacy has renewed a long-standing interest in interdisciplinary approaches. This review has identified a number of possibilities, and a number of challenges for interdisciplinary mathematics. First, there is a dearth of research that would clearly indicate to us the best approaches, and what the outcomes might be. There is wide variability in the nature of integration in the initiatives that have been studied, and variation in the research methods used and outcomes focused on. There is a generally persistent finding that interdisciplinary mathematics curricula lead to improvement in attitudes of students, and to teachers expanding their pedagogical range, but the research is mixed on the effect on student conceptual outcomes. It has been argued, however, that an improvement in student attitudinal responses to mathematics, even if there are no demonstrable short-term gains in learning outcomes, could in the end be a valuable outcome in terms of longer-term learning gains.

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Part of the problem with preparing for and supporting system-wide curriculum reform towards interdisciplinary mathematics is that the gains most associated with these approaches―attitudes, problem solving, and metadisciplinary knowledge and skills―are not those traditionally valued and measured. It is also clear that there are a range of blocking factors for interdisciplinary practice in secondary schools, including timetables, organizational structures, teacher training and habits of thinking, and assessment regimes. In order to effect sustainable changes towards interdisciplinary mathematics in STEM, significant commitment is needed at the school and system levels to overcome these barriers, including the development of assessment regimes reflecting STEM skills, such as critical mathematical thinking and creative problem solving. In terms of disciplinary epistemic integrity, there is evidence that many versions of interdisciplinary STEM tasks fall short of developing significant mathematical thinking and working. Mathematics teachers need to learn new skills, perhaps involving new perspectives on the nature of foundational mathematics concepts, in designing and supporting such mathematical practices in interdisciplinary settings. Paradoxically, it may be that the nature of mathematical disciplinary thinking could be best understood through its development in exploratory real world or interdisciplinary contexts (Lehrer et  al., 2000; Williams et  al., 2016, p.  16), rather than through the structured within-mathematics practice that currently prevails. Interdisciplinary approaches are particularly problematic for mathematics partly because of its epistemic character and also the structured and sequential nature of the traditional curriculum. Because of this, advocacy of interdisciplinary mathematics tends to be restricted to short term STEM projects, with the mathematics core pursued without reference to other subjects. However, the work of Lehrer and others opens up possibilities of thinking of ways to pursue a wider range of mathematical topics in a structured way, but within interdisciplinary sequences. It seems clear, however, that this curriculum work cannot easily be done by classroom teachers working within the constraints of traditional schooling structures. There needs to be a serious commitment by systems, supported by significant research and development, if we are to bring the learning possibilities of interdisciplinarity mathematics to fruition. What Is Needed for this to Occur Is • A system wide commitment to a mathematics curriculum that meaningfully contributes to developing the STEM knowledge, skills, and attitudes that will prepare youth for the future. • A program of research and development focused on: –– Investigating what mathematical learning outcomes should be the focus of a curriculum responding to STEM perspectives –– Investigating what models of interdisciplinarity, in what topics, lead to engagement of students with these learning outcomes –– Developing programs of assessment that support such curriculum innovation –– Developing, in partnership with systems and teachers, structured activity sequences that represent exemplar interdisciplinary curricular practice and

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–– Developing professional learning approaches that support teachers in interdisciplinary mathematics. Acknowledgement  This chapter is an adaptation of a position paper funded by the OECD to contribute to the Mathematics 2030 Learning Framework.

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Chapter 4

Facilitating STEM Integration Through Design Lyn D. English

Contents 4.1  STEM and Innovation 4.1.1  Implications for STEM education 4.2  Issues in STEM Integration 4.3  STEM Integration Through Design 4.4  Learning Through Design in Integrated STEM Problems 4.4.1  Optimisation 4.4.2  Sketching 4.4.3  Reflecting and Improving 4.5  Example of STEM Integration Through Design: Aerospace Engineering 4.5.1  Background 4.5.2  Disciplinary Content 4.5.3  Study Design 4.5.4  Implementation Procedures 4.5.5  Data Collection and Analysis 4.5.6  Samples of Students’ Responses 4.5.7  Sample of Students’ Responses to Design Questions 4.5.8  Load Impact: Predictions and Outcomes 4.6  Concluding Points References

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Integrated STEM education, indeed even STEM education itself, has been a much-­ debated topic for several years. With STEM-related skills and knowledge increasingly needed across a broader range of fields, educators worldwide, as well as business and industry leaders, are highlighting the need to lift the STEM achievements of students (e.g., Canada 2067; Committee on STEM Education of the National Science & Technology Council, 2018; Education Council, 2015; European (EU) STEM Coalition (n.d.); Masters, 2016; Price Waterhouse Cooper, 2016; Rosicka, 2016). As Price Waterhouse Cooper noted in a 2016 report, “building a STEM capable workforce begins with education and the primary years are crucial L. D. English (*) Queensland University of Technology, Kelvin Grove, Brisbane, QLD, Australia e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_4

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in establishing foundational skills, knowledge, and curiosity about STEM concepts” (p. 11). Common global concerns for how to improve STEM education are compounded by the longstanding debates on the nature of STEM education, on whether the disciplines should be integrated and how, and on whether STEM education is preparing our students adequately for an ever-changing world. Despite these well-documented reports recommending increased attention to STEM education, there are those who appear sceptical (e.g., Chesky & Wolfmeyer, 2015; Smith & Watson, 2018). Claims that STEM is just another “fad”, that it is overrated (e.g., Charette, 2013), and that it is being emphasised at the expense of the humanities, are not uncommon. A further frequently expressed concern is whether STEM integration adequately develops the content knowledge of the respective disciplines (English, 2016, 2017; Guzey, Ring-Whalen, Harwell, & Peralta, 2019; Honey, Pearson, & Schweingruber, 2014; Shaughnessy, 2013). Despite debates regarding STEM integration, we cannot dismiss the challenges of multidisciplinary problems in today’s world and the escalating impact of STEM innovations. It would thus seem paramount to engage students in integrated experiences from the earliest grades (Daugherty & Carter, 2018; English, 2016, 2017; Honey et al., 2014; Park, Park, & Bates, 2018; Rennie, Venville, & Wallace, 2018). Indeed, the rapid impact of disruptive technologies on almost all aspects of our lives behoves us to provide opportunities for our students to deal skilfully with these disruptions. In the first part of this chapter, I consider how global disruptions emanating from developments in the STEM fields are impacting our daily lives and how STEM integration provides a valuable foundation for dealing with these rapid changes. Next, I explore design as a significant component of both innovation and of disciplinary integration. Finally, I report on an aerospace problem activity in which grade 5 students applied design processes together with integrated STEM disciplinary knowledge to problem solution.

4.1  STEM and Innovation Disruption arising from innovations in the STEM fields is rapidly becoming mainstream in almost all spheres of life, including industry, business, politics, culture, and the media. Disruptive innovation (Christensen, 1997; Christensen, Horn, & Johnson, 2016) traditionally refers to a technological development that significantly affects the way markets or industries operate. The internet, for example, significantly changed the way companies did business, negatively impacting those companies unwilling to adapt to the new technology. Across business and industry, a myriad of articles and media reports are warning of this disruption that threatens the survival of companies, with only “the paranoid” surviving (Crittenden, Crittenden, & Crittenden, 2017, p. 14; Grove, 1996). Such upheavals trigger disruptive thinking, where perspectives on commonly accepted (and often inefficient) solutions to problems are rejected for more innovative approaches and products. These

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innovations are sparked by STEM developments, in which the disciplines operate in an integrated manner, not in isolation. A common example is car manufacturing, which faces unprecedented challenges from the self-driving car industry, with many longstanding companies making significant changes in their designs and manufacturing (Rusko et al., 2018). However, as Rusko et al. indicated, driverless cars are still developing because the key technology and production mechanisms are yet to be fully realised. Specialists from across the STEM spectrum are needed to improve driverless cars, such as digital mapping engineers to develop the complex 3-D maps required. These technological disruptions are stimulating unexpected cooperation between competing companies—for example, Google has now invested in self-driving cars, where sensors and software detect objects, including pedestrians. Major car companies are not only cooperating with technology firms but also with ride-hailing service companies, such as Uber Technologies Inc., to create a network of on-demand, driverless vehicles in the US.  These companies can enter this new market and develop a competitive edge that otherwise would be difficult to achieve. These cases provide just a few examples of how STEM integration in the real-world is foundational to major innovations. The implications for STEM education in schools are manifold.

4.1.1  Implications for STEM education Educators can ill afford to ignore the rapid growth in innovations emanating from advances in the STEM fields. Unlike business and industry, where disruption creates a “force-to-innovate” approach (Crittenden et al., 2017, p. 14), much of school education seems unable or reluctant to prepare students for disruptive forces or at least are restricted in doing so by set curricula. The need to equip students with the skills for “disruptive thinking” is recognised by governments (e.g., Committee on STEM Education of the National Science & Technological Council, 2018; Innovation and Science Australia, Australian Government, 2017), yet it is questionable whether we are accomplishing this, at least in Australia. As the chairman of Innovation and Science Australia warned, “Unless we change our education system, we won’t be able to equip our kids with the skills they will need for a rapidly changing economy (The Australian, 30th Jan., 2018, p. 20). In a similar vein, Christensen et al. (2016) warned that if we hope to stay competitive from academic, economic, and technological perspectives, we need to reassess our educational system and re-­ energise our commitment to learning. In other words, we need disruptive innovation in our education systems. STEM educators cannot ignore these warnings. For several years, industry leaders have been emphasising the importance of both STEM competencies, including digital literacy and a range of twenty-first century skills (Commonwealth of Australia, 2017; Canada 2067: Global Shapers Report, 2017; Partnership for twenty-first Century Skills, 2006). Employee capabilities that are commonly

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highlighted and have implications for rethinking STEM education include the development of: agility, innovative insights, diversity of thought, flexible strategies, complex problem solving, creative ideas and solutions, adaptable behaviours and judgement, and decision making (e.g., The World Economic Forum, 2018). These twenty-­first century skills, however, do not replace disciplinary knowledge—they cannot operate in a vacuum. One cannot reason critically or be adaptive or creative in the absence of a knowledge base. Disciplinary knowledge and thinking skills go hand-­in-­hand—both are essential to effective STEM problem solving and learning. STEM problems that challenge students’ existing ideas and approaches, invoke different applications of disciplinary knowledge, and draw on twenty-first century thinking skills can generate disruptive thinking. Such thinking goes against conventional or expected responses (Sternberg, 2017) and can contribute to the foundations for an innovative society. Yet, despite STEM education being in a prime position for preparing students for disruption, we are not realising the potential of these disciplines. STEM education needs to be at the forefront of problem solving that encourages students to apply their learning in innovative ways, not blindly follow given rules or procedures. As in the outside world, where industries, businesses, and companies in general need to continually innovate in order to survive or avoid being taken over, education must do likewise. The world is becoming too complex and challenging to do otherwise.

4.2  Issues in STEM Integration The best STEM education provides an interdisciplinary approach to learning, where rigorous academic concepts are coupled with real-world applications and students use STEM in contexts that make connections between school, community, work, and the wider world. (Committee on STEM Education of the National Science & Technological Council, 2018, p. 1).

Integrated STEM education is the ideal vehicle for developing foundations for innovation. Numerous interpretations of STEM education and integrated STEM learning abound, with viewpoints varying in scope and specificity (e.g., Bryan, Moore, Johnson, & Roehrig, 2016; Bybee, 2013; Pearson, 2017; Vasquez, Schneider, & Comer, 2013). The perspectives of Vasquez et al. (2013) are frequently cited, with different forms of boundary crossing displayed along a continuum of increasing levels of interconnection and interdependence among the disciplines. These STEM approaches range from a focus on single disciplines, where concepts and skills are learned separately in each content area, through to multidisciplinary forms involving concepts and skills in each discipline being learned separately but within a common theme, and finally, transdisciplinary formats, where knowledge and skills learned from two or more disciplines are applied to real-world problems and projects, thus defining the total learning experience. One definition of STEM integration that seems especially apt is that of Shaughnessy (2013), namely,

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STEM education refers to solving problems that draw on concepts and procedures from mathematics and science while incorporating the team work and design methodology of engineering and using appropriate technology (p. 324).

Rennie et  al. (2018) present an alternative perspective on STEM integration. Eschewing the continuum concept of disciplinary connections, which belies the complexity of integration and could imply that one end of the continuum is better than the other, Rennie et al. (2018) proposed six categories of STEM integration: “synchronised, thematic, project-based, cross-curricular, school specialised, and community-focused programs” (pp. 95–96). It is beyond the scope of this chapter to examine each of these; suffice to say that they offer a wider range of possible approaches that accommodate individual curriculum documents and school contexts. For example, many schools are located in environments that are ideal for community-focused STEM projects, such as local creeks or rain forests, or a local airport. Project-based approaches are popular and usually require the application of knowledge and skills from more than one STEM discipline and frequently entail the construction of an artefact of some kind (Holmlund, Lesseig, & Slavit, 2018). Issues regarding loss of disciplinary coverage in STEM integration, especially with respect to the mathematics and science concepts being targeted, cannot be dismissed (English, 2017; Guzey et  al., 2019; Honey et  al., 2014; Shaughnessy, 2013). Deficiencies in STEM content learning have also been reported in technology education, where students’ application of disciplinary knowledge to support their design processes has been limited, with trial-and-error common. Many students thus fail to develop an understanding of how science and mathematics knowledge supports their learning and problem solving in technology (Fan & Yu, 2017; Lewis, 1999; Mativo & Wicklein, 2011). Likewise, Shaughnessy (2013) warned that programs might be defined as “STEM” but can be merely a STEM veneer, where instructional approaches do not genuinely integrate the disciplines and thus learning in one domain can take precedence over another. Furthermore, as with many problem-solving activities, students can simply work procedurally, often preoccupied with the problem context at the expense of the disciplinary content (Reiser, 2004; Watkins, Spencer, & Hammer, 2014). These disciplinary concerns highlight the need for STEM integration to be “intentional” and “specific”, with consideration given to both content and context. As Moore and Smith (2014) emphasise, integrating STEM content per se does not guarantee that students will be aware of the contributions of the respective disciplines to problem solution. Targeting students’ awareness of their disciplinary learning and how they are applying this in solving an integrated STEM problem is thus an important step (Bryan et al., 2016; Honey et al., 2014; Moore et al., 2014; Nathan et al., 2013). Discussing examples of STEM integration in the world around them can also help students appreciate the natural connections across the disciplines. STEM education in schools should take advantage of these connections and capitalise on the rich learning such linkages, sometimes unanticipated, can offer. In this spirit, it is worth reiterating the points made by Rennie et al. (2012b), namely:

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L. D. English … we are suggesting that STEM curricula provide a mix of disciplinary and integrated knowledge, set in carefully chosen local problems that can be applied to more global issues. The nature of that mix, finding the point of balance and the degree of connection, is dependent on the particular educational context, and will vary from school to school and from place to place. (Rennie, Venville, & Wallace, 2012b, p. 140).

Unfortunately, current practices frequently ignore these real-world connections, instead focusing on narrow approaches to learning that are readily measurable in achievement tests (Rennie et al., 2018). Rennie and her colleagues (e.g., Rennie et al., 2012b; Rennie, Venville, & Wallace, 2012a; Venville, Sheffield, Rennie, & Wallace, 2008) have demonstrated how engaging students in activities involving integrated, interdisciplinary knowledge reflecting situations in their world can be a powerful means for connecting other domains, such as social, environmental, and global issues. Core discipline knowledge is essential here, but this needs to be developed along with twenty-first century skills (P21, 2015) and a facility with disruptive thinking. In other words, content knowledge and these thinking skills operate hand-in-hand in solving authentic STEM problems. Design, which is foundational within the engineering and technology domains, provides a natural link across the disciplines, yet is largely ignored in STEM programs, especially in the elementary years (Asunda & Quintana, 2018; Crismond & Adams, 2012; Daugherty & Carter, 2018; DiFrancesca & McIntyre, 2014; English, 2017; English & King, 2019; Moore & Smith, 2014). This lack of attention to design is concerning, especially given its increasing importance in an innovative world.

4.3  STEM Integration Through Design The integration of the STEM disciplines through design is recognised as an increasingly important area of research (Crismond & Adams, 2012; English, Adams, & King, 2020; McFadden & Roehrig, 2019). Design has received substantial attention in studies of engineering education as well as technology, especially in the secondary school and university years (e.g., Fan & Yu, 2017; Froyd & Lohmann, 2014; Lammi, Denson, & Asunda, 2018; Mentzer, Becker, & Sutton, 2015). The contribution of design to mathematics and science education has received less attention, however, particularly in the elementary grades (Fan & Yu, 2017; Jones, Buntting, & de Vries, 2013; Kelley, Brenner, & Pieper, 2010). Of concern is the common view that design is beyond young children’s capabilities, along with teachers’ lack of knowledge and confidence in implementing design-based experiences (Bagiati & Evangelou, 2018; McFadden & Roehrig, 2019). Design and design thinking have gained in popularity in recent years, with design now being applied to a diverse range of fields as broad as business and medicine (Dorst, 2011). Design has been defined broadly as “the ways in which human beings modify their environments to better satisfy their needs and wants” (Kangas & Seitamaa-Hakkarainen, 2018, p.  597). For STEM education, however, design is usually defined in reference to problem solving in engineering and technology (e.g., English & King, 2019; Lucas, Claxton, & Hanson, 2014; Tank et al., 2018). From

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this perspective, design comprises a number of phases, including: problem scoping (understanding problem boundaries, identifying goal and problem constraints); generating ideas and planning; designing and constructing (sketching, contemplating possible outcomes, transforming design into product); testing and reflecting on outcomes (checking goal attainment and meeting of constraints); redesigning and reconstructing (reflecting on first design, identifying improvements, transforming new design into a better product); and reflecting and communicating (with respect to overall processes of designing and constructing). As such, design processes have wide applicability in integrated STEM problems and projects. Typically, design-based projects involve real-world, hands-on experiences that enable multiple approaches and solutions. The applications of design processes in solving an integrative STEM problem can assist students in developing new knowledge and capabilities (Fan & Yu, 2017). Importantly, design can facilitate an understanding of connections among the STEM disciplines and develop skills in drawing together these links to generate more effective solutions (Burghardt & Hacker, 2004; Bybee, 2013; Fan & Yu, 2017). Systems thinking comes into play here as students recognise these disciplinary connections and understand how interactions among problem components (the system) can have unanticipated consequences in problem solution (Lammi & Becker, 2013; McBride, 2005). Such thinking is increasingly important in today’s world, where problems need to be considered as interconnected and interdependent components, rather than as a number of independent parts (Salado, Chowdhury, & Norton, 2018). STEM integration through design has several features that facilitate problem solving beyond engineering-based or technology-based problems. As such, the application of design processes and the supporting thinking skills could overcome some of the weaknesses identified in earlier mathematics problem-solving approaches (e.g., heuristics or strategies), which proved not as effective as hoped (e.g., Lester Jr., 1980). A particular feature of STEM integration through design is the range of learning opportunities afforded throughout problem solution. Learning while designing is thus a key contribution of design-based problem solving (Crismond & Adams, 2012; English & King, 2019).

4.4  Learning Through Design in Integrated STEM Problems As students work through a STEM problem involving design, they become more cognisant of the disciplinary knowledge they are applying or need to apply, and are thus in a better position to make and explain knowledge-based decisions instead of simply following a given strategy or using trial-and-error (Guzey et  al., 2019). These problems require designing an initial solution while keeping in mind the problem goal, boundaries, and constraints, and then testing the outcomes of their initial designs. As students undertake these actions, their disciplinary knowledge base guides them in making informed decisions and, subsequently, improving on their initial ideas in the redesign process.

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4.4.1  Optimisation Integrated STEM problems frequently involve optimisation, where the iterative design process involves balancing trade-offs, such as performance competition versus costs, robustness versus social constraints, and tourist revenue versus environmental impacts (Bennett & Ruchti, 2014; Lammi & Becker, 2013). More than one test is usually required to obtain a design that yields maximum optimisation (McFadden & Roehrig, 2019; Next Generation Science Standards, 2013). Traditional problem types do not normally require or encourage this important test-and-improve aspect, which provides opportunities for students to learn core STEM concepts as they analyse their progress, increase the feasibility and efficiency of their design ideas, and optimise their problem outcomes (Fan & Yu, 2017).

4.4.2  Sketching A fundamental feature of design is sketching, which further enhances learning as students document and convey their understanding and solution approaches (Dym, Agogino, Eris, Frey, & Leifer, 2005; Kelley & Sung, 2017; Song & Agogino, 2004). A design sketch can involve various forms of representation that display the main features of the product or problem situation being envisioned (Song & Agogino, 2004). Students need to draw on and connect their disciplinary knowledge in generating and annotating their sketches, while keeping in mind the problem goal and constraints. Sketching thus fosters systems thinking (Katehi, Pearson, & Feder, 2009; Lammi & Becker, 2013), as students need to determine how the various components should interact to yield maximum optimisation of outcomes. Systems thinking encourages students to become flexible in their actions, and think adaptively and divergently (Lammi & Becker, 2013). Insights into students’ thinking can subsequently be gained from studying their annotated sketches (Anning, 1997). Not surprisingly, the important roles of sketching in problem solving do not appear to be acknowledged in the elementary grades, possibly because of a common assumption that young learners lack the necessary skills or are reluctant to sketch (MacDonald & Gustafson, 2004; Smith, 2001; Welch, Barlex, & Lim, 2000). It has also often been claimed that younger students do not use sketching as a means to develop and communicate their design plans; instead they proceed immediately to constructing (e.g., Crismond & Adams, 2012; Welch et al., 2000). Consequently, some studies have focused on teaching sketching, instead of scaffolding its development (e.g., Kelley & Sung, 2017; Welch et al., 2017). Yet my research on integrated STEM problems has shown how grade 4 students appreciate the value of sketching. For example, in designing and constructing their own pairs of shoes (English & King, 2019), students engaged in a class discussion on how their shoe designs helped them in creating their shoes. Students considered their design sketching to be of considerable assistance, as one student explained

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… because at the start I was thinking what on, what on earth am I going to do, and um, if I just started randomly making the shoe it would not work because I would have no idea what I was doing. And the design would help because you would know where to put the parts and um, how it would look and everything.

Another student expressed similar appreciation of their initial sketching commenting: “It was good that you had to draw your design so you actually had a good idea of what it was going to look like.” Other comments included the value of sketching in assessing the feasibility of one’s ideas, for example: “Say you had this idea and you thought it was amazing, … when you draw it out, oh, when you think about it, it seems awesome, you draw it out and you see that it won’t work” (English & King, 2019).

4.4.3  Reflecting and Improving It is important that young students reflect on their actions and become aware of the disciplinary knowledge they apply in solving complex integrated STEM problems (Crismond & Adams, 2012). In testing whether their product meets the problem goals and constraints, and is a feasible and an effective solution, students need to review their application of appropriate disciplinary knowledge, such as basic principles of flight. They can then reflect on the strengths and weaknesses of their design to determine how it might be changed to yield an improved outcome. Subsequent redesign and reconstruction require identifying, understanding, and applying core concepts and principles of the relevant STEM disciplines in the redesign phase in an effort to optimise goal attainment (Kangas, Seitamaa-Hakkarainen, & Hakkarainen, 2013; Wendell, Wright, & Paugh, 2017). For example, adjusting the size and shape of a paper plane’s wings can improve its speed and the distance travelled. The iterative nature of design prompts students to engage in these reflect-and-­ improve actions, which appear to receive limited attention in the elementary grades. Yet these actions have the potential to promote more effective learning both about and from a problem (cf., McKenna, 2014). Such learning is especially significant in integrated STEM activities, where students often do not make the important connections between the disciplines (Moore et al., 2014).

4.5  E  xample of STEM Integration Through Design: Aerospace Engineering In the next section, I consider an integrated aerospace activity (designing paper planes), which was implemented in two grade 5 classes (10-year-olds; N = 42) in an all-girls school in a middle socio-economic suburb of an Australian city. The multi-­ component problem activity was conducted over two school days as part of students’ participation in a longitudinal STEM program (grades 3-6).

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4.5.1  Background Designing, constructing, and flying paper planes appears straight forward at first, but understanding how the best paper planes can be developed is a difficult and dynamic problem (Cook, 2017). As Cook notes, paper planes “possess unstable aerodynamics, and beyond the point of launch they experience entirely uncontrolled flight” (p. i). Interestingly, it appears that the Wright Brothers used paper planes in their early developments of their first flying machines, which subsequently inspired further iterations of the paper craft (Cook, 2017). Some of the characteristics of paper plane designs include the total area of the wing, the wingspan (distance between tips of each wing at their widest point), and fuselage depth (length of folded centre section of plane, measured from wings to base) (Cook, 2017).

4.5.2  Disciplinary Content The planes problem activity was housed within an aerodynamics engineering context, with such a context affording numerous avenues for interdisciplinary learning (Wright, 2006). The STEM disciplinary content included: Mathematics: linear measurement, working with data (collecting, organising, representing, and analysing), and geometry (location, direction, shape, and transformation of shapes). Science: aerodynamic forces and how they act on objects. Mathematics and science: determining which variables might affect fair testing; observing, measuring, and recording data accurately; constructing and using a range of representations (e.g., tables, graphs); and interpreting patterns or relationships in data collected. Technology and engineering: generating design ideas that match constraints; communicating and testing design through a 3-D model; exploring the work of aerospace engineers and aerospace design.

4.5.3  Study Design The activity was part of a longitudinal, design-based research study (Cobb, Jackson, & Dunlap, 2016), with such an approach catering for complex classroom situations that comprise multiple variables and real-world constraints. Adopting a design research approach would also enable the desired learning to be introduced, built upon, and sustained from one school year to the next. Specifically, design research would facilitate intervention involving the creation and refinement of learning experiences with a focus on developing students’ STEM competencies over time.

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4.5.4  Implementation Procedures Applying the foregoing disciplinary content, student groups designed, constructed, and tested their paper planes with the goal of optimising the distance travelled. Students initially designed and tested their individual plane constructions across three trials, then selected the most effective individual design as a basis for designing and constructing a new, group plane. They subsequently measured, recorded, and represented the distances travelled by their group plane over five trials. To explore the effects of load, students investigated the impact of adding paper clips to the group plane, for each of three load positions on the fuselage. Students collected, organised, represented, and analysed data from each trial and across trials for flights with and without loads. Each student completed her own workbook in which she sketched her individual and group designs, recorded and represented the data for all trials, conducted data analysis, documented predictions regarding load impact, and answered other questions pertaining to the activity. The students were not given any teacher directions, rather, the workbooks served to scaffold “complex learning” by giving structure to the investigation and problematising the disciplinary content and practices (Reiser, 2004, p. 273).

4.5.5  Data Collection and Analysis Several forms of data collection were undertaken, including audio and video recordings of small group interactions, as students completed the investigation, as well as whole class discussions. Two groups in each class (referred to here as focus groups) were chosen for videorecording and in-depth analyses. These groups comprised three or four students of mixed achievement levels, selected on the basis of their ability to converse and work together. All focus group interactions and class discussions were transcribed, and provided further evidence of the students’ developments in their STEM learning. All data from each student’s workbook were scanned and analysed. Both qualitative and basic quantitative analyses of the workbook data were undertaken. The latter commenced with a form of open coding (Strauss & Corbin, 1998) after repeatedly studying the students’ workbook responses. An experienced senior research assistant, who attended all the classroom sessions with the author, assisted in the coding and multiple refinements of the codes. The analyses of the focus group and whole class transcripts adopted the form of iterative refinement cycles for in-depth evidence of students’ learning (Lesh & Lehrer, 2000). Through repeated analyses of the transcripts, examples of the focus group students’ responses to key components of the activity (e.g., factors causing variation in data, predictions for loaded plane) were identified.

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4.5.6  Samples of Students’ Responses Consideration is next given to students’ plane design sketches, followed by a sample of their responses to other aspects of the problem activity, including their predictions on the impact of adding load to their planes and the actual outcomes on testing their predictions. Students’ (n = 42) design sketches were analysed in terms of the perspectives displayed and the annotations included as follows: Perspectives 1: top view, 2: side view, 3: both top and side views and/or three-­ dimensional view. Annotation 1: measurements included, 2: plane features labelled, such as the nature of the wings, 3: purpose of features indicated. For the annotations of the group designs, two additional codes were needed to account for the increase in detail displayed, namely, 4: measurements and plane features only displayed, and 5: measurements, plane features, and purposes of features included. As would be expected, students’ design sketches displayed varying degrees of sophistication, with respect to the perspectives indicated and the extent and nature of the annotations included. As can be seen in Table 4.1, just over half of the students’ individual sketches featured both top and side views and/or a three-­ dimensional perspective. Individual sketches that showed a top view only (“bird’s view”) were also common. Students’ individual sketches did not include as great a range of annotations as their group sketches, discussed next. As can be seen in Table 4.1, almost half the students indicated plane features only, while fewer students also included the purpose of these features. Twenty percent of the students, however, did not include any annotations, possibly due to their preoccupation with the actual sketching process or to time factors. For their group sketches, students displayed similar responses with respect to the perspectives displayed (Table 4.2). Again, the inclusion of both top and side views and/or a 3-dimensional perspective was common in the group sketches, as were top views only. As noted, the group sketches showed a greater range of annotations, with nearly half incorporating measurements, plane features/characteristics, and their purposes. For example, some indicated how the size of a particular plane component impacted on the flight path (e.g., “small body for faster movement”). Some Table 4.1  Frequencies of responses for individual plane sketches, N = 41 (1 absent) Perspectivea Annotationb

0 0 0 8 (20%)

1 15 (37%) 1 1 (2%)

2 3 (7%) 2 20 (49%)

3 23 (56%) 3 12 (29%)

a Perspective 0: none displayed. 1: top view. 2: side view. 3: both top and side views, and/or a 3-dimensional view b Annotation 0: none displayed. 1: measurements included, 2: plane features indicated only, 3: purpose of the features also included

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Table 4.2  Frequencies of responses for group plane sketches Perspectivea Annotationsb

0 1 (2%) 0 6 (15%)

1 15 (37%) 1 1 (2%)

2 3 (7%) 2 5 (12%)

3 23 (56%) 3 8 (20%)

4 1 (2%)

5 20 (49%)

N = 41 (1 absent) Perspective 0: none displayed. 1: top view. 2: side view. 3: both top and side views, and/or a 3-dimensional view b Annotation 0: none displayed. 1: measurements included. 2: plane features indicated only. 3: purpose of the features also included. 4: measurements and plane features only displayed. 5: measurements, plane features, and purposes of features included a

reference to aerospace concepts was also evident (e.g., aerodynamic, lift, air resistance, stability, glide, acceleration [thrust].) Figures 4.1 and 4.2 display one student’s (student M) individual plane sketch and her group’s sketch, respectively. Student M displayed multiple perspectives in her individual sketch, with her primary concern being the air resistance. The way in which she intended to overcome this problem was to reduce the area “touching the air” and “add a fin on the back”. Student M’s group design sketch included measurements of the plane components, an indication of the component sizes (“thin, bigger wings, longer”) and some reference to aerospace concepts (air resistance, lift, stability). Likewise, student S’s group design (Fig. 4.3) included plane measurements and the functions of the plane components, together with their reasons for deciding on their design. Design sketching is such an important component of so many integrated STEM activities, that it cannot be left to “chance”. Students need to know and appreciate how design sketching contributes to a STEM investigation, including its key role in communicating and refining ideas, and in developing prototypes for testing and development (Kelley, 2017; Strimel, Kim, Grubbs, & Huffman, 2020). In the absence of specific instruction, students’ design sketches displayed some of the “fundamentals” of design sketching, including labelling, annotating, and incorporating multiple views (Kelley, 2017), illustrating elementary students’ design capabilities. In generating and annotating their sketches, students had to draw on their disciplinary knowledge (science, mathematics, engineering design processes), while keeping in mind the problem goal and constraints, including consistency in launching techniques. As previously noted, sketching encourages systems thinking (Katehi et al., 2009; Lammi & Becker, 2013), where students need to determine how the various plane components and the aerodynamic forces might interact to optimise the outcomes. Such systems thinking was also evident in students’ responses to some of the design questions in their workbooks.

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Fig. 4.1  Student M’s individual design sketch

4.5.7  Sample of Students’ Responses to Design Questions Students displayed mixed views on how plane design affects distance travelled, with some claiming that larger wings increase the distance, while others expressed the opposite. For example, when sketching their plane design, one group was undecided on how the size of the plane components would impact on the distance travelled: Student A: The wings are big so that the wind can like fly … Student B: It can windsurf!

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Fig. 4.2  Student M’s group design sketch

Fig. 4.3  Student S’s group design sketch

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L. D. English Student C: So that’s for the wings. Student A: So bigger wings are better, (other students in the group agreeing) … to catch the wind …. so that the wind can get under it and make it fly. Student B: But then a smaller plane is better … so, smaller body, big wings. Student C: Yes, smaller body, big wings; pointy end, even weight.

In contrast, other groups opted for different design specifications, such as a “full wing span, small wings for less friction, and a nose to fly for longer”. Another group chose a “traditional plane because it travels fast and far. [it has] smaller body for faster movement. [it has] small wings for fast movement”. Students had not tested the outcomes of their designs at this initial sketching phase, so these different perspectives are perhaps not surprising. Wing span and body mass affect both distances travelled and times in the air; changing one design feature may impact on one or more of the other features, such as increasing fuselage depth will decrease the wing span (Cook, 2017). Together with systems thinking, the plane activity generated disruptive thinking, as was evident in students’ predictions of the impact of adding load to their plane and their actual findings.

4.5.8  Load Impact: Predictions and Outcomes Students tended to predict that the addition of load to their planes would result in smaller distances covered, and in some cases, predicted that the load would cause the plane to descend rapidly. For example, one student explained: I think that if load is added it would go not as far as it did without load because it would be heavier and would probably fall as soon as you throw it.

One group of students drew on their knowledge of cargo planes in predicting that a shorter distance would be covered: The distance should be shortened because the weight would weigh down the plane making their average miles covered shorten, so that the plane would take longer and require more fuel to reach a point than a plane with lighter cargo. A reason that the flights with larger cargo are shorter [is]because fuel cost is huge.

On the other hand, several student groups took into account other possible factors in their load predictions, again suggesting systems thinking. For example, one group considered the launching of the plane as well as the force of gravity: I predict that it would all depend on the angle at which it is thrown. If it was thrown straight it would keep gliding because if it were spread evenly it would all be even enough for it to keep flying. If it were thrown upward or downward, the load would weigh it down because it wouldn’t have the capacity to fly so high with a load, and gravity would pull it down anyway if it was thrown downward.

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Another group posed a scenario involving load movement: If the paper clips fall down to the tip of the plane it will be vertical not horizontal. If the paper clips fall and make it vertical the wind will either go with it or against.

A consideration of load size and position was also apparent, as one group reflected on the outcomes of their flights without load, for example: I think that if we add load on the front and twice as much at the back the plain (plane) will be more steady. Because when I flew my plane it went straight down nose first. The nose will stay up if we add load.

Other variables incorporated within the students’ predictions included the impact of load on both time and distance: If a load was added to the paper aeroplane it would most likely make the journey much longer if the weight was added. But travel a shorter distance.

Student groups faced disruption in their thinking when the outcomes of their load testing contradicted their predictions. Interesting explanations for the outcomes were offered, with some groups referring to the load increasing the plane’s stability. As one student explained: “I predict the distance will be shorter if load was added to my plane. It would go shorter (distance) because it will drag the plane down.” On testing, however, she explained: “The load added helped the plane go a lot further because the load helped it balance it out a lot more so the weight was more even.” Other students offered similar explanations, with a focus on the load “evening out” the plane, for example: “With the paperclips um, I don’t know about this but maybe like it evened out the weight from the front and … so that when it was in the air it could glide more easily through the air.” Likewise, other students expressed opinions such as, “I think having load on your plane made it heavier but also evened out the weight so you got it further.” Further consideration of load placement was evident in responses such as, “I think it glided because the paperclips were in the middle and not like on one side; they were in the middle so it was like evening out everything”; and “I believe that the load made our flight better because it slotted into places that’s needed more weight.”

4.6  Concluding Points In this chapter., I have argued for the importance of engaging students in integrated STEM experiences from the early grades, where the foundations for solving complex, multidimensional problems are formed. As highlighted in the report on STEM Education from the National Science & Technological Council (2018), we need to “engage students where disciplines converge” (p.15), providing opportunities for students to identify and solve real-world problems using knowledge and processes from across disciplines. Adopting an integrated STEM approach to problems and investigations, where students apply both disciplinary knowledge and twenty-first

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century thinking skills, can provide important foundations for dealing effectively with an ever-changing world. The powerful role of design in connecting the STEM disciplines has been illustrated with just one of many classroom examples. Design can facilitate the development of new knowledge and new ways of thinking, including students’ understanding and appreciation of the connections among the STEM disciplines. Systems thinking, an important twenty-first century skill, can be fostered, as students recognise these disciplinary links and understand how interactions among problem components can have unanticipated consequences in problem solution. Systems thinking is underrepresented in our education programs (Salado et al., 2018), but is essential to dealing with world problems that impact us all. We see so many instances in society today, where particular courses of action are advocated or mandated, while the impact on other systems is perilously ignored. Systems thinking should be introduced early through challenging problems that involve interactions among parts impacting on the whole. Yet as Salado et al. (2018) indicate, we know little about the developmental and cognitive components of systems thinking. Clearly, further research is required on how we can foster this and other twenty-first century thinking skills, along with design processes, across the school grades. Such an endeavour is challenging, especially in the secondary years, where existing school cultures and curriculum programs can present hurdles in STEM integration (Rennie et al., 2012a). Acknowledgements  This study was supported by funding from the Australian Research Council (ARC; DP150100120). Views expressed in this paper are those of the author and not the ARC. Participation of the students and teachers is gratefully acknowledged.

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Chapter 5

A Review of Conceptions of Secondary Mathematics in Integrated STEM Education: Returning Voice to the Silent M Erin E. Baldinger, Susan Staats, Lesa M. Covington Clarkson, Elena Contreras Gullickson, Fawnda Norman, and Bismark Akoto

Contents 5.1  Motivating Literature 5.1.1  STEM Integration Models 5.1.2  Mathematics Learning in Relation to Science 5.1.3  Differing Epistemologies 5.2  Methods 5.2.1  Journal Selection 5.2.2  Stage 1: Focus of the Article 5.2.3  Stage 2: Identifying References to Mathematically Rich Proficiencies and Practices 5.2.4  Stage 3: Article Focus, Findings, and Approaches to Integration 5.2.5  Stage 4: Identifying Themes 5.2.6  Limitations of Method 5.3  Findings 5.3.1  Participants and Research Settings 5.3.2  STEM Integration Approach 5.3.3  Mathematics Content 5.3.4  Mathematics Practices and Learning Approach 5.4  Thematic Discussion 5.4.1  Mathematical Communication 5.4.2  Task Authenticity 5.4.3  Social Awareness in STEM Integration Research 5.4.4  Informal Learning Spaces 5.5  Conclusion References

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E. E. Baldinger (*) · S. Staats · L. M. Covington Clarkson · E. C. Gullickson F. Norman · B. Akoto University of Minnesota, Minneapolis, MN, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_5

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The professional practices of science, technology, engineering, and mathematics (STEM) are so frequently interrelated that their educational integration might seem at first to be a straightforward endeavor. Current STEM education research, however, suggests that mathematics may actually be the least deeply integrated of the four disciplines (English, 2016; Fitzallen, 2015). Integration of mathematics with science, engineering, and technology poses challenges in every dimension of educational research: teaching strategies, curricular models, and in models or assessments of student learning (e.g., Becker & Park, 2011; Walker, 2017; Zhang, Orrill, & Campbell, 2015). Despite at least a century of educational interest in connections between mathematics and science (Berlin & Lee, 2005), the role of mathematics in integrated STEM teaching and learning remains unclear, understudied, and misunderstood. An enduring issue is the notion that mathematics is simply a tool for solving a science or engineering problem (Fitzallen, 2015; Frykholm & Glasson, 2005; Walker, 2017). Mathematics can be positioned as an unproblematic, supporting activity when students take measurements, when they graph or otherwise represent data, or when they perform arithmetic or algebraic procedures to analyze data. Although these uses of mathematics arise authentically through the needs of many STEM contexts and are intelligible activities to students, “(t)his perception of ‘mathematics as tools’ may fall short of how some in the mathematics education community define mathematics and promote its study in the K–12 experience” (Frykholm & Glasson, 2005, p. 139). Mathematics becomes a tool when it is used to support science, technology, or engineering learning goals without associated conceptual mathematics learning goals. When students use mathematics in STEM contexts, they will likely uncover problematic or underdeveloped conceptions in their mathematical knowledge and generate productive new questions about mathematical properties (Pirie & Kieren, 1994). However, science or engineering teachers may not have the preparation to guide productive mathematical discussions (e.g., Stein, Engle, Smith, & Hughes, 2008) or to support the development of mathematical proficiencies beyond procedural fluency (e.g., National Research Council [NRC], 2001). As Shaughnessy (2013) warns, “the M will become silent if not given significant attention” (p. 324) when implementing integrative STEM education programs. This chapter provides a literature review of current approaches to integrated STEM education research that highlights the place of mathematics. This review identified articles focused on mathematically rich approaches in secondary-level STEM teaching and learning published from 2013 to 2018 in international science, technology, engineering, and/or mathematics-focused journals. The study tracked the mathematical topics, proficiencies, and practices present in each article. The discussion focuses on cross-cutting themes in mathematically rich integrated STEM studies, including communication, task authenticity, the centrality of inquiry, and the importance of informal learning spaces. The chapter closes with priorities for further international research on mathematically-accountable STEM integration.

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5.1  Motivating Literature 5.1.1  STEM Integration Models Many existing models for conceptualizing STEM integration treat the four disciplines, in Venn diagram fashion, as bounded units that can be nested, overlapped, or sequenced (Bybee, 2013), echoing positions articulated in scholarship on curricular integration (Fogarty, 1991; Kysilka, 1998). While useful, these modular approaches to integration may contribute to the uneasy position of mathematics in secondary-­ level STEM teaching and learning by deflecting attention from mathematics’ distinctive epistemological stances and ways of knowing. Commonplace models for secondary-level STEM integration are separated, sequenced, and science-focused approaches. Many students, for example, learn STEM disciplines separately, in “silos” (Bybee, 2013) or “fragmented” curricula (Fogarty, 1991). Intentionally sequencing topics within separate classes is a longstanding integration model (Bybee, 2013; Kysilka, 1998). For example, a mathematics class covers the creation and interpretation of bar graphs before being used in science. Another common approach is to use a science classroom as the setting for integrating topics from other STEM disciplines (Becker & Park, 2011; Berlin, 1989; Berlin & Lee, 2005; Hurley, 2001). A concern with this nested approach to STEM integration is that the disciplinary linkage often serves the primary discipline (science) more strongly than others (Honey, Pearson, & Schweingruber, 2014). Efforts to incorporate engineering and technology education in schools have introduced new ways of framing STEM integration. Engineering or technology-­ focused activities might become the mechanism for linking science or mathematics learning (Bybee, 2013). Engineering education, for example, often involves a systematic and iterative cycle of creating objects or procedures, evaluating them, and improving them (Mendoza Díaz & Cox, 2012; Roehrig, Moore, Wang, & Park, 2012). These design challenges are commonly referred to as “hands-on” learning activities, meaning that central experiences include students’ manipulation of materials in building objects or creating empirical tests of objects (Mendoza Díaz & Cox, 2012; Stohlmann, Moore, & Roehrig, 2012). The engineering design challenge approach, with its experiential, materials-­ based focus, can be highly creative and engaging, but it may predispose students to use mathematics in a manner that could be restricted to measurement and computational skills: The analytical element of the engineering design process allows students to use mathematics and science inquiry to create and conduct experiments that will inform the learner about the function and performance of potential design solutions before a final prototype is constructed. (Kelley & Knowles, 2016, p. 5, emphasis added)

In this view, mathematics is not positioned as a site of learning itself, but rather a scientific tool in service of experimental moments in the design process. Moreover, engineering or technology-focused curricular materials may inadvertently equate mathematics with measurement and routine, procedural work.

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At a broad level, these integration models share an inherent modularity that is both a strength and a weakness. Modularity provides a broad-level descriptive vocabulary for different integration strategies, but it dismisses the focus needed to leverage disciplinary perspectives into robust and reliable guidance for teaching and learning.

5.1.2  Mathematics Learning in Relation to Science Two influential reviews report on learning outcomes in the integration model of linking science and mathematics (Becker & Park, 2011; Hurley, 2001). In integrated settings, effect sizes for mathematics learning are usually lower than for science (Becker & Park, 2011; Hurley, 2001). However, when mathematics and science topics are taught sequentially, higher effect sizes for mathematics compared to science learning have been observed (Hurley, 2001). While this is encouraging, Hurley cautioned that this effect could be due less to integration and more to careful planning and teaching of mathematics. Becker and Park (2011) found stronger learning outcomes in primary and middle-school STEM integration activities than for secondary or postsecondary ones, though they advocate for STEM integration efforts throughout all grade levels. Scholarship on secondary-level STEM integration has developed recently compared with research at the primary and middle grades (Berlin & Lee, 2005). Together, these studies suggest that scholarship on integrated STEM teaching and learning has yet to identify effective integration models at the secondary level.

5.1.3  Differing Epistemologies Positioning mathematics in integrated STEM teaching and learning research is complicated by the fundamental epistemological stances across the four STEM disciplines. Mathematics, engineering, and the sciences possess differing perspectives about the objects of their analyses, their processes of conjectural validation, and the potential results of conjectural validation. Mathematics investigates abstract representations, whereas science investigates worldly, tangible phenomenon (Wasserman & Rossi, 2015). Most mathematical conjectures, including those relevant to integrated STEM experiences, can be proven to be true or false, whereas scientific hypotheses can only be falsified (Popper, 1963). Many scientific disciplines rely on inductive, empirical, and experimental investigations to support or refute hypotheses, whereas mathematical proof relies on deductive reasoning. The engineering design process is concerned most strongly with identifying solutions that work well within constraints, not fundamentally with sorting conjectures according to their truth or falsity.

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Developing mathematical proficiency entails developing not only procedural fluency but also conceptual understanding, strategic competence, adaptive reasoning, and productive disposition (NRC, 2001). Students must engage in mathematical practices, such as generalization, justification, and representation (Ball, 2003). In integrated STEM contexts, when mathematics is positioned solely as a tool for learning science or engineering concepts, playing merely a supporting role, then procedural fluency might stand out as a more prominent commitment than conceptual understanding. However, if mathematics learning outcomes are identified as central alongside learning outcomes in other STEM disciplines, then mathematical practices of proof and justification, creating and analyzing representations, and generalization may be visible in integrated STEM curricula. Imagining effective integrated STEM research at the secondary level is complicated by several factors. Scholarship in this area is relatively recent (Berlin & Lee, 2005) but has not demonstrated robust outcomes for mathematics (Becker & Park, 2011; Hurley, 2001). The relative autonomy of secondary teachers compared to primary teachers means that integration requires extensive coordination. Existing models of STEM integration pay little attention to epistemological differences among the disciplines. However, these limitations speak not of impossibilities but of questions that are yet to be answered. There is a need for models of secondary-level STEM integration that allow mathematics to fully voice its disciplinary power. As a preliminary step along this path, this literature review addresses the following research question: What conceptions of teaching and learning mathematics are evident in the literature on integrated STEM education at the secondary level?

5.2  Methods This study used multiple stages of deductive, structural coding to identify research accounts of mathematically rich, secondary-level STEM integration (Saldaña, 2010). Literature reviews often rely on search syntax on indexing websites, but because this approach could overlook articles that use disciplinary-based keywords instead of STEM, STEAM, integration, or similar phrases (c.f., Becker & Park, 2011), this study involved direct reviews of every article in a selection of journals from the years 2013–2018. Four stages of analysis reduced 4072 articles to 32 articles that address teaching and learning secondary mathematics integrated with other STEM disciplines.

5.2.1  Journal Selection This study reviewed articles in 19 peer-reviewed journals with international readership, which include research on STEM education in one or more of the STEM disciplines (see Table  5.1). Given the focus on mathematics, multiple prestigious

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Table 5.1  Journals included in literature review, 2013–2018, with number of articles reviewed and included Journal American Educational Research Journal Canadian Journal of Science, Mathematics and Technology Education Educational Studies in Mathematics Educational Technology Research and Development International Journal of Engineering Education International Journal of Mathematical Education in Science and Technology International Journal of Science and Mathematics Education International Journal of Science Education International Journal of STEM Education Journal for Research in Mathematics Education Journal of Engineering Education Journal of Mathematics Teacher Education Journal of Pre-College Engineering Education Research Journal of Research in Science Teaching Journal of STEM Education Journal of STEM Teacher Education Journal of Technology Education Mathematical Thinking and Learning School Science and Mathematics

Reviewed (n = 4072) 278 162

Included (n = 32) 0 2

411 290 2 307

2 0 0 2

498

3

730 108 171 149 168 54 199 159 24 68 86 208

1 0 1 2 2 3 0 3 2 0 0 9

mathematics education journals were included in the review. Due to the breadth of review, in most cases, one researcher read each article. Throughout, researchers carefully documented dilemmas or uncertainties about inclusion or exclusion criteria or coding for particular articles. The full research team met multiple times to discuss and resolve each uncertainty and to refine coding procedures.

5.2.2  Stage 1: Focus of the Article In this initial stage, the Abstract and Methods section of each of the 4072 articles were reviewed to identify articles that involved mathematics at the secondary level (learners aged 12–18) and at least one other STEM discipline. At this stage, it was not required that the disciplines be integrated. Articles were excluded if they focused on participants’ beliefs related to STEM or perceptions around STEM careers rather than STEM teaching or learning. Coding noted the participants (e.g., secondary students, secondary teachers, and secondary teacher educators) and study setting

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(e.g., secondary classrooms, secondary teacher education, or professional development). Stage 1 coding resulted in 91 articles for further analysis.

5.2.3  S  tage 2: Identifying References to Mathematically Rich Proficiencies and Practices The second stage sought to identify articles that might move beyond the “mathematics as tool” approach by examining the reference section of each article for sources on mathematical proficiencies and practices. Examples of references include mathematics teaching standards, such as the US Common Core State Standards for Mathematics (National Governors Association for Best Practices & Council of Chief State School Officers [NGACBP & CCSSO], 2010); mathematics teaching practices (e.g., Ball & Forzani, 2009); mathematical modeling (e.g., Blum & Niss, 1991); problem-solving (e.g., English & Gainsburg, 2016; Törner, Schoenfeld, & Reiss, 2007); ethnomathematics or culturally relevant pedagogy (e.g., D’Ambrosio, 2001; González, Andrade, Civil, & Moll, 2001); or references with titles concerning conceptual approaches to teaching or learning mathematics (e.g., Artigue, 2002; Pardhan & Mohammad, 2005). References to general or non-mathematical inquiry-­ based learning only were not sufficient for continued inclusion in the study. Despite the wide review and fairly expansive inclusion criteria, Stage 2 returned only 62 articles, from 15 of 19 journals surveyed, which mention secondary STEM education with some grounding in mathematical proficiencies and practices.

5.2.4  S  tage 3: Article Focus, Findings, and Approaches to Integration The first two stages of coding identified publications that potentially would offer mathematically rich accounts of integrated STEM teaching and learning. In Stage 3, each article was read carefully by one researcher to identify studies that actually realized these goals. During this close reading, researchers attended to whether an integrated approach was apparent in the description of study activities. Studies were excluded if the STEM disciplines were treated as separate, “fragmented,” or “siloed” (Bybee, 2013; Fogarty, 1991). The mode of integration of the remaining articles was coded as either science and mathematics connected by technology and/or engineering (e.g., English, Hudson, & Dawes, 2013; Lesseig, Nelson, Slavit, & Seidel, 2016), treating the disciplines in interrelated ways (e.g., Delgado, 2013; Gilliam, Bouris, Hill, & Jagoda, 2016), or technology used to support mathematical learning (e.g., Cayton, Hollebrands, Okumuş, & Boehm, 2017; Jacinto & Carreira, 2017). Researchers noted whether mathematics was treated as the primary or secondary discipline and whether mathematics was blended with other disciplines in the study.

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Mathematics was considered primary when the setting was primarily a mathematics classroom, learning goals were primarily mathematical, the research questions were focused primarily on mathematics, or the study findings were primarily focused on ideas related to mathematics teaching and learning (e.g., Gómez-Chacón & Kuzniak, 2015). Mathematics was considered secondary when the setting was primarily outside of mathematics, learning goals were primarily in other disciplines, the research questions focused primarily on other disciplines, or the study findings were primarily focused on ideas related to teaching and learning in other STEM disciplines (e.g., Wilson-Lopez, Mejia, Hasbún, & Kasun, 2016). Articles were coded as blended if they brought a perspective of systematic attention to both mathematics and another discipline, particularly in the articulation of the research question, the study location, and the study activities (e.g., Nickels & Cullen, 2017). Articles coded as blended could receive a second code, because these studies could also treat mathematics as primary (e.g., Psycharis & Kalogeria, 2018) or secondary (e.g., P. J. Weinberg, 2017). For more detail, see Sect. 5.3. As researchers reviewed each study’s research questions, findings, and approaches to STEM integration, they retained only those articles that included explicit mentions of mathematical practices or direct evidence of engagement with mathematical content. Researchers documented attention to mathematical practices, such as generalization, proof or justification, attending to mathematical representations, and communication (NGACBP & CCSSO, 2010), and attention to the development of procedural fluency or conceptual understanding (NRC, 2001) for particular mathematical content. As an example, Jackson and Mohr-Schroeder (2018) describe a study focused on teacher learning in a robotics summer course. The study documented teachers’ STEM learning and took the integration perspective that mathematics and science were connected through technology and engineering. However, the limited description of mathematics in the study did not allow researchers to determine if there was a focus on conceptual understanding, procedural fluency, or mathematical practices, causing it to be excluded. Researchers also coded for participants, study setting, and the disciplinary backgrounds of teachers in each article. Open-ended notes and quotations captured the authors’ descriptions of their research, especially relating to the focus of the study, key study findings, and the mathematical content and mathematical practices addressed in each study. This process of determining which articles had adequately described findings to make inferences about the place of mathematics within integrated STEM education resulted in 32 articles from 12 journals (denoted in reference list with asterisk).

5.2.5  Stage 4: Identifying Themes In the final stage of analysis, researchers identified themes and patterns across all of the codes and notes applied to the final set of 32 articles. This process included regular discussion about the codes and the articles themselves, seeking confirming and

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disconfirming evidence as the research team generated hypotheses about potential patterns evident in the data.

5.2.6  Limitations of Method This comprehensive examination of 4072 publications from 19 journals, during 2013–2018, though extensive, has some limitations. Other journals could have been included. The review was restricted to English language publications. Only one researcher coded each article, though the full group participated in frequent discussion to ensure consistent applications of codes. Despite these limitations, these results highlight important considerations related to the place of mathematics within the research literature on integrated STEM education at the secondary level.

5.3  Findings This review identified recent articles that intentionally incorporate mathematically rich approaches to secondary-level STEM integration. This section provides an overview of the research contexts, discussion of modes of STEM integration, an exploration of the range of mathematics content, and teaching and learning approaches expressed in the articles.

5.3.1  Participants and Research Settings A majority of the 32 articles included secondary students as study participants (24 articles, see Table 5.2). Teachers were included as participants in 13 of the articles. Their backgrounds include mathematics (3 articles), science (2 articles), or multiple STEM disciplines (8 articles). In some cases, the articles focused on the teacher in relation to students (e.g., Burghardt, Lauckhardt, Kennedy, Hecht, & McHugh, 2015; Lambert, Cioc, Cioc, & Sandt, 2018; Nathan et al., 2013), whereas in other cases, the teachers were participating in teacher education or professional development contexts (e.g., Judson, 2013; Popovic & Lederman, 2015; A. E. Weinberg & Sample McMeeking, 2017; Wilkerson, Bautista, Tobin, Brizuela, & Cao, 2018). Two articles included teacher educators or instructional coaches as participants, and three articles included participants such as school administrators or adults from the community. Many articles included participants from more than one of these categories (e.g., Burghardt et al., 2015; Cox, Reynolds, Schunn, & Schuchardt, 2016; Lesseig et al., 2016). Finally, four articles did not have study participants (e.g., Bennett & Ruchti, 2014; Stohlmann, 2018).

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Table 5.2  Participants and research settings Article Bakker, Groenveld, Wijers, Akkerman, and Gravemeijer (2014) Bennett and Ruchti (2014) Bowen and Peterson (2018) Burghardt et al. (2015) Cayton et al. (2017) Cox et al. (2016) de Toledo e Toledo, Knijnik, and Valero (2018)

Participantsa S 78

Study setting Science classrooms

NP S 53 S 1,667, T 22 T3 S, T 5 S9

Delgado (2013) Geiger, Goos, and Dole (2015)

S 137 S, T

Conceptual article Math classrooms Science classrooms Math classrooms Science classrooms Math and science classrooms Classroom (unspecified) Physical education classroom Technology classroom Web-based competition Science classrooms Clinical setting Technology classroom Teacher education Teacher education

Gilliam et al. (2016) Jacinto and Carreira (2017) Jackson, Wilhelm, Lamar, and Cole (2015) Judson (2013) Kwon (2017) Lambert et al. (2018) Lesseig et al. (2016)

S 144 S1 S 455 T 54 S 47 S 413, T 41 S 45, T 34, TE 2, OP LópezLeiva, Roberts-Harris, and von Toll (2016) S 16, T 1 Meli, Zacharos, and Koliopoulos (2016) Morrison, Roth McDuffie, and French (2015)

S2 S, T, OP

Nathan et al. (2013)

S 37, T 2

Ngu, Yeung, and Phan (2015) Nickels and Cullen (2017) Popovic and Lederman (2015) Quinnell, Thompson, and LeBard (2013) Stohlmann (2018) Valtorta and Berland (2015) Weinberg and Sample McMeeking (2017) Weinberg (2017) Whitacre and Saul (2016) Wilkerson et al. (2018) Wilson-Lopez et al. (2016)

S 26 S1 T7 NP NP S 31 T 62 S 102, OP 10 S 61 T9 S 25

Zhang et al. (2015)

S 516

Math and science classrooms Science classrooms STEM school classrooms Digital electronics classroom Science classrooms Clinical setting Teacher education Conceptual article Literature review Engineering classroom Clinical setting Clinical setting Science classrooms Clinical setting Classroom and community Clinical setting

NP no people, OP other people, S students, TE teacher educators, T teachers; when possible, the number of participants of each type is given

a

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Not surprisingly, 19 articles took place in classroom settings. Notably, seven occurred only in science classrooms, and two took place in both science and mathematics classrooms. Just two studies were set only in mathematics classrooms (Bowen & Peterson, 2018; Cayton et al., 2017). The remaining studies took place primarily in engineering or technology classes (e.g., Gilliam et  al., 2016; Kwon, 2017; Valtorta & Berland, 2015), and one was set in a physical education class (Geiger et al., 2015). Six of the studies took place in more clinical settings, such as interviews or surveys. Three of these studies included students as participants (Nickels & Cullen, 2017; P. J. Weinberg, 2017; Zhang et al., 2015); the other three included teachers (Judson, 2013; A.  E. Weinberg & Sample McMeeking, 2017; Wilkerson et  al., 2018). Additionally, three studies took place in teacher education settings, such as university coursework or professional development (Lambert et al., 2018; Lesseig et al., 2016; Popovic & Lederman, 2015). These results highlight that although research in integrated STEM education includes mathematics teachers as participants and is occasionally situated in mathematics classrooms, it is largely conducted outside of focused mathematical spaces. Integrated STEM education research is often conducted in explicitly science-­ focused spaces and is almost equally as often conducted in primarily technology or engineering-focused spaces. This suggests that further research might be needed on the nature of integrated STEM education in the context of secondary mathematics classrooms.

5.3.2  STEM Integration Approach Table 5.3 summarizes the varied approaches to integrating mathematics with other disciplines shown in these articles. These codes, developed through considering Bybee’s (2013) descriptions, included whether there was coordination across disciplines, or whether mathematics and science were linked through a technology or engineering experience. In total, 19 articles took a coordination across disciplines approach to STEM integration (e.g., Quinnell et al., 2013). It was not necessarily the case that each of these articles incorporated all four STEM disciplines; in fact, many coordinated only mathematics and science, and most included science as one of the disciplines. In contrast, only four articles took the approach of connecting mathematics and science through technology or engineering. Nine articles had integration approaches less easily captured by Bybee’s (2013) framework. Four of these articles integrated mathematics and technology only, where technology was used as a support for mathematical learning (e.g., Cayton et  al., 2017). Two others integrated mathematics and engineering (Nathan et  al., 2013; Wilson-Lopez et  al., 2016). One described the use of mathematics in a

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Table 5.3  Approaches to STEM integration Article Bakker et al. (2014) Bennett and Ruchti (2014) Bowen and Peterson (2018) Burghardt et al. (2015) Cayton et al. (2017) Cox et al. (2016) de Toledo e Toledo et al. (2018) Delgado (2013) Geiger et al. (2015) Gilliam et al. (2016) Jacinto and Carreira (2017) Jackson et al. (2015) Judson (2013) Kwon (2017) Lambert et al. (2018) Lesseig et al. (2016) LópezLeiva et al. (2016) Meli et al. (2016) Morrison et al. (2015) Nathan et al. (2013) Ngu et al. (2015) Nickels and Cullen (2017) Popovic and Lederman (2015) Quinnell et al. (2013) Stohlmann (2018) Valtorta and Berland (2015) Weinberg and Sample McMeeking (2017) Weinberg (2017) Whitacre and Saul (2016) Wilkerson et al. (2018) Wilson-Lopez et al. (2016) Zhang et al. (2015)

Integration approach Science math connected Coordination Coordination Coordination Technology supports math Coordination Coordination Coordination Coordination Coordination Technology supports math Coordination Math in science Technology supports math Science math connected Science math connected Coordination Math in a physics class Coordination Engineering and math Coordination Technology supports math Coordination Coordination Coordination Science math connected Coordination

Mathematics focus Secondary Primary, Blended Primary, Blended Blended Primary Secondary Primary, Secondary Blended Primary, Blended Secondary Primary Blended Secondary Secondary Secondary, Blended Blended Blended Secondary, Blended Blended Blended Secondary Blended Primary, Blended Secondary Primary Primary, Blended Blended

Coordination Coordination Modeling Engineering and math Coordination

Secondary, Blended Secondary, Blended Primary, Blended Secondary Blended

physics classroom (Meli et al., 2016), another described the place of mathematics in science more generally (Judson, 2013), and the remaining article considered scientific and mathematical modeling (Wilkerson et  al., 2018). This multitude of approaches to STEM integration signals the lack of consensus around a definition of integration (Berlin & White, 1994; Bybee, 2013; Davison, Miller, & Metheny, 1995; Honey et al., 2014; Hurley, 2001; Pang & Good, 2000). It also illustrates how many different ways mathematics can be approached in the context of integrated STEM.

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Table 5.3 also summarizes the relative place of mathematics in each integration effort. As might be expected, given the number of articles that took an integration approach of coordinating across disciplines, ten articles situated mathematics as blended across disciplines only. For example, Nickels and Cullen (2017) blended mathematics and technology learning through a robotics intervention that supported student mathematical learning and confidence. Zhang et al. (2015) documented students’ conceptual reasoning strategies in both science and mathematics. In this article, the research intentionally considered mathematics and science reasoning together, though students tended to use different types of reasoning on mathematics and science items. Six additional articles positioned mathematics as primary while also blending across disciplines. For instance, Bennett and Ruchti (2014) foregrounded mathematical practices in their cross-disciplinary interpretation of the Standards for Mathematical Practice (NGACBP & CCSSO, 2010). Four articles had mathematics as a secondary focus while also blending it across disciplines. A study of physics learning, for example, analyzed students’ use of polynomial equations and trigonometry, but the primary focus is on physics learning outcomes (Meli et al., 2016). Similarly, a study in a teacher education setting portrayed teachers learning to coordinate mathematical concepts with science topics, such as force, motion, and kinetic energy, but with a primary focus on science (Lambert et al., 2018). In all, 20 articles blended mathematics with other disciplines in some way. Of the remaining 12 articles, 8 positioned mathematics only as a secondary focus. For example, Judson (2013) explored the development of a classroom observation tool designed to look for evidence of “the integration of mathematics into science … . The instrument likewise would not be designed for the integration of science into mathematics” (p.  58). This intentionally positioned mathematics as a secondary focus of that study. Three articles positioned mathematics as the primary discipline. For example, in Stohlmann’s (2018) commentary, he explicitly distinguishes STEM from “steM,” STEM integration research with an intentional focus on mathematics. One article (de Toledo e Toledo et al., 2018) treated mathematics as primary and secondary. Participants were interviewed about their experiences as learners in mathematics courses, situating mathematics as primary, and their experiences in agricultural education courses, situating mathematics as secondary. Table 5.3 shows that mathematics is a secondary focus more often than a primary focus, drawing attention to the challenge of integrating mathematics into STEM environments.

5.3.3  Mathematics Content The included articles attended to a wide range of mathematical content (see Table 5.4). There were 15 articles addressing topics in number and operations, 14 addressing geometry, 17 addressing algebra and functions, 12 addressing data and statistics, and 6 addressing other mathematics content (e.g., logic, Boolean algebra). In terms of specific algebraic content explored, equations and expressions, linear

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Table 5.4  Mathematics content Article Bakker et al. (2014) Bennett and Ruchti (2014) Bowen and Peterson (2018) Burghardt et al. (2015)

Numbera RP

Cayton et al. (2017)

RP

Cox et al. (2016) de Toledo e Toledo et al. (2018) Delgado (2013) Geiger et al. (2015) Gilliam et al. (2016)

RP NC

Geometryb

Algebrac GTE

MT

SY

P&Sd

Othere

CP, PY DA

LG

LR, NS, SY, GTE, EE

UC RP

Jacinto and Carreira (2017) Jackson et al. (2015) Judson (2013) Kwon (2017) Lambert et al. (2018)

RP

Lesseig et al. (2016) LópezLeiva et al. (2016) Meli et al. (2016) Morrison et al. (2015)

RP

TF, AP, MT, SC, TG, SM, TR, QR GTE, EE MT, SC GTE, EE

TF, AP

DC, DR FA

EE, LR, QU

MT, SC, GV RP RP

GV, TF, MT, AN GC

VT LN, GTE, ID, DA, SV EE GTE, EE, DT

TR TR, TG

LR LR, GTE, DT DA, DC, DR, LB

Nathan et al. (2013) Ngu et al. (2015) Nickels and Cullen (2017) Popovic and Lederman (2015) Quinnell et al. (2013) Stohlmann (2018)

Valtorta and Berland (2015) Weinberg and Sample McMeeking (2017)

LG, DG

BA, LG CC

EE LR, GTE

RP, FD, NS NC RP, CN

MT, SC, AN, AP, VM, SM, CC

LR, IN, EE, DT

DC, DR, DA

AP, MT, VM

LR, EE, QU

LB, MN, DA, DC, PY

UC, NC

MT

EE

UC

EE

BA

DA, DC, DR

MM (continued)

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Table 5.4 (continued) Article Weinberg (2017) Whitacre and Saul (2016) Wilkerson et al. (2018) Wilson-Lopez et al. (2016) Zhang et al. (2015)

Numbera

Geometryb TR, CC

Algebrac

P&Sd

Othere

DA

DT

DA, DC, DR DA, BG

CN complex numbers, FD fractions/decimals/percent, NC number calculations, NS number systems, RP rates and proportions, UC unit conversions b AN angles, AP area and perimeter, CC circle relationships, GC graphing on a coordinate plane, GV geometric visualization, MT measurement, PT Pythagorean theorem, QR quadrilaterals, SC scaling, SM similarity, TF transformations, TG triangles, TR trigonometry, VM volume c EE equations and expressions, DT distance/rate/time, GTE graphing/tables/equations, ID independent/dependent variables, IN inequalities, LR linear relationships, NL nonlinear relationships, QU quadratics, SY slope/y-intercept d BG bar graph, CP combinations and permutations, DA data analysis, DC data collection, DR data representation, FA frequency analysis, LB line of best fit, MN mean, PY probability, SV statistical variability e BA Boolean algebra, DG decoding ciphers, FR fractals, LG logical reasoning, MM mathematical modeling, VT vectors a

relationships, and graphs, tables, and equations were common topics. LópezLeiva et  al. (2016), for example, used motion detectors to enable the students to learn about motion relationships by creating tables and graphs to help find patterns and formalize formulas for speed and rate. With respect to geometry, Weinberg (2017) documented rich mathematical reasoning about circles in relation to machines. Common geometry topics included measurement, transformations, and scaling. With regard to number and operations or probability and statistics, one might anticipate these content areas being associated with treating mathematics as a tool for learning other disciplines. However, there were multiple instances where articles addressed these content areas in ways that did not treat mathematics as a tool. For example, Bakker et al. (2014) focused on proportional reasoning in an integrated context. In their study, students used computer simulations to explore what happened to different solutions as they added more water. Students then tried to create a solution given dilution parameters and to generalize their thinking. Other topics in number and operations included unit conversions and numerical calculations. Data analysis was a prominent topic within the category of data and statistics. In one

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example of this, Whitacre and Saul (2016) described the scope of inferences students made when presented with graphical representations of data. Other articles focused on topics, such as data collection or data representation (e.g., Geiger et al., 2015; Popovic & Lederman, 2015).

Table 5.5  Mathematics practices and learning approach Article Bakker et al. (2014) Bennett and Ruchti (2014) Bowen and Peterson (2018) Burghardt et al. (2015) Cayton et al. (2017) Cox et al. (2016) de Toledo e Toledo et al. (2018) Delgado (2013) Geiger et al. (2015) Gilliam et al. (2016) Jacinto and Carreira (2017) Jackson et al. (2015) Judson (2013) Kwon (2017) Lambert et al. (2018) Lesseig et al. (2016) LópezLeiva et al. (2016) Meli et al. (2016) Morrison et al. (2015) Nathan et al. (2013) Ngu et al. (2015) Nickels and Cullen (2017) Popovic and Lederman (2015) Quinnell et al. (2013) Stohlmann (2018) Valtorta and Berland (2015) Weinberg and Sample McMeeking (2017) Weinberg (2017) Whitacre and Saul (2016) Wilkerson et al. (2018) Wilson-Lopez et al. (2016) Zhang et al. (2015)

Practices G, R, C G, P, R, C, O G, R, C P, C G, P, R, C R, C G, R, C G, C R, C R, C G, P, R, C O G, R, C, O R, C P, O P, C G, R, C G, R, C P, C, O P, R, O C G, P, C, O O C R, C, O

Learning approach PF, CU, MP MP PF, CU, MP PF, CU, MP PF, CU, MP CU, MP PF, CU, MP PF, CU, MP CU, MP PF, MP CU, MP PF, CU PF, CU, MP PF, CU, MP PF PF, MP PF, CU, MP PF, MP PF, CU, MP MP MP PF, MP PF, CU, MP MP PF, MP PF, CU PF

G, R, C R, C R, C, O

CU, MP CU, MP CU, MP PF CU, MP

P, R, C

C communication, G generalization, P proof/justification, R representation, O other, CU conceptual understanding, MP mathematical practices, PF procedural fluency

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5.3.4  Mathematics Practices and Learning Approach In terms of mathematical practices (see Table 5.5), 25 articles addressed mathematical communication (e.g., Ngu et al., 2015), and 19 addressed representation (e.g., Gilliam et al., 2016). The emphasis on these two related practices shows their prominence within integrated STEM settings. Twelve articles addressed generalization and ten discussed proof/justification. These two practices encapsulate part of the epistemology that distinguishes mathematics from the other STEM disciplines. Finally, ten articles addressed other mathematical practices, such as geometric spatial visualization (Jackson et al., 2015). The review identified articles that explicitly addressed developing conceptual understanding, procedural fluency, or mathematical practices (e.g., Ball, 2003; NGACBP & CCSSO, 2010; see Table  5.5). Encouragingly, 11 of the 32 articles were coded as attending to conceptual understanding, procedural fluency, and mathematical practices, whereas only three articles focused solely on procedural fluency. Additionally, seven articles addressed conceptual understanding and mathematical practices, and four addressed mathematical practices only. In total, this means that 29 articles either did not address procedural fluency at all or did so only alongside either conceptual understanding or mathematical practices. Though procedural fluency is an important component of mathematical proficiency, it is particularly imperative to address it in the context of other strands of proficiency. Of the articles that did address procedural fluency, five addressed mathematical practices and procedural fluency, and two addressed conceptual understanding and procedural fluency. Overall, these results highlight that among these 32 articles, researchers are approaching mathematics learning with attention to multiple strands of proficiency. The breadth of content covered along with the prominence of multidimensional approaches to mathematics teaching and learning suggests that a small portion of recent research intentionally gives voice to the M in STEM. However, given that these are only 32 articles out of 4072, much work remains to be done.

5.4  Thematic Discussion This final section identifies themes that were common in the 32 articles, including frequent attention to communication, task authenticity, inquiry, and learning in informal spaces. A synthetic reflection on the findings points towards recommendations for future research on mathematically rich integrated STEM education at the secondary level.

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5.4.1  Mathematical Communication A prominent theme that emerged from the consideration of these articles, especially those situated in classroom settings, was the importance of mathematical communication, and engagement in mathematical practices more broadly. As Weinberg (2017) points out, authentic communicative engagement with mathematics depends on the intentional selection of mathematical content that problematizes students’ mathematical understanding. Communication and representation were extremely common across the articles, and the articles describing the deductive practices of generalization and proof/justification almost always address communication or representation as well. This supports Bennet and Ruchti’s (2014) suggestion that mathematical practices can be valuable lenses for STEM integration. When students are able to use rich mathematical language, they deepen their understanding and have stronger retention of the mathematical content (Boaler & Staples, 2008; Brodie et  al., 2010; Chazan & Ball, 1999). Thus, an emphasis on mathematical communication can be seen as an important way to develop a mathematically rich approach to STEM integration. However, leveraging mathematical communication requires skillfully orchestrating discussions (e.g., Stein et al., 2008), a complex, challenging teaching practice.

5.4.2  Task Authenticity A second theme that emerged was the importance of promoting mathematical engagement through authentic tasks. Integrative, real-world tasks can create authentic need to resolve mathematical questions beyond merely being an opportunity to practice mathematical routines (Bowen & Peterson, 2018). Examples of task authenticity include slopes and y-intercepts used in building code specifications (Bowen & Peterson, 2018) and engineering practices to resolve community issues (Wilson-Lopez et al., 2016). Even the act of measurement can extend beyond procedures when set in relevant contexts. For example, those who use the metric system conceptualize unit conversions more meaningfully than those raised with the United States’ customary unit system (Delgado, 2013). Tasks that are relevant to students’ lived experiences push them to think critically and nurture the conceptual understanding of mathematical topics (Bakker et al., 2014).

5.4.3  Social Awareness in STEM Integration Research An “inquiry” approach to integrated STEM education may increase student engagement (e.g., Jackson et al., 2015; LópezLeiva et al., 2016) and mathematical content learning (e.g., Burghardt et al., 2015; Kwon, 2017; Morrison et al., 2015; Nickels &

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Cullen, 2017), and ideally these benefits would be evident for all learners regardless of race, ethnicity, gender, and social class. Reports conflict, however, on the value and neutrality of the construct of “inquiry.” On one hand, LópezLeiva et al. (2016) and Jackson et al. (2015) found that their inquiry-based approaches were particularly supportive and engaging for traditionally marginalized groups, including girls and students of color. On the other hand, the inquiry frame can unwittingly marginalize students (Cedillo, 2018). The interactional meaning of questions, less-guided exploration, and the intended authenticity of tasks can be experienced differently by different students. Cedillo (2018) explains that in the United States, adopting inquiry pedagogies as a corrective for schools with low standardized test performance may covertly seek to “correct” or assimilate students of color, and their ways of acting and knowing, towards Whiteness. Among the 32 reviewed articles, Geiger et al.’s assertion that “approaches to the teaching and learning of numeracy must accommodate for social, contextual and critical aspects of the use of mathematics in action” (2015, p. 1131) goes for all areas of STEM education research. Researchers can incorporate social awareness into their research paradigms by attending to the political purposes to which pedagogies contribute and by understanding the interactional processes of exclusion that can occur in all classrooms.

5.4.4  Informal Learning Spaces A final notable theme was that mathematically rich integrated STEM activities often took place in informal or nontraditional spaces, including summer school (Kwon, 2017), a hospital (Nickels & Cullen, 2017), a web-based competition (Jacinto & Carreira, 2017), community spaces (Wilson-Lopez et  al., 2016), and a museum (Popovic & Lederman, 2015). Nontraditional spaces seem to support moving beyond a fragmented, bounded approach to disciplinary learning. Through analyzing Programme for International Student Assessment (PISA) results, Zhang et al. (2015) found that students’ perception of mathematics and science as separate disciplines seemed to inhibit meaningful integration. This perception can be challenged in informal and nontraditional spaces.

5.5  Conclusion In what ways, then, is mathematics silenced within integrated STEM research at the secondary level? While this area of research currently occupies an exceedingly small part of the journal landscape, the articles reviewed here highlight areas of varied and creative research focused on mathematically rich integrated STEM education, along with areas that are barely being addressed. Within this small pool of 32 articles, there is a strong emphasis on classroom-based research that involves

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students as participants, but only two of these cases were set in mathematics classrooms. Although a wide range of mathematical content areas were incorporated, comparatively few studies centered on mathematics as the primary focus. Mathematics teachers and researchers are much better positioned to recognize opportunities to develop mathematical proficiency than are their counterparts in other disciplines. A possible area for new research is to design integrated STEM curricula that can be implemented by secondary mathematics teachers in mathematics classrooms, so that the mathematical affordances can be fully explored. This research should also seek to document mathematically rich approaches to integrated STEM that are inclusive rather than marginalizing. There has been comparatively little secondary-level research using clinical methods to understand teachers’ or students’ reasoning strategies in integrated STEM environments. Few studies have been set in teacher education environments. Future research could investigate these settings more deeply, with consideration of the epistemological differences across the STEM disciplines and how they arise in these specific situations. For example, one avenue for this research might consider how pedagogies of practice in teacher education might support learning to enact specific integrated STEM teaching practices, building on the work in the separate disciplines (e.g., Baldinger, Selling, & Virmani, 2016; Davis et al., 2017). English (2016) and Fitzallen (2015) argue that mathematics receives the least attention in the literature on integrated STEM. One reason for this, they contend, is that the M in STEM is viewed primarily as a tool that supports the other disciplines or may arise only incidentally. The articles reviewed here support that position at the secondary level, in the sense that only 32 articles out of 4072 met the inclusion criteria for this study. On the other hand, these 32 articles offer a vision of mathematically rich integrated STEM at the secondary level, giving voice to the M in STEM in a substantial way. Learning from these articles and building on this work is critical for continuing to recognize the M in STEM.

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Chapter 6

What Is the Role of Statistics in Integrating STEM Education? Jane Watson, Noleine Fitzallen, and Helen Chick

Contents 6.1  Introduction 6.2  Variation: An Essential Part of STEM 6.3  The “Big Ideas” Shared by Statistics and STEM 6.4  The Place of Statistics in the School Curriculum 6.5  STEM Literacy and Statistical Literacy 6.6  The Needs of STEM Careers 6.7  Classroom Experiences to Foster STEM Integration 6.8  Research on Student Outcomes in STEM Including Statistics 6.9  A Research Program on Primary School Statistics and Integrated STEM Activities 6.10  Conclusion References

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6.1  Introduction In most school curricula, Statistics appears as part of the subject of Mathematics (e.g., Australian Curriculum, Assessment and Reporting Authority [ACARA], 2019), which places it firmly on the STEM agenda. This chapter goes further, to argue that because of the potential of statistical practice to assist in making decisions based on data collected across the fields of Science, Technology, and Engineering, Statistics offers a mechanism for integrating the disciplines from the beginning of students’ experiences at school. The argument is built on the fundamental nature of variation across STEM contexts and the role of statistics to harness variation for useful purposes in society. The chapter then develops the notion of ‘big ideas’ across disciplines, considers the content of the school curriculum, and highlights the growing interest in ‘STEM literacy’. This leads to focusing on the needs of the STEM careers that impact on Statistics across STEM education. Finally, J. Watson (*) · H. Chick University of Tasmania, Hobart, TAS, Australia e-mail: [email protected] N. Fitzallen La Trobe University, Melbourne, VIC, Australia © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_6

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some of the initiatives taking place in schools to build the understanding necessary to integrate Statistics across the STEM curriculum are canvassed, including what research tells us about some of the potential outcomes for students.

6.2  Variation: An Essential Part of STEM “Variety’s the very spice of life, that gives it all its flavor!” (Cowper, 1785, lines 606–607). This often-quoted line of poetry could be translated today as “Variation’s the very spice of STEM that gives it all its meaning!” Variation is the property that underpins the implementation of projects of invention, particularly in Science, Technology, and Engineering. ‘Improving’ designs and ‘quantifying’ performance, for example, rely on measurements that may vary with changes in design, changes in performance conditions, and repeated measurement. Quantifying variation and representing the measures using statistical techniques, such as the transnumeration of raw data into graphical representations (Pfannkuch & Wild, 2004), provides the evidence needed to persuade people that changes to conditions, procedures, or apparatus have indeed impacted on performance. Even in Mathematics, the creation of equations to model designs in the other disciplines must be tested against data, which involves fitting and judging the usefulness of the mathematical models (Crites & St. Laurent, 2015). Variation is such a ubiquitous phenomenon that it is often assumed to be fundamental and understood, and yet often remains undefined. Moore (1990, p. 135), for example, does not define “variation,” but, in listing the five core elements of statistical thinking, focuses on variation in four of them: (1) the omnipresence of variation in processes; (3) the design of data production with variation in mind; (4) the quantification of variation, and (5) the explanation of variation. Indeed, dealing with variation and uncertainty could be a goal of all meaningful STEM investigations. Related to the fundamental nature of variation in statistics and STEM fields is ‘context’. Context is the creator of variation and, for the application of statistics, the two are inseparable. As pointed out by Cobb and Moore (1997): The focus on variability naturally gives statistics a particular content that sets it apart from mathematics itself and from other mathematical sciences, but there is more than just content that distinguishes statistical thinking from mathematics. Statistics requires a different kind of thinking, because data are not just numbers, they are numbers with a context. (p. 801, emphasis in original)

Cobb and Moore were not the first to emphasize context. Over 40 years ago, the Indian statistician Rao claimed, Statistics ceases to have meaning if it is not related to any practical problem. There is nothing like a purely statistical problem which statistics purports to solve. The subject in which a decision is made is not statistics. It is botany or ecology or geology and so on. (Rao, 1975, p. 152)

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Rao was writing for secondary schools at a time when exploratory data analysis (Tukey, 1977), which relies on context for interpretation, was beginning to be introduced in schools. Rao’s list of subjects can now, of course, be extended to any of the STEM discipline areas. The cohesion between context and variability is fundamental to understanding data and decision-making (Royal Statistical Society, 2018). To support student development of decision-making, the American Statistical Association developed a conceptual framework for promoting statistical problem solving as an investigative process, which is presented in its Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report (Franklin et al., 2007). The GAISE framework (see Fig. 6.1), often referred to as “the practice of statistics” (e.g., Watson, Fitzallen, Fielding-Wells, & Madden, 2018), reflects “the spirit of genuine statistical practice” (Franklin et al., p. 37). The description of the framework emphasizes variation at every stage of a statistical investigation: 1 . Formulating questions, anticipating variability 2. Designing and implementing a plan to collect data, acknowledging variability 3. Analysing data with appropriate graphical and numerical methods, accounting for variability 4. Interpreting the results of the analysis in relation to the original question, allowing for variability The framework not only provides a structure for working with statistics but also incorporates the essential underpinning concept of statistics: variation.

Fig. 6.1  GAISE model for the practice of statistics at school (Franklin et al., 2007, p. 11)

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Variation is inherent in many man-made and natural systems. For example, in engineering systems, variation in input variables propagates through a system resulting in variation of the system outputs. Hence engineers monitor variation with the ultimate goal of reducing variation to achieve consistent production and to maintain quality (Dodson, Hammett, & Klerx, 2014). In Design Technology, variation takes many forms, which include statistical process variation evidenced by fluctuations in voltage and temperature in electronic integrated circuits. Although some variation can be mitigated in the design process, monitoring performance over time to determine the changes due to degradation of components remains necessary (McConaghy, Breen, Dyck, & Gupta, 2013). Science provides natural contexts, in which the properties of organisms and objects vary continuously (Tibell & Harms, 2017). For example, the properties of water change when it boils, melts, evaporates, freezes, or condenses, and the rate of change varies for each process. The practice of statistics provides a framework that promotes new knowledge about variation across these STEM contexts and supports evidence-based decision making.

6.3  The “Big Ideas” Shared by Statistics and STEM Given the importance of the concept of variation across STEM contexts, it must be proposed as one of the ‘big ideas’ of STEM. That big ideas are important in the integrated STEM classroom is emphasized by Stohlmann, Moore, and Roehrig (2012) as one of their six major “recommendations on how teachers should approach student knowledge: … Organize knowledge around big ideas, concepts, and themes” (p. 30). In their work in the field of STEM education, Chalmers, Carter, Cooper, and Nason (2017) state that “Big ideas refer to key ideas that link numerous discipline understandings into coherent wholes” (p. S27). They go on to suggest that big ideas form a continuum and are of three types: (1) within-discipline big ideas that also have application in other disciplines, (2) cross-curriculum big ideas, and (3) encompassing big ideas. This leads to the questions, what are the big ideas in the discipline of statistics, and how do they fit in Chalmers et al.’s three categories for STEM? As part of the Australian Association of Mathematics Teachers’ Top Drawer Teachers project, Watson, Fitzallen, and Carter (2013) developed an on-line resource for teachers that included the big ideas underpinning the statistics component of mathematics in the Australian Curriculum (ACARA, 2019). The five interrelated big ideas suggested are shown in Fig. 6.2. Variation as the cornerstone is acknowledged throughout, recognizing that statistics is concerned about quantities that vary, which may not be able to be measured consistently, or which may be impacted by other variables. Expectation arises when harnessing variation and summarizing data, for example, with averages or probability estimates; it is concerned with identifying what is typical, likely, or ‘expected’ to occur. Distribution is the lens, usually identified via graphical representations, through which variation and expectation are identified and described; it recognizes that data sets have a ‘shape’, and that the

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Fig. 6.2  The big ideas of statistics

nature of the shape (e.g., normally distributed, skewed) tells us something about the data. Randomness captures the fact that random phenomena are observed in many investigations; furthermore, randomness is the basis for sampling techniques that lead to increased confidence in the informal inferences drawn from the practice of statistics. Informal inference is the evidence-based process that considers variation and expectation in order for sample data to be used to answer a meaningful question about a population, while acknowledging uncertainty (Makar & Rubin, 2009). That question and population may be embedded in any context, including any of the STEM disciplines, but, additionally and importantly, extending to social, civic, environmental, and media information. To see how the big ideas of statistics connect to Chalmers et al.’s big ideas (2017), consider first the encompassing big ideas category (3), which Chalmers et  al. describe as … concepts, principles, theories, strategies or models shared across the STEM disciplines that not only subsume but also enable one to integrate and build upon sets of more localized/specific STEM big ideas. (p. S31)

Their examples include representations, relationships, and change. Certainly variation, distribution, and expectation can be similarly put forward as encompassing big ideas across STEM. Cross-discipline big ideas, category (2) of Chalmers et al., are content or process ideas located in two or more STEM disciplines, with Chalmers et al.’s examples including variables, patterns, models, reasoning and argument (p. S30). Certainly, the process of creating an informal inference through reasoning and argumentation is part of a scientific inquiry (Bybee, 2011). Finally, randomness is a within-discipline big idea (i.e., from Chalmers et  al.’s category (1)) in statistics, which has application in the other disciplines, given the relevant contexts within those disciplines, for example, a chance enquiry in mathematics or a particular sampling experiment in science or technology. These references across the STEM disciplines provoke a need to look more closely at the curriculum in schools to determine the extent to which statistics is acknowledged in the STEM disciplines.

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6.4  The Place of Statistics in the School Curriculum Cobb and Moore (1997) and Trewin (2005) refer to statistics as a ‘mathematical science’. This could be interpreted as suggesting an expanded conception of statistics at the intersection of the S and the M of STEM. This view can be supported by a number of national curricula. In the Australian Curriculum (ACARA, 2019), the tools of statistics—for example, mean, range, bar graph, and box plot—are introduced in the content of the Mathematics curriculum. Additionally, the Mathematics curriculum identifies four proficiencies, including problem solving and reasoning, that, among other suggestions across topics, incorporates “involving planning methods of data collection and representation” (Year 3), “interpreting data displays” (Year 6), “interpreting sets of data obtained through chance experiments” (Year 7), “collecting data from secondary sources to investigate an issue,” and “using statistical knowledge to clarify situations” (Year 9), and “investigating independence of events” and “interpreting and comparing data sets” (Year 10). The Science curriculum, however, identifies a Science Inquiry Skills strand across all years, with an extended description of the complete process of carrying out a scientific investigation: Questioning and predicting; planning and conducting; processing and analysing data and information; evaluating; and communicating. The Inquiry Skills employ the statistical tools and problem-solving found in the Mathematics curriculum. This description exactly parallels the practice of statistics as described, for example, by the GAISE Report (Franklin et al., 2007), where “planning and conducting” includes collecting data. In the United States, the Next Generation Science Standards (National Research Council, 2013) cover not only Science but also Engineering and Technology (p. 1), with emphases throughout on “analyzing and interpreting data” as a Scientific and Engineering Practice (p. 3). Across every grade level of the document and across all topics covered, the word ‘data’ appears. As well as under the specific heading related to data, the “planning and carrying out investigations” heading often includes reference to planning investigations, “based on fair tests, which provide data to support explanations or design solutions” (e.g., p. 5). An example of the continuous need for statistics across the Standards is found in the topic of Forces and Interactions, which ranges from Pushes and Pulls in kindergarten to supporting Newton’s Second Law of Motion in high school. The reference to using data occurs in all 16 subtopics under the four general headings for high school: Physical Sciences, Life Sciences, Earth and Space Sciences, and Engineering Design. Further, in high school, Using Mathematical and Computational Thinking usually include ‘statistical analysis’ appropriate for the grade level. In Australia, the curricula for Design Technology and Digital Technology also contain references to the need for and use of data (ACARA, 2019). For example, in Years 3–4, in Digital Technologies Processes and Production skills, students “Recognise different types of data and explore how the same data can be represented in different ways” and “Collect, access and present different types of data

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using simple software to create information and solve problems.” In Years 5–6, students “Acquire, store, and validate different types of data, and use a range of software to interpret and visualise data to create information.” Further, the Process and Production Skills strand in Design Technologies includes “Evaluating,” which requires developing criteria for success in evaluating the design ideas, processes and solutions, and their sustainability. In many instances, this will require collecting data and employing the practice of statistics. Across the STEM-related portions of the school curriculum, the need for data and their analysis is readily seen, thus providing evidence for the suggestion that statistics presents opportunities to assist understanding in many contexts across the curriculum. This evidence supports Cobb and Moore’s (1997) claim that data are intrinsically entwined with context. Any single STEM context or combination of STEM contexts may hence supply an environment for data to be collected and analysed. There is conclusive evidence of an intersection of statistics with all the other STEM fields as they are encountered in school. This is illustrated in Fig. 6.3, adapted from ACARA’s STEM Connections Report (2016). The addition of statistics to the ACARA diagram of STEM illustrates the connectionist metaphor that statistics is a thread central to all of the STEM disciplines.

Fig. 6.3  Statistics integrating STEM (figure modified with permission from Fig. 6.1 of ACARA, 2016, downloaded from the Australian Curriculum website www.australiancurriculum.edu.au, 27/7/2018, © Australian Curriculum, Assessment and Reporting Authority, 2018)

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6.5  STEM Literacy and Statistical Literacy Evolving from the definition of STEM education (Education Council, 2015) is the closely related notion of STEM literacy. One of the early definitions of STEM literacy highlights the importance of the distinct disciplines and of the potential for drawing them together and foreshadows the need to address both perspectives in student learning. STEM literacy is the ability to identify, apply, and integrate concepts from science, technology, engineering, and mathematics to understand complex problems and to innovate to solve them. To understand and address the challenge of achieving STEM literacy for all students begins with understanding and defining its component parts and the relationships between them. (Balka, 2011, p. 7)

This definition has been accepted in many quarters with very little change (e.g., Department of Education Tasmania, 2017; Zollman, 2012). It involves, however, more than just being aware of the literacies associated with each of the disciplines, as suggested. It demands becoming able to select the ones appropriate and use the affordances they offer to maximize the benefits of the massive technological and scientific advances taking place in society. The US Department of Education, Office for Elementary and Secondary Education (n.d.), You for Youth site extends the definition offered by Balka (2011) to include “interdisciplinary strategies, in order to make informed decisions, create new products and processes, and solve problems” (para. 1). It, then, concisely defines the required separate STEM literacies. These definitions are devoid of explicit reference to the role of data, but there is, however, implicit reference to the practice of statistics in the Technological and Mathematical literacies. Scientific literacy is the ability to use knowledge in the sciences to understand the natural world. Technological literacy is the ability to use new technologies to express ideas, understand how technologies are developed and analyze how they affect us. Engineering literacy is the ability to put scientific and mathematical principles to practical use. Mathematical literacy is the ability to analyze and communicate ideas effectively by posing, formulating, solving and interpreting solutions to mathematical problems. (para. 1)

Historically, more has been written about statistical literacy than about STEM literacy. The research on statistical literacy has led to it being founded on an extensive research base. Back as far as her American Statistical Association (ASA) 1992 keynote address, Wallman (1993) laid the foundation for discussion on this topic: ‘Statistical Literacy’ is the ability to understand and critically evaluate statistical results that permeate our daily lives – coupled with the ability to appreciate the contributions that statistical thinking can make in public and private, professional and personal decisions. (p. 1)

The next step was a more complete description of the statistical literacy needs of adults by Gal (2002) in two parts:

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1. People’s ability to interpret and critically evaluate statistical information, data-­ related arguments, or stochastic phenomena, which they may encounter in diverse contexts, and when relevant, 2. Their ability to discuss or communicate their reactions to such statistical information, such as their understanding of the meaning of the information, their opinions about the implications of this information, or their concerns regarding the acceptability of given conclusions. The critical evaluation and evidence-based decision-making aspects of this definition are important because they underpin the individual STEM literacies. Recognizing evidence-based decision-making as part of all the STEM literacies recognizes the place of statistics in integrated STEM contexts. For the Australian Bureau of Statistics (Trewin, 2005), statistical literacy is “the ability to understand, interpret and evaluate statistical information” and it “is indispensable to help [citizens] understand the world around them and in making sensible, informed decisions” (pp. 11–12). At the school level, Watson (2006) suggested a relationship between statistical literacy and the broader curriculum, reinforcing an early start to building the skills necessary for participating in the STEM curriculum: Statistical literacy is the meeting point of the data and chance curriculum and the everyday world, where encounters involve unrehearsed contexts and spontaneous decision-making based on the ability to apply statistical tools, general contextual knowledge, and critical literacy skills. (p. 11)

Statistical literacy, which derives from the knowledge of the practice statistics, should develop at the same time as STEM literacy is emerging from learning about the STEM subjects at school. This implies statistical literacy can thus play an essential role in linking the other STEM literacies to make meaningful evidence-based decisions.

6.6  The Needs of STEM Careers In considering potential STEM pathways for students, Sawchuk (2018) and Sparks (2018) suggest that calculus, traditionally considered the peak of high school mathematics, may not be the best signal for success in STEM. Rather, they say, the new gateway course in today’s data-rich world should be statistics. This view supporting statistics over calculus is also advocated by Markarian (2018). He claims, “the American economy has entered a new age of data” (para. 3), which requires workers to analyse data to improve productivity and reduce costs. Markarian goes further to suggest specifically that more attention be given to statistics and probability in the secondary years of schooling. Although not downplaying the place of calculus in the curriculum, the National Council of Teachers of Mathematics (NCTM) in the United States has long been a supporter of the importance of statistics in the curriculum. In a 1989 curriculum

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document, long before STEM was a favoured acronym, the NCTM commented at the end of its Standard for grades 9–12: Statistical data, summaries, and inferences appear more frequently in the work and everyday lives of people than any other form of mathematical analysis. It is therefore essential that all high school graduates acquire, at the appropriate level, the capabilities identified in this standard. This expectation will require that statistics be given a more prominent position in the high school curriculum. (p. 170)

By 2018, the NCTM, in its Catalyzing Change book, was still working for improvement in relation to the focus on statistics at the school level, based on the explosion of data leading to the idea of big data and the need to understand and make sense of such data as part of many career options. In a recent US News and World Report (n.d.) article on the ‘best’ jobs in STEM, Statistician was second only to Software Developer, giving an indication of the need for Statistics by the STEM fields in the world of research and development. The US Bureau of Labor Statistics (2017), in forecasting more broadly the growth in all occupations in the United States from 2016 to 2026, placed Statisticians seventh out of the top 10, with projected growth of 33.8% and the third highest median annual salary of the 10 occupations in May, 2017. These predictions should encourage students interested in STEM-related subjects at school to include statistics in their choices. The University of Melbourne (n.d.) reinforces this view for Australia: There is currently a very marked shortage of professional Statisticians across a range of disciplines in Australia. … The methodology division of the Bureau of Statistics reports that the output of honours graduates in statistics is no longer sufficient to fill its annual recruitment needs. The need for Statisticians is more recognised than ever before in Australia, and there are far more employment opportunities. (para. 7)

With a statistics background being a key ingredient for the growth of STEM industries, these concerns about shortages are linked to the more general question of the participation of students in mathematics and science courses at the high school level. Kennedy, Lyons, and Quinn (2014) provide a comprehensive report on enrolment numbers in Australia for Mathematics and Science courses. They express concern about the shift in enrolment patterns in Mathematics to less demanding courses, suggesting one cause of this may be concern about achieving scores for university entrance rather than future career options (p. 45). Their concluding remarks, related to the decline in participation in post-compulsory school science and tertiary-­ enabling mathematics, include the following question and answer. … should government, industry and the educational sector be alarmed by these trends? Yes. If school STEM is to continue to be a cornerstone of creating scientifically aware and literate citizens then it is important to understand why students are electing not to continue the study of school science. (p. 45)

Kennedy et al. suggest that the declines are happening not only in Australia but also in other developed countries, for example, the United Kingdom (Smith, 2011), Japan (Schleicher & Ikeda, 2009), and France (Charbonnier & Vayssettes, 2009). In particular, with respect to studying statistics in the United States in 12th grade, 75% of schools offer a stand-alone statistics course, but only 23% of students

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actually take one (National Assessment of Educational Progress [NAEP], 2015). In relation to Advanced Placement Statistics, which has been offered in the United States since 1997, when 7667 students enrolled, the number completing in 2018 was 221,031 (C. Franklin, personal communication, June 21, 2019). This is an encouraging trend, but the NAEP reported that, in 2015, the 184,766 students taking Advanced Placement Statistics represented only 8% of students in schools that offered any type of stand-alone statistics course. In many countries, such as Australia, there are no separate secondary courses in statistics and sometimes it is only an elective component within a mathematics course. This puts in jeopardy the adequate supply of qualified and experienced statisticians in the future and questions what is needed during the compulsory years of schooling to encourage students to persist with statistics later in their studies. Laying the foundations for future careers in statistics, by providing learning experiences that utilize the practice of statistics for many purposes and within multiple contexts across the compulsory years of schooling, will potentially give students the background needed to imagine that a career in statistics is possible.

6.7  Classroom Experiences to Foster STEM Integration Sources of classroom activities based in STEM contexts are beginning to be available widely around the world, especially in the United States (e.g., Huling & Dwyer, 2018). In Australia, for example, the national science and technology education centre, Questacon, provides links to STEM activities developed and shared by Australian schools (www.questacon.edu.au) and there are many on-line commercial vendors. Exploration of each source is required to discover if and how data are employed for each activity. Many organizations with links to Technology and Engineering are also now suggesting activities for school students that provide contexts for meaningful STEM investigations. The Australian Academy of Technology and Engineering (2016), for example, has sponsored the STELR program (Science and Technology Education Leveraging Relevance), which has developed 12 modules for middle and high schools, appealing to students’ concerns about global warming, climate change, and sustainability. Of the 12 modules, six include data collection and some form of analysis. These six modules include Electricity and Energy, Water in the twenty-first Century, and Car Safety. The assumption of STELR is that the Australian Curriculum (ACARA, 2019) provides the skills required to carry out the analyses, including data representation. Journals, such as The Mathematics Teacher, The Science Teacher, techdirections, and The Journal of STEM Education, have occasional articles that include data in association with STEM activities; for example, having students construct and test catapults (Fitzgerald, 2001), design and evaluate acceleration cars (Stump, Bryan, & McConnell, 2016), organize “data jams” (Forster et al., 2018), and use renewable energy applications (Pecen, Humston, & Yildiz, 2012). These activities are again for middle and high schools.

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The National Science Teachers Association in the United States has supported building links to STEM through science by publishing a STEM Student Research Handbook (Harland, 2011), including a list of 59 STEM topics, with tools, instruments, and tests (pp.  6–8). Beginning with background research, the Handbook moves to writing hypotheses; organizing a laboratory notebook with descriptive statistics, graphical representations, inferential statistics and data interpretation, documentation and research paper setup; writing the STEM research paper; and presenting the STEM research project orally. This careful design follows the practice of statistics and the Science Inquiry Skills of the Australian Curriculum (ACARA, 2019). As interest in STEM education has filtered down to the early childhood level, recommendations have focused on embedding principles from the best early childhood educational practice. In the United States, the Early Childhood STEM Working Group (2017) published a policy report with guiding principles, including, “Representation and communication are central to STEM learning.” Instruction in the STEM disciplines often over-emphasizes procedural competencies and “hands-on” experiences—applying an algorithm to a set of practice problems in a math workbook, measuring and combining ingredients when studying chemistry, or testing a solution in engineering—and under-emphasizes communication about those activities and representations that stem from the activities, such as drawing pictures, making data tables and graphs, and writing numerical representations. While hands-on activities are necessary parts of studying STEM disciplines, they do not, in and of themselves, activate thinking and conceptualization. … Representations are essential tools in STEM that can also make it possible to notice things that otherwise could not be perceived, such as changes over time, patterns or trends across examples, and so on. (p. 15)

Unfortunately, later in the document, when providing a sample of “Big Ideas in STEM Disciplines” (pp.  30–31), the examples from mathematics only refer to Patterns and Measurement, without a further mention of data. This contrasts with the Australian Curriculum (ACARA, 2019) suggestions for students in the Foundation year of early schooling: Answer yes/no questions to collect information and make simple inferences (ACMSP011) [with the following elaborations]. • posing questions about themselves and familiar objects and events, • representing responses to questions using simple displays, including grouping students according to their answers, • using data displays to answer simple questions such as “how many students answered ‘yes’ to having brown hair?”

The question may arise in some circles about introducing STEM as a “subject” in national curricula. Although this is not practical from the standpoint of the fundamental concepts required in the four siloed curriculum areas of Science, Digital Technologies, Design Technologies, and Mathematics (including Statistics), in Australia, there exists the possibility of introducing STEM as a Cross-curriculum Priority. Cross-curriculum Priorities are intended to add depth and richness to student learning across the disciplines (ACARA, 2016, 2019) and STEM-based activities certainly have the potential to do this in a manner similar to that of one of the

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current cross-curriculum priorities, Sustainability. Conceptualising STEM as a Cross-curriculum Priority in the Australian Curriculum has implications for initial teacher education and the development of appropriate resources to support integrating the STEM disciplines within meaningful real-world contexts.

6.8  R  esearch on Student Outcomes in STEM Including Statistics The time is ripe for research examining student outcomes from STEM-based work generally, and the role of statistics as a central thread that helps to integrate STEM. Recent research has shown that very young children are capable of engaging in story contexts that involve STEM-related issues, such as the environment. Kinnear (2013) worked with 5-year-old children in their first term of formal schooling, using a picture book on recycling. She found the children could make sense of data extracted from the story and communicate the message derived. English (2012, 2013) used similar contexts with Year 1 students and found they could also create representations of the data in the stories. These studies illustrate the desires of the Early Childhood STEM Working Group (2017) about representation and communication using contexts linked to STEM through Science and Sustainability. Much of the STEM research conducted at the school level focuses on the outcomes of implementing the engineering design process in various contexts. Outcomes reported include students’ perceptions of and attitudes, engagement, motivation, performance, and self-efficacy in relation to STEM (Hafiz & Ayop, 2019). Although modelling and the use of graphical representations are considered key elements of the implementation of the engineering design process (Mentzer, Huffman, & Thayer, 2014), rarely are the models and representations produced by students data-related. Of the few studies that have focussed on students’ application of statistical practices, Glancy, Moore, Guzey, and Smith (2017) reported on the issues faced by Year 5 students, who completed a physics investigation. Of particular concern, after the initial problems of collecting the measurement data, was the linking of the data with an explanation of the force required to balance a load and its distance from the fulcrum of a lever. The authors concluded, … that simply asking students to collect and interpret data, even when the activity itself is accessible to the students, does not guarantee that students will make meaningful connections between the data they measured and the science and engineering concepts with which they are engaged” (p. 75).

Fitzallen, Wright, and Watson (2019), however, reported that Year 5 students were able to make meaningful connections to the other STEM disciplines of Engineering and Technology, when asked to use the representations created from data collected to make decisions about potential changes needed to improve a seed dispersal device. Clearly, further research into the pedagogical approaches that facilitate

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students making the connections across disciplines is needed and, in particular, how students learn to see how data can inform understanding of STEM concepts.

6.9  A  Research Program on Primary School Statistics and Integrated STEM Activities The authors and their colleagues have conducted a longitudinal research program in Australia, examining the use of statistical understanding and techniques in a series of integrated STEM activities with primary school-age children (ages 8–12). Following professional learning with teachers and trials with Year 1 and Year 3 classes (Watson, Skalicky, Fitzallen, & Wright, 2009), the first year of the study involved research with Year 3 classes that presented children with a STEM manufacturing context where the children compared hand-made Play-doh™ licorice sticks with those made by a Play-doh™ extruder “machine” (Watson, Fitzallen, English, & Wright, 2019). Focussing on the big idea of variation, students considered the differences seen in the variation in the mass of the sticks between the two methods. Because the expectation for the two methods was that the masses would be the same, student attention could be directed to the variation in the two contexts (see Fig. 6.4).

Fig. 6.4  Class plots of hand-made (right) and machine-made (left) licorice sticks in Year 3

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Descriptions provided by the students of the shapes of the distributions ranged from imaginative (e.g., “handmade is like a city but machine-made is like a tower”) to closely tied to the data (e.g., “one was in between 10g and 16g and the other was between 6g and 28g. The machine is more accurate.”) Eighty-six percent of students (n = 70) could make a statement that showed appreciation of the difference in variation between the two methods. During the 3 years after this first activity, a program of activities accessed through the Science curriculum, but with links to the Design and Digital Technologies curriculum (ACARA, 2019), was developed. The second scenario for 53 of these students in Year 3 exposed them to the big idea of variation again, this time in three different but related contexts. Students measured and recorded the drop in temperature of hot water in insulated and non-insulated plastic cups over 30 minutes as seen in Fig. 6.5 (Chick, Watson, & Fitzallen, 2018). After 10 min, ice water was added to the tray. The outcomes for the context of heat included the student conceptions of heat transfer (Fitzallen, Wright, Watson, & Duncan, 2016). Students recorded data on stylised graphical representations prepared for them to visualize the variation seen (see Fig. 6.6), described the meaning in context, and made predictions over a longer period of time. This process linked students’ use of data intuitively to the two other statistical big ideas of distribution and expectation (Fitzallen, Watson, & Wright, 2017). In Year 4, students created on-line surveys to compare life-style and climate with a class in another part of Australia. The activity linked the practice of statistics to technology through use of an on-line survey as shown in Fig. 6.7, as well as acknowledging aspects of science, for example, through questions about the weather and wildlife (Watson, Fitzallen, & Wright, 2019). Students posed and refined questions, answered them on-line, analysed the data by creating representations, and drew conclusions about life in the two cities. In carrying out the practice of statistics, 87% (n = 53) of students recognized the importance of displaying all of the data collected in their representations, with 64% using conventional graph types and 23% using informal formats (see Fig. 6.8). In drawing conclusions, 78% of students acknowledged some level of uncertainty, from a simple “not very sure” (30%), to Fig. 6.5  Measuring water temperature

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Insulated Cup – Hot water

Non-insulated Cup – Hot water

Water bath – Iced water

Fig. 6.6  Data recorded on stylised thermometer graph

questioning the accuracy of the responses (18%), to recognition of the potential deficiencies of the sample (30%). Later, in Year 4, students took part in an activity in which small catapults were used to launch ping pong balls, which involved collecting data on the distance the ping pong balls travelled, “improving” the catapults, collecting more data after improvements were made, and analysing the data to decide if the improvements to the catapults had increased the distance travelled by the ping pong balls (Fitzallen, Watson, Wright, & Duncan, 2018; Fitzgerald, 2001). This activity was an extension of the statistical ideas developed in the Licorice activity because now there was a difference in the expectation for the typical distance the ping pong balls would travel. As well, students were introduced to entering and exploring the data in the statistical software package TinkerPlots (Konold & Miller, 2015) and began to create representations to show the differences in their groups’ data before and after the changes to the catapults. Using TinkerPlots allowed greater opportunity for creativity in plots to tell the story of the experience. Figure 6.9 shows the integration across STEM for this activity, highlighting the ideas of science (force and energy), technology (software for data analysis), engineering (modifying the design of the catapult), and mathematics (measurement and data analysis). Six aspects of the activity are shown in Fig. 6.10: (1) the basic catapult, (2) the launching of ping pong balls in the school hall, (3) the fair trial rules for launching the ping pong balls, (4) a hand-drawn representation for the first 12 distances, (5) a TinkerPlots representation comparing the two trials for one group, and (6) one class’s data for all trials. Seventy percent (n = 50) of students were able to show the change in distance travelled by the ping pong balls for the two settings of the catapult. In Year 5, the Science topic was viscosity and students considered two scenarios. First, they tested five concentrations of a liquid by measuring the distance travelled down a slope in 30 s and using the data collected to estimate the concentration of a mystery substance. Second, they used a viscous liquid to model lava flow down a

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Fig. 6.7  Collecting data with technology

volcano by timing the “lava flow” to each of six sections of the volcano and predicting how long it would take to progress to ten sections. The swapping of the variables of time and distance was a challenge for some students, but demonstrated the power of mathematics to answer questions in varying contexts. Examples of students’ use of drawing “lines of best fit” on TinkerPlots data sets are shown in Fig. 6.11 (a) to predict the mystery concentration (interpolation) and (b) to predict how long the lava would take to travel across ten sections (extrapolation). Later, in Year 5 students, working in groups of three, designed, tested, and improved their designs for wind dispersal of seeds either by helicopter, parachute, or sail, collecting data from trials with wind created by standard fans (Fitzallen et  al., 2019; Smith, Fitzallen, Watson, & Wright, 2019). In this activity, design

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Fig. 6.8  Conventional and informal graph formats for analysing students’ questions

Fig. 6.9  Integration across STEM

features of the Technology curriculum were a focus, as students made decisions in their groups about which of three designs to improve before final testing. As seen in Fig. 6.12, the engineering design process is in close correspondence with the practice of statistics as described by Franklin et al. (2007). Figure 6.13 shows one design for a sail and the model created from it, whereas Fig. 6.14 shows the carrying out of trials and the data collected by one class.

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(1)The catapult

(2) Launching the catapults in the school hall

(3) Rules for conducting a fair trial

(4) Hand-drawn representation of individuals’ first four throws from all three group members

(5) TinkerPlots representation of data from two sets of trials for one group

(6) TinkerPlots representation of data from two sets of trials for one whole class

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Fig. 6.10  Stages in the progression of the Catapults activity

The importance of this progression of activities over 3 years included (1) demonstrating the various stages of the practice of statistics, (2) showing explicit integration of statistics and the STEM contexts of the activities, and (3) creating an interest in continuing to study Science and Technology courses in later years of schooling, alongside Mathematics. As yet, the longitudinal impact of these activities, including a fourth year, has not been explored fully, but a straightforward check of the total score from link items used across surveys of statistical literacy, involving questions about interpreting data and representations and making decisions based on statistical information, for the students who completed surveys at the beginning of Year 3 and the end of Year 5, produced promising results for the first 3 years. A paired t-test with n = 50, produced a t-value of 3.73, with a standard error of 0.644, and a two-­ tailed p-value of 0.0005, indicating a statistically significant difference, with an

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Fig. 6.11  Using “lines of best fit” to make predictions in TinkerPlots

Fig. 6.12  Similarity of the practice of statistics and the engineering design process

effect size of 0.63, suggesting that students’ statistical literacy improved over the 3 years. A further summary of other research based on STEM-context activities for primary school students involving data collection and analysis is found in Fitzallen and Watson (2020).

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Fig. 6.13  A design and a model for a sail method of seed disposal

Fig. 6.14  Trialling and the results for one class’s testing of wind dispersal devices

The research beginning to be carried out in primary schools reinforces the potential integration among the practice of statistics, science inquiry skills, data handling and design evaluation in the Mathematics, Science, and Technologies curricula. In considering the many varied contexts within which STEM activities are conducted, the longitudinal research on outcomes across topics focussing on the data analysis aspects is likely to be particularly valuable. A search for reports of research on student outcomes related to STEM activities integrating data and the practice of statistics at the high school level yielded no results. Obviously, the field is open and offering great opportunities for research in this aspect of integrating STEM in the classroom.

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6.10  Conclusion Tytler, Prain, and Hobbs (2019) suggest that if mathematics classrooms would place greater premium on the invention and refinement, and contextual application of representational systems, … teachers and students would find a greater role for mathematics in interdisciplinary projects, in which mathematics was naturally, temporally entwined with the other STEM disciplines. (p. 17)

As the methodology for analysing the data arising naturally in STEM problem-­ solving contexts, statistics potentially provides an integrating ‘thread’ that is entwined among all investigations where data are collected. If students master the practice of statistics, they will be able to use it time after time as a fundamental ingredient across STEM projects and within individual disciplines, when making decisions from data generated from investigations. There is also the potential for students to apply the practice of statistics when undertaking investigations in other fields, such as the social sciences. The power that statistics has to inform, explain, and unify the STEM disciplines is only beginning to be tapped effectively at the school level, yet it is vital that this power is recognized in order to produce the evidence-­based STEM outcomes required to meet the needs of society. Acknowledgements  This chapter was supported in part by an Australian Research Council (ARC) Discovery Grant (DP150100120). Any opinions, findings, conclusions, or recommendations expressed are those of the authors and do not necessarily reflect the views of the ARC.

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Chapter 7

Numeracy Across the Curriculum as a Model of Integrating Mathematics and Science Anne Bennison and Vince Geiger

Contents 7.1  I ntroduction 7.2  S  TEM Education and Numeracy 7.2.1  Approaches to STEM Education 7.2.2  Approaches to Numeracy 7.3  Theoretical Framework 7.4  Numeracy in Science 7.4.1  STEM and Numeracy in the Australian Curriculum 7.4.2  Research Design 7.4.3  Integrating Mathematics and Science Through Numeracy Across the Curriculum 7.5  Discussion 7.6  Concluding Remarks References

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7.1  Introduction There is increasing recognition internationally of the importance of Science, Technology, Engineering and Mathematics (STEM) capability and literacy for national prosperity, personal well-being and informed citizenship (e.g. Curriculum Development Council, 2015; Executive Office of the President of the United States, 2013; Office of the Chief Scientist, 2014). Australia’s Chief Scientist, for example, has argued that building a competitive economy requires “a long-term strategic view of STEM’s pivotal role in securing a stronger Australia” (Office of the Chief

A. Bennison (*) University of the Sunshine Coast, Sunshine Coast, QLD, Australia e-mail: [email protected] V. Geiger Institute for Learning Sciences and Teacher Education, Australian Catholic University, Brisbane, QLD, Australia © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_7

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Scientist, 2014, p. 6). In many countries, however, there are concerns that the education system is not providing adequate pathways into STEM careers through strategies that include increasing student engagement and participation in STEM subjects (e.g. Education Council, 2015; Executive Office of the President of the United States, 2013). Career pathways into vital STEM careers are limited if students do not engage with STEM subjects while at school. In Australia, participation rates in senior secondary school chemistry, physics and biology have declined (Kennedy, Lyons, & Quinn, 2014). This worrying trend is also seen in mathematics subjects that are important for entry into STEM careers (Barrington & Evans, 2017). In addition, the performance of Australian students on the Programme for International Student Assessment (PISA) indicates that many Australian students lack the mathematical literacy and/or scientific literacy to effectively participate in life situations related to mathematics and science, respectively (Thomson, De Bortoli, & Underwood, 2017). In addressing the challenge of providing adequate pathways into STEM careers, Australia has developed the National STEM School Education Strategy (Education Council, 2015). Five key areas for national action are identified. The first of these is to increase student STEM ability, engagement, participation and aspiration. This area for action directly addresses some of the challenges faced in building Australia’s STEM capacity: declining enrolments in STEM subjects in senior secondary schooling and the performance of Australian students in international testing in mathematical and scientific literacy. The strategy recognises that STEM education not only encompasses teaching the individual disciplines of science, technology, engineering and mathematics but also promotes an integrated approach that has potential to increase students’ interest in STEM-related fields. This position is reinforced through the Australian Curriculum (ACARA, 2017a) via the discipline knowledge developed in STEM-related learning areas and the General Capabilities—numeracy, ICT capability and critical and creative thinking—developed as a vehicle for integrating important knowledge and capabilities across subjects. Our focus in this chapter is on how the integration of mathematics and science can be achieved through an across the curriculum approach to numeracy (referred to as mathematical literacy in some international contexts). In attending to this purpose, we also demonstrate how explicitly attending to numeracy—the capability to use mathematics to solve real-world problems—can be leveraged to promote student knowledge and understanding in science, enabling students to see the relevance of mathematical knowledge beyond the mathematics classroom. We illustrate this form of curriculum integration by drawing on data from a project that was based on promoting teacher engagement with a rich cross-curricular model of numeracy (Goos, Geiger, & Dole, 2014). The aim of this project was to assist teachers to develop the capability to take advantage of the numeracy demands and opportunities that exist within all subjects. Two vignettes are described and analysed in order to address the following research question: How can an across the curriculum approach to numeracy provide a new model of integration between mathematics and science?

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In the next section, we offer a brief overview of approaches to STEM education and numeracy and, in doing so, highlight some similarities and differences. We then outline the theoretical framework that underpins our research. Information about the Australian context and research design follows. Next, we present two vignettes to illustrate how explicit attention to the numeracy General Capability provides opportunities to integrate mathematics and science. Finally, we discuss how explicitly attending to numeracy opportunities in science can promote deeper and more effective learning.

7.2  STEM Education and Numeracy In this section, we begin by highlighting the diversity of integrated curriculum approaches that exist within STEM education. The focus then turns to numeracy and how an across the curriculum approach to numeracy adds to existing integrated approaches to STEM education.

7.2.1  Approaches to STEM Education One of the challenges of identifying strategies to improve student engagement and participation in science, technology, engineering and mathematics (STEM) is that there is not a universal understanding of what STEM education is and how it is best implemented in schools (English, 2016, 2017; Herschbach, 2011). The range of approaches to STEM education varies in both the disciplines that are integrated and the nature of this integration. In a meta-analysis of 28 studies on the effects of STEM integration on student learning, Becker and Park (2011) identified seven different models of STEM education based on the disciplines that were integrated (e.g. science and mathematics, science, technology and mathematics). A more fine-­ grained approach was possible in a study by Hobbs, Cripps, and Plant (2018), who were able to identify five models that characterise different forms of teacher collaboration and curriculum approaches. Each of these models involved all four disciplines but with differing approaches (e.g. SteM in which all four disciplines are taught by a single teacher but there is more emphasis on science and mathematics). The nature of integration in these approaches and other approaches is captured in Vasquez’s (2014/2015) use of an inclined plane to represent a continuum of increasing levels of STEM integration—from disciplinary to multidisciplinary to interdisciplinary to transdisciplinary approaches. Disciplinary approaches, in which disciplines are taught separately, can offer few opportunities for students to make connections across the STEM disciplines. This approach, however, is seen in many schools because of the traditional organisation of the school curriculum around discrete subjects (e.g. ACARA, 2017a). As the level of STEM integration increases,

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the boundaries between the disciplines become increasingly blurred. Multidisciplinary approaches, for example, involve teaching separate disciplines linked by common themes, whereas in transdisciplinary approaches, disciplinary boundaries are absent, and students draw on knowledge and skills from two or more of the STEM disciplines as they engage in real-world problems and projects (Vasquez, 2014/2015). Hobbs et al.’s (2018) use of three models to frame STEM for education is another way of capturing different approaches to STEM integration. The Holistic Model encompasses both disciplinary and interdisciplinary activities, the Interconnected Model is limited to interdisciplinary activities and the Amalgamated Model is a transdisciplinary approach which sees STEM as a meta-­ discipline that draws on all four STEM disciplines. Clearly, there is a plethora of integrated approaches to STEM education. One of the criticisms of integrated approaches to STEM education is that not all disciplines are represented equally (English, 2016, 2017). In particular, there are concerns that the role of mathematics is being diminished (English, 2016; Fitzallen, 2015). Fitzallen (2015), for example, pointed to a number of studies which suggest that the STEM disciplines provide a context for developing mathematical concepts but fail to take advantage of the way that “mathematics can influence and contribute to the understanding of ideas and concepts of the other STEM disciplines” (p. 241). There are also a number of challenges in implementing integrated approaches to STEM education in schools, especially secondary schools. For example, the STEM Connections Project (ACARA, 2016) offers useful insights into these challenges. Project implementation varied across participating schools, but in all cases, time was required for extensive collaboration among specialist mathematics, science and technologies teachers. Such collaboration is sometimes difficult in secondary schools because of timetabling arrangements and the location of teachers in discipline-­based staffrooms. Across the study, mathematics was identified as the most difficult learning area to plan for. Other challenges identified for teachers in the STEM Connections Project include the need to provide students greater autonomy resulting in increased demands on classroom management and planning during these extended tasks. The need for an integrated approach to assessment and reporting was identified but not addressed in the project. The challenges identified in this project point to the need for schools to develop a STEM vision that can be promoted and is sustainable within the affordances and constraints offered by specific school contexts (Hobbs et al., 2018). The challenges of implementing integrated approaches to STEM education suggest that a school’s STEM vision is likely to draw upon more than one model of STEM integration. Such a STEM vision is consistent with English’s (2017) view that STEM education should not be limited to a transdisciplinary approach. Explicit attention to numeracy within the other STEM disciplines provides an additional model of STEM integration with potential to increase the prominence of mathematics and its contribution to learning in the other STEM disciplines. In contrast to other models of STEM integration, which require teachers from other disciplines to work collaboratively to design and implement STEM projects, explicit attention to

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numeracy relies on teachers of all disciplines identifying numeracy within their subject areas and attending to demands and opportunities.

7.2.2  Approaches to Numeracy Although there is increasing interest in research on numeracy (e.g. Callingham, Beswick, & Ferme, 2015; Diezmann & Lowrie, 2012), the use of the term varies between countries. While mathematics is the discipline that underpins numeracy, there is widespread agreement that knowledge of mathematics alone does not enable individuals to cope with the mathematical demands of life at work and at home and to participate effectively in community and civic life (e.g. OECD, 2016: Quantitative Literacy Design Team, 2001). This is because being numerate requires the accommodation of both mathematical and extra-mathematical aspects of a real-world problem, that is, “to make sense of non-mathematical contexts through a mathematical lens; exercise critical judgement; and explore and bring to resolution real world problems” (Geiger, Forgasz, & Goos, 2015, p. 531). The extra-mathematical aspects associated with numeracy are aligned with skills that are common across the STEM disciplines, such as understanding the nature of evidence in order to make judgements about the accuracy and reliability of information (see Hobbs et al., 2018). While the development of numeracy capabilities is often expected to take place within traditional mathematics classes, the need to make sense of non-mathematical contexts and solve real-world problems suggests that subjects other than mathematics will provide meaningful contexts for students’ numeracy development (Quantitative Literacy Design Team, 2001). Two broad categories of integrated curriculum approaches to numeracy have shown promise (Geiger, Goos, & Forgasz, 2015): one involves a continuum of integration approaches where mathematics is combined to varying degrees with one or more subjects, and the other involves exploiting numeracy learning opportunities in subjects across the curriculum. Multidisciplinary, Interdisciplinary and Transdisciplinary Approaches Approaches that integrate mathematics with one or more subjects to develop students’ numeracy capabilities include multidisciplinary, interdisciplinary and transdisciplinary approaches similar to those identified for integrated STEM education (Vasquez, 2014/2015). When the focus is on numeracy, however, the subjects involved are not limited to the other STEM disciplines. Miller (2010) has argued that an important aspect of numeracy is the ability to communicate mathematical information that forms part of other subjects, for example, the results of an experiment in science or the interpretation of population data in social studies. She advocates a multidisciplinary approach that draws on mathematics, English and other subjects such as science and social studies. In this approach, English contributes to students’ numeracy development by providing a

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vehicle for developing essential communication skills. At the other end of the spectrum is a curriculum that is problem-centred and based around tasks, such as those designed by the Common Problem Solving Strategies as links between Mathematics and Science (COMPASS) project (Maass, Garcia, Mousoulides, & Wake, 2013). Further examples from across the range of integration approaches can be found in research conducted in Australian middle schools in which the focus was also on mathematics and science (Wallace, Sheffield, Rennie, & Venville, 2007). The forms of integration identified included synchronised approaches where similar content was taught in separate subjects, thematic approaches where various school subjects were linked by themes and project-based approaches where students worked on projects and the subject boundaries were blurred. Although the COMPASS project and the study conducted by Wallace et al. (2007) were concerned with integrating mathematics and science, and so could also be seen as examples of integrated approaches to STEM education, we would argue that potential learning outcomes include the development of students’ numeracy capability. Across the Curriculum Approaches In an across the curriculum approach, numeracy is seen as an integral part of all school subjects. Exploiting numeracy learning opportunities develops students’ numeracy capabilities and enhances subject learning. Within STEM education, such an approach provides an additional mechanism for integrating mathematics and other STEM disciplines (see, e.g. Geiger, 2019) and is especially valuable in situations where there is a disciplinary approach to STEM education. Numeracy in science can be seen as the application of “mathematical thinking and reasoning within the discipline frame of science” (Quinnell, Thompson, & LeBard, 2013, p. 810). Proportionality, for example, underpins many scientific concepts from across the sub-disciplines of biology, chemistry, earth and space sciences and physics (Hilton & Hilton, 2016). While teachers do not often explicitly address mathematical aspects when teaching science (Howe et al., 2015), an across the curriculum approach to numeracy can take advantage of opportunities that exist. Understanding scale is important for many scientific concepts (Taylor & Jones, 2013), and a scaled timeline, for example, can be used to assist students to understand the extent of geological time (Bennison, 2015). An appreciation of the scientific context is also important. Ramful and Narod (2014) identified five levels of increasing complexity in the proportional reasoning required to solve stoichiometry problems in chemistry. The levels arose from needing to understand what is meant by the term “mole”, the use of extensive and intensive quantities (e.g. mass and concentration, respectively) and the nature of chemical equations, which represent proportionality in terms of molar ratio rather than equality in terms of quantities. Further opportunities to pay explicit attention to numeracy exist when conducting scientific investigations. This scientific practice requires not only the collection, analysis and representation of data but also a critical appraisal of the results

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(Quinnell et al., 2013). However, teachers tend to focus on the concepts of a discipline (Hilton & Hilton, 2016; Howe et al., 2015), which may mean that the opportunity for students to exercise critical capabilities may be lost. The examples presented above illustrate the potential benefits of an across the curriculum approach to numeracy to contribute to learning in science and to help students develop the inclination to use a mathematical lens to make sense of their world. One of the challenges for science teachers is to help students make connections between their mathematical knowledge and the practice of science (Quinnell et  al., 2013). An across the curriculum approach to numeracy has potential to address this challenge by providing a means to integrate mathematics and science within the discipline of science, thereby helping students to develop the attributes needed to practice science. Such an approach shifts the “focus from the incidental nature of mathematics in learning activities to a focus on the instrumental nature of the mathematics” (Fitzallen, 2015, p. 242).

7.3  Theoretical Framework Planning to take advantage of numeracy learning opportunities that exist in subjects across the curriculum can be challenging for teachers because of the multifaceted nature of numeracy. Drawing on a synthesis of research literature, Goos et al. (2014) constructed a model of numeracy for the twenty-first century (Fig. 7.1) for use in a series of research and development projects aimed at enhancing numeracy teaching

Citizenship

Dispositions Confidence

Representational

Flexibility

Physical

Initiative Risk

Personal and Social

Tools

Contexts

Digital

Problem Solving

Work

Estimation Concepts Skills

Critical Orientation

Mathematical Knowledge

Fig. 7.1  A model for numeracy in the twenty-first century (Goos et al., 2014; Goos, Geiger, & Dole, 2010)

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Table 7.1  Descriptions of the elements of the 21st Century Numeracy Model (Goos et al., 2014; Goos, Dole, & Geiger, 2012) Element Mathematical knowledge Contexts Dispositions Tools

Critical orientation

Description Mathematical concepts and skills, problem-solving strategies and estimation capacities Capacity to use mathematical knowledge in a range of contexts, both within schools and beyond school settings Confidence and willingness to engage with tasks and apply mathematical knowledge flexibly and adaptively Use of physical (models, measuring instruments), representational (symbol systems, graphs, maps, diagrams, drawings, tables) and digital (computers, software, calculators, Internet) tools to mediate and shape thinking Use of mathematical information to make decisions and judgements, add support to arguments and challenge an argument or position

practice across a number of disciplines. The 21st Century Numeracy Model represents numeracy as five interconnected dimensions: contexts, mathematical knowledge, tools and dispositions that are embedded in a critical orientation. These dimensions are described more fully in other publications (e.g. Geiger, Goos, & Dole, 2015; Goos et al., 2014; Goos, Dole, & Geiger, 2011) but are summarised in Table 7.1. The model has been validated as effective in assisting teachers to plan for implementation of lessons aimed at promoting student numeracy capability (Goos et al., 2014), design numeracy tasks (e.g. Geiger, 2016) and document their developmental trajectories in relation to enhancing numeracy teaching practice (Geiger, Forgasz, & Goos, 2015).

7.4  Numeracy in Science In this section, we provide information on the Australian Curriculum  (ACARA, 2017a). We then outline our study and present two vignettes to illustrate the potential of an across the curriculum approach to numeracy to provide an additional model for integrating mathematics and science.

7.4.1  STEM and Numeracy in the Australian Curriculum The Australian Curriculum (ACARA, 2017a) was developed in response to the Melbourne Declaration on Educational Goals for Young Australians (Ministerial Council on Education, Employment, Training, and Youth Affairs, 2008), which recognised the new demands being placed on Australian education in the face of increasing globalisation and technological change taking place in the twenty-first

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century. Discipline knowledge, skills and understanding are built through eight learning areas: English, Mathematics, Science (including physics, chemistry, biology, and earth and space sciences), Humanities and Social Sciences, the Arts, Languages, Health and Physical Education and Technologies (Design and Technologies and Digital Technologies). Numeracy, along with literacy, critical and creative thinking, ICT capability, intercultural understanding, personal and social capability and ethical understanding, is identified as a General Capability to be developed across the curriculum. For each learning area, a numeracy icon identifies numeracy demands, and there is advice on how numeracy is developed and applied. In Science, for example, practical measurement and the collection, representation and interpretation of data are identified as key aspects of numeracy (ACARA, 2017b). In the Australian Curriculum, STEM is realised through the teaching of Science, Technologies and Mathematics and the General Capabilities of numeracy, ICT capability, and critical and creative thinking. Engineering is not taught as a separate subject but is addressed through the design aspects of the relevant Technologies learning area. Thus, one approach to STEM education in the Australian context is to address numeracy in other STEM disciplines.

7.4.2  Research Design Our research was conducted in Australia in two states (Queensland and Victoria) over 3 years (2012–2014). The purpose of the research was to determine the effectiveness of the 21st Century Numeracy Model (Goos et al., 2014) in assisting teachers to plan for the implementation of numeracy-­ embedded activities in their classrooms—within subject areas across the curriculum. Although the research was not specifically focused on the STEM disciplines, the findings provide insights into how an across the curriculum approach to numeracy can be leveraged to promote student knowledge and understanding in science. Sixteen teachers were recruited from six schools—three in each state. Schools were selected to balance school sector (public versus private), socioeconomic status and location (metropolitan versus regional). Five public schools and one private school, including one school from outside the metropolitan area of one of the capital cities, agreed to participate in the project. Teachers who volunteered to participate in the project included generalist primary teachers, middle school teachers and specialist secondary teachers from a range of disciplines, including English, history, mathematics and science. Three of the participating teachers taught science in secondary school settings. Teachers participated in a series of workshops that promoted engagement with the 21st Century Numeracy Model (Goos et al., 2014) described in Sect. 7.3 and were provided with opportunities to plan and share numeracy-rich tasks. The purpose of these tasks was to address numeracy demands identified in the Australian Curriculum (2017a) or to take advantage of numeracy opportunities identified by teachers alongside the equally important goal of enhancing subject learning.

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Numeracy opportunities exist in all subject areas but are invisible unless teachers are able to “see” them (Goos et al., 2012). For this reason, one of the goals of the workshops was to increase teachers’ sensitivities to the many numeracy opportunities that exist in subjects across the curriculum. The workshops were followed by school visits where teachers were observed and interviewed. Field notes were used to record lesson observations which focused on tasks teachers used and how these tasks promoted both numeracy and subject learning. Artefacts created by teachers, such as PowerPoint presentations and task sheets, were collected to complement field notes. One of the forms of analysis we conducted was to use the 21st Century Numeracy Model as a lens to identify and document the extent to which dimensions of numeracy were evident in the tasks the teachers used. This analysis also allowed us to make suggestions about ways in which tasks could be modified to more fully exploit the numeracy learning opportunity they provided. Additionally, we inspected the relevant subject curriculum documents to identify specific links between tasks and subject learning. Teachers were interviewed following lessons and asked about their reasons for using particular tasks, challenges they faced in implementing the tasks and how they would modify tasks for future use. Interviews were audio recorded and transcribed. Interview data were analysed through a process of constant comparison with the dimensions of the 21st Century Numeracy Model. Drawing on these data and analyses, case studies were developed for each teacher.

7.4.3  I ntegrating Mathematics and Science Through Numeracy Across the Curriculum The Australian Curriculum: Science F-10 (ACARA, 2017a) has three interrelated strands (Science Understanding, Science Inquiry Skills and Science as a Human  Endeavour)  that collectively address the practice of science. Students develop knowledge (Science Understanding) and skills (Science Inquiry Skills) that help them to understand the world in which they live (Science as a Human Endeavour). There are many numeracy demands and opportunities across these strands that can be utilised to enhance learning in science. The two vignettes presented in this section illustrate how an across the curriculum approach to numeracy can provide a non-superficial means of integrating mathematics and science. The vignettes are described and analysed using the 21st Century Numeracy Model (Goos et  al., 2014) and, therefore, also provide evidence that this numeracy model has potential to be used as a planning tool to assist teachers to integrate mathematics and science in meaningful ways. Karen and Michael (pseudonyms) taught in a mid-sized secondary school (approximately 900 students) located in a low socioeconomic area in a metropolitan city. Prior to grade 10, students were taught mathematics and science by the same

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teacher, but the curriculum was not integrated in any way, and there was no STEM program in the school. Vignette 1 Karen was an early career teacher who had completed applied science (major in biology) and education degrees. She was formally qualified to teach mathematics and science up to grade 10. Before engagement with the project, opportunities for her to learn about addressing the numeracy General Capability had been limited. Nonetheless, she felt that addressing numeracy in science came naturally because “the context is already there and you’ve just got to make the opportunities, find the opportunities that are already there”. She found it more difficult to address numeracy in mathematics because of difficulties in finding appropriate contexts for some mathematical content. This vignette is based on a lesson observed during the third round of school visits which occurred after Karen had attended three whole day teacher meetings. It comes from a grade 9 lesson in which Karen’s students investigated the process of radioactive decay. The relevant content descriptor from the chemical sciences sub-strand of the Australian Curriculum (ACARA, 2017a) is: All matter is made of atoms that are composed of protons, neutrons and electrons; natural radioactivity arises from the decay of nuclei in atoms (ACSSU177).

Karen wanted her students to understand what the half-life of a radioactive isotope is: “you can’t predict a single event, but you can predict what is going to happen to a whole group of them [atoms] and that’s kind of what half-life is about”. She also saw an opportunity to attend explicitly to representing data graphically, an area that caused “anxiety” for her students. Karen began the activity by indicating that radioactive decay is a random process, telling students that there was a 50% chance that any atom of a radioisotope would decay. She gave each pair of students a cup containing a number of M&M’s® (small button-shaped candied lollies with manufacturer’s mark on one side). Karen told students that this was a small sample of a radioactive isotope with a half-life of 2 min. To simulate radioactive decay, students were asked to shake the cup, empty the contents onto a sheet of paper and remove those lollies where the manufacturer’s mark was showing. The procedure was to be repeated at 2-min intervals until there were no M&M’s remaining. The initial number of M&M’s in the cup and the number remaining at the end of each interval were to be recorded. A sample of student data is shown in Table 7.2. Following a brief discussion about how to represent the data graphically (including choice of scale and variable for each axis), each pair of students was asked to produce a graph of their results by hand. Karen pointed out to students that although the scales on the axes would change for different radioactive isotopes, the general shape of the graph would not. She illustrated this by showing a website simulation of sodium-25 (T1/2 = 59 s) where the number of sodium-25 atoms remaining at any time was represented as a percentage

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No of M&M’s 83 49 20 11 6 2 1

of the original number of atoms. She also used this website to demonstrate how the half-life of a radioactive isotope could be read from these graphs. For carbon-14, a slider was moved to the point on the vertical axis where 50% remained, and the half-­ life was read from the horizontal axis. In reflecting on the lesson, Karen identified several areas where there was an opportunity to further exploit the potential of the task for helping students to understand the process of radioactive decay (her goal for science learning in the lesson), including placing greater emphasis on the random nature of decay by comparing group results and using Excel to produce graphs, which was not possible because of a lack of individual student access to computers. Karen demonstrated her current understanding of the 21st Century Numeracy Model (Goos et al., 2014) by identifying some of the dimensions she saw in the task: So the context was obviously half-life. Radioactivity. The mathematical skills and knowledge was to do with probability…then they used representational tools of graphing…In terms of dispositions it’s [pause] I feel that graphing is something that kids do have a lot of anxiety about because they do find it very difficult to come up with a graph from nothing. You find at this level with the Year 9s they do require a fair bit of scaffolding in terms of which variable goes on which axis and what scale…I actually meant to do a bit more of the critical orientation side of things with comparing the results between the groups…I meant them to realise these are random events.

Our analysis of the task with reference to the 21st Century Numeracy Model (Goos et al., 2014) reveals several dimensions of numeracy evident in the task Karen used and allows us to make suggestions for further enhancement. The task is situated in the context of learning about radioactive decay (see ACSSU177 above) and provides opportunities for students to develop their capacity to collect and represent data, skills that are essential in practicing science. Mathematical knowledge about probability was used, but the random nature of probability could have been explored further through critical appraisal of the data obtained. For example, Karen could have asked students to compare the results obtained by each group, collate and examine combined class results and finally compare group and class results with those obtained through a computer simulation. Representational tools (a table and graph) were used to record and display data collected in the physical simulation, respectively. A digital tool in the form of a computer simulation was used, and as noted by Karen, there was potential to use Excel to generate graphs. Karen

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identified representing data graphically as challenging for her students; thus the activity provides an opportunity to develop the disposition of confidence in this area. There was potential for Karen to problematise the task further by including questions of a more critical nature. For example, students could have been asked to find the half-life of selected radioactive isotopes and discuss why some radioactive isotopes have practical uses yet others present challenges for society (e.g. iodine-235 has a half-life of 8 days and is used in medicine for testing the activity of thyroid glands; the half-life of carbon-14 of 5370 years makes it useful for determining the age of once living organic material; uranium-235 is used in nuclear reactors to generate power, but the waste from this process is difficult to store because the half-life of this isotope is 4.5 × 109 years). This gives meaning to the term half-life and introduces a critical orientation. In summary, Karen was able to take advantage of some of the numeracy demands and opportunities the task offered, but our analysis suggests that there were additional opportunities to further enhance science learning as well as consolidate students’ mathematical understanding. For example, further investigation of the meaning of half-life would contribute to students’ understanding of the impact of science on the world in which they live, and greater exploration of probability would consolidate students’ understanding of randomness in probability. Vignette 2 Michael was a mid-career teacher who had completed a dual degree program in applied science (major in human movement) and education. During this program, he studied curriculum subjects in physical education and mathematics but not science and thus could be considered to be teaching science out-of-field. Like Karen, there had been few opportunities for him to learn how to address numeracy in science. Michael could see a relationship between mathematics and science but acknowledged he had not provided opportunities for students to develop their numeracy capabilities in his science lessons as much as he should: I definitely see that there is a role of numeracy in science and we do do it. But I probably don’t do it enough…It is incorporated into the unit of work so there is a lot of graphing and interpreting tables and values and that sort of stuff as well.

This vignette is based on a lesson observed during the second round of school visits which occurred after Michael had attended two whole day teacher meetings. It comes from a grade 9 lesson in which Michael’s students explored the impact of rabbits on the populations of three native species (bandicoots, wallabies and dingoes). The relevant content descriptor and elaboration from the biological sciences sub-strand of the Australian Curriculum (ACARA, 2017a) are as follows: Ecosystems consist of communities of interdependent organisms and abiotic components of the environment; matter and energy flow through these systems (ACSSU176) • Examining factors that affect population sizes such as seasonal changes, destruction of habitats and introduced species

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Although the task was set within the biology curriculum, Michael’s goals for the lesson were focused on displaying and interpreting data: “to show me how they can display data for a start, for a table, to compare data as well…interpret what they found from the data, from the graph”—important skills for the practice of science. To introduce the activity, Michael led a discussion to elicit students’ prior knowledge of introduced species and showed an excerpt from a documentary on the history of rabbits in Australia, Invaders—Feral animals and pests in Australia (Film Australia Limited (Producer), 1999). He presented students with the following scenario: Two areas of land were studied over a five-year period. Both areas had populations of bandicoots, dingoes, and wallabies. A small number of rabbits were introduced to one of the areas at the beginning of the study. Bandicoots eat roots, seeds, and leaves; dingoes eat bandicoots, wallabies, and rabbits; wallabies eat grass, and leaves. [The scenario did not include information about what rabbits eat.]

Students were asked to predict the effect of rabbits on the populations of the three native animal species. Following a brief whole class discussion, Michael presented data from the study (see Table 7.3 and Table 7.4). The class discussed what needed to be considered in order to display the information graphically; however, Michael did not allow discussion of the suitability of various graph types. When a student suggested using a bar graph, Michael told students that they would be constructing a line graph without giving a reason for this choice of graph type. The meaning of dependent and independent variables, the need for a title for the graph and the choice of scale were discussed (i.e. Could the same scale be used for both axes? Could the same scale be used for both graphs?). Following this discussion, students were given time to construct a graph for each table of data. This was done manually as students did not have access to computers. Students wrote individual descriptions and analysis of the data after a brief whole class discussion about potential reasons for the observed changes. Table 7.3  Data provided to students for the area without rabbits Year Bandicoots Dingoes Wallabies

1 310 5 90

2 488 11 197

Without rabbits 3 505 11 281

4 505 12 293

5 505 10 290

4 500 12 72 5114

5 505 10 73 5120

Table 7.4  Data provided to students for the area with rabbits Year Bandicoots Dingoes Wallabies Rabbits

1 310 5 90 6

2 475 11 199 412

With rabbits 3 495 11 199 5122

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In the post-lesson interview, Michael said that he had initially used the 21st Century Numeracy Model (Goos et al., 2014) to help his planning but “probably not as thoroughly as I should have”. With prompting, he was able to describe dimensions of numeracy evident in the task, so even though his use of the numeracy model for planning had been limited, it provided a helpful means of reflecting on how numeracy had been addressed in the task. Our analysis with reference to the 21st Century Numeracy Model uncovered several dimensions of numeracy in the task Michael used. The task was situated within the context of learning about the impact of introduced species on native populations—a specific link to content within the Australian Curriculum: Science F-10 (ACARA, 2017a). Students employed their mathematical knowledge of statistics to represent and interpret the data they were given, using tables and graphs (representational tools) to mediate their thinking about the situation. Being able to represent data appropriately is an important skill within the discipline of science. Michael’s class discussion of variables and scale was important for helping students to develop this capacity, but additional discussion of appropriateness of graph types would enhance this aspect of the lesson. Most of the lesson was devoted to constructing the graphs by hand, so the opportunities for students to interpret the data or apply a critical orientation by asking questions about the data itself were limited. For example, the origin of the data (real or contrived) was not questioned nor were experimental conditions. Greater attention to this aspect of the data aligns with the need for students to consider the quality of evidence available when making judgments based on scientific data. Perhaps a lack of disciplinary knowledge of science meant that Michael was unable to explicitly attend to these aspects. There was potential in the task to address the dispositions of initiative and risk-taking, but these opportunities were not explored: students were not asked to consider the appropriateness of graphs other than line graphs or consider what could be gained by graphing the population of each species with and without rabbits. In summary, Michael’s focus on representing data revealed the devastating impact of introduced species on the populations of native species and provided opportunities for students to develop their capacity to represent and draw conclusions from data. Our analysis suggests that further explicit attention to numeracy (mathematical knowledge and critical orientation in particular) would have provided additional opportunities to enhance science learning and consolidate students’ understanding of statistics.

7.5  Discussion Karen and Michael both identified a scientific concept that could be made more accessible to students by explicit attention to the numeracy General Capability and took advantage of some of the many opportunities available. The vignettes and our analyses of the tasks illustrate how the approach has potential to address learning in science and mathematics. Additionally, they point to the potential of the 21st

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Century Numeracy Model (Goos et al., 2014) to assist teacher planning. We make three key observations from these vignettes. First, the scientific concepts targeted in the two lessons, radioactive decay and the impact of introduced species on native populations, were explored through examination of data—explicit attention to numeracy providing a means to aid understanding of scientific concepts. In the Australian Curriculum, collection and handling of data are identified as ways in which numeracy is developed and applied in science (ACARA, 2017b) and are an important aspect of the Science Inquiry Skills strand (ACARA, 2017a). There were, however, possibilities to further students’ understanding of how to translate observations into explanations via the use of data representations  – a key aspect of the practice of science (Quinnell et  al., 2013). Both teachers asked students to represent data graphically and initiated this part of the activity with a discussion of independent and dependent variables and appropriate scales for the axes. These discussions could have been more extensive (e.g. the appropriateness of different graph types), and there was limited attention paid to interpretation or critical appraisal of the data. Second, the lessons provided opportunities for students to develop their understanding of mathematical concepts. In Karen’s lesson, a more explicitly mathematical examination of radioactive decay though the simulation could have increased students’ understanding of probability and provided a more extensive qualitative introduction to exponential functions. There was an opportunity in Michael’s lesson to examine the percentage increase and decrease in the populations to further develop students’ proportional reasoning skills—a mathematical concept that underlies many scientific concepts (Hilton & Hilton, 2016). Extending the lessons in these ways would also have assisted students to transfer their mathematical knowledge from the mathematics classroom to science, revealing to students how mathematics and science are interwoven (Quinnell et al., 2013). Finally, Karen and Michael engaged to different degrees with the 21st Century Numeracy Model (Goos et al., 2014) to assist their planning for the integration of mathematics into a science lesson. These teachers may need more support before they are able to effectively use the numeracy model during planning to enrich the tasks, especially in the case of a critical orientation. This aspect of numeracy seems to be the most difficult for teachers to incorporate (e.g. Geiger, Forgasz, & Goos, 2015) but is a vital foundation for scientific enquiry. One of the limitations of our study in addressing integrated approaches to STEM education is the small number of science lessons on which we were able to draw. The focus of the project from which the data were drawn was to assist teachers to plan for numeracy in subject areas across the curriculum. For this reason, participating teachers were from a range of discipline areas and included only three secondary science teachers. As a consequence, only a limited number of science lessons were observed.

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7.6  Concluding Remarks There are many integrated approaches to STEM education (e.g. Becker & Park, 2011; Hobbs et al., 2018; Vasquez, 2014/2015). Addressing some of the criticisms of integrated approaches (e.g. English, 2016; Fitzallen, 2015) and challenges to implementation (e.g. ACARA, 2016) suggests that a school’s STEM vision is likely to draw on multiple approaches. The findings of our research add to new knowledge by (1) providing a new model for STEM integration and (2) proposing a mechanism through which to plan for the integration of mathematics (through the numeracy General Capability) and science. First, we offer a new model of STEM integration. We have presented two vignettes to illustrate how an across the curriculum approach to numeracy, which integrates mathematics and science through the numeracy General Capability, has potential to add to the existing models of STEM integration. We do not see this as a stand-alone approach to STEM education but as one that can sit beside other models in a school’s STEM vision. The vignettes demonstrate possibilities that exist for mathematics and science integration via an across the curriculum approach to numeracy. While we make no attempt to generalise from a limited number of vignettes, this research provides evidence of the potential for the natural integration of science and mathematics in secondary school contexts. In the type of the integration reported here, mathematics is used to promote ideas and concepts in another STEM subject—in this case science—as well as receiving explicit treatment in its own right. Thus, the vignettes point to ways forward in responding to criticisms of STEM teaching and approaches such as the diminished role of mathematics (English, 2016) and a failure to take advantage of mathematics in developing student capability in other STEM learning areas (Fitzallen, 2015). Our second contribution to new knowledge is to propose the use of the 21st Century Numeracy Model (Goos et al., 2014) as an effective tool through which to plan for the integration of mathematics (through the numeracy General Capability) and science. There was evidence in the vignettes that the numeracy model provided a mechanism through which teachers could plan and reflect on tasks. Additionally, our analyses of the tasks point to the potential of the numeracy model to be used as a planning tool to enhance the integration of mathematics and science. Finally, the vignettes also infer a potential shortcoming in STEM teaching and learning—an emphasis on knowledge acquisition and concept development (Hilton & Hilton, 2016; Howe et al., 2015) over attention to critical reflection on the findings of scientific enquiry, a finding consistent with commentary from Quinnell et al. (2013). As the processes of enquiry are vital to any STEM endeavour, further research is needed to address how teachers can provide greater emphasis on mathematics to promote critical aspects of science learning. Acknowledgement  This article reports on research funded by the Australian Research Council (Discovery Grant DP120100694). We acknowledge the contribution of the participating teachers.

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Chapter 8

Investigating the Epistemic Nature of STEM: Analysis of Science Curriculum Documents from the USA Using the Family Resemblance Approach Wonyong Park, Jen-Yi Wu, and Sibel Erduran

Contents 8.1  8.2  8.3  8.4 

Introduction Epistemic Nature of STEM Theoretical Framework: Family Resemblance Approach (FRA) Epistemic Nature of STEM Disciplines in SfAA and NGSS 8.4.1  Curriculum Documents 8.4.2  Content Analysis 8.4.3  Findings 8.5  Implications for Curriculum Policy in STEM Education References

                          

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8.1  Introduction Science, Technology, Engineering and Mathematics (STEM) education has been ubiquitous in recent curriculum policy and research literature during the past two decades (National Science and Technology Council, 2013; The Royal Society Science Policy Centre, 2014). It mainly has been advocated as an instructional approach that integrates different disciplines of human knowledge (Brown, Brown, Reardon, & Merrill, 2011; Bybee, 2010; Honey, Pearson, Schweingruber, and National Academy of Engineering,, and National Research Council, 2014), while the precise epistemic nature of STEM and how such epistemic nature applies in education remain relatively understudied (Chesky & Wolfmeyer, 2015). By “epistemic nature” we mean not only the characteristics of STEM knowledge but also the processes through which STEM knowledge is produced, evaluated and revised (Erduran & Dagher, 2014a; Hodson, 2014). An epistemic perspective on STEM

W. Park (*) · J.-Y. Wu · S. Erduran University of Oxford, Oxford, UK e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_8

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may help to highlight the shared features of the component STEM disciplines as well as differences among them. For example, all STEM disciplines might strive to achieve objectivity in their respective fields, but not all STEM disciplines share the same characterisations of what counts as a theory. What an engineer mean by a theory may not necessarily correspond to what a biologist might mean by the same term. In this chapter, we use the framework of the Family Resemblance Approach (Erduran & Dagher, 2014a; Irzik & Nola, 2011) as a basis for highlighting the epistemic similarities and differences between the constituent STEM disciplines as represented in key science curriculum documents. FRA presents the possibility to consider STEM as a cognitive-epistemic and social-institutional system whereby each constituent discipline is contrasted relative to aims, values, practices, norms, knowledge, methods and social context. Drawing on Wittgenstein’s linguistic philosophy, FRA allows for comparing and contrasting constituent disciplines of STEM as members of a “family” that share particular features but also highlights domain specificity where particular knowledge and practices are specific to the respective discipline. We focus on the epistemic components of each disciplinary system, highlighting the theoretical framework on the aims and values, practices, methods and knowledge. The aim is to help curriculum makers and teachers to recognise epistemic underpinnings of STEM disciplines and their importance in integrating STEM in both curriculum and pedagogy. After laying out the background and main ideas of FRA, we present an analysis of two curriculum policy documents, the Science for All Americans (SfAA) (AAAS, 1989) and the Next Generation Science Standards (NGSS) (NGSS Lead States, 2013), to examine their respective coverage of epistemic aspects of STEM. As a vision document, SfAA identifies what is important for the next generation to be scientifically literate and highlights the connections among the natural and social sciences, mathematics and technology. On the contrary, NGSS is a standards document and comprises performance expectations which incorporate all three dimensions from the science and engineering practices, core disciplinary ideas and crosscutting concepts. We selected these two documents to illustrate from the standpoint of science education how the epistemic aspects of STEM in different formats of curriculum documents could be analysed and to draw implications for curriculum policy with regard to integrated STEM education. Although we focus on the science curriculum documents in this chapter, similar analyses can be made to the curriculum documents in the other disciplines to inform STEM integration in each disciplinary context. The analysis was guided by our research question: What epistemic natures of STEM disciplines are addressed in the two key science curriculum reform documents?

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8.2  Epistemic Nature of STEM The history of science curriculum profoundly reveals a persistent tension between the products of science (i.e. scientific knowledge) and the process through which it is generated and accepted. Since the early twentieth century, when British science educator Henry Armstrong called for the inclusion of “scientific method” as a core curricular component (Armstrong, 1910), science educators have emphasised “scientific inquiry” (Schwab, 1958), “procedural knowledge” (Black, 1990) and “scientific practice” (NGSS Lead States, 2013)—all of which concerns how scientific knowledge is generated, evaluated and shared, albeit with varying motivations and focuses. Underlying these emphases was a shared belief that the epistemic aspects of science should be made explicit throughout all levels of formal education (Gott & Murphy, 1987; Osborne, 2016), in addition to scientific content knowledge. Infusing the epistemic nature of science has been advocated for its benefits in enhancing students’ understanding of scientific objects and processes, informed decision making, responsible citizenship and so on (Driver, Leach, Millar, & Scott, 1997; Hodson, 2014; Lederman, 2007). At the same time, research has suggested that these epistemic aspects are not naturally learned by simply engaging in the disciplinary practices (Bell, Mulvey, & Maeng, 2016; Pleasants & Olson, 2018) but should be instructed in an explicit teaching approach (Abd-El-Khalick, 2005; Akerson, Abd-­El-­Khalick, & Lederman, 2000). The emphasis on the context of disciplinary knowledge production has not been limited to science education. In technology education, nature of technology (NOT) and nature of engineering (NOE) have recently been established as a research and policy theme (Clough, Olson, & Niederhauser, 2013; International Technology Education Association, 2007; National Academy of Engineering, 2010; National Academy of Sciences & National Academy of Engineering, 2009; National Research Council, 2012). What is technology? What do engineers do? How does technology relate to society? These questions have stimulated technology educators’ interest in the distinct features of technology to be included in the curriculum (De Vries, 2005; DiGironimo, 2011; Gil-Pérez et al., 2005; Pleasants & Olson, 2018; Waight, 2014) and teachers’ and students’ ideas about these features (Fralick, Kearn, Thompson, & Lyons, 2009; Hammack, Ivey, Utley, & High, 2015; McRobbie, Ginns, & Stein, 2000; Rennie, 1987). Similarly, the epistemic nature of mathematics (NOM) has been of interest to a number of mathematics educators, most frequently with respect to how teachers’ beliefs about mathematics influence their teaching practice (Collier, 1972; Ernest, 1989a; Handal, 2003; Shahbari & Abu-Alhija, 2018). One interesting observation here is that while some epistemic features of different disciplines are very similar, others seem to be applicable only to a subset of STEM. For example, scientific knowledge and technological knowledge are similar in that they both rely on mathematical relationships and are subject to change and are fallible. However, as de Vries (2005) sharply noted, on the fundamental level, technological knowledge is distinguished from scientific knowledge in terms of its “normative” character, in that knowing technology encompasses making “judgements” about the functions and processes. Also, optimisation of solutions is much

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more important in engineering than in pure science (Pleasants & Olson, 2018). What makes the situation even more complex is that such disciplinary divergence in terms of epistemic practices occurs even within natural sciences and also varies from research group to research group. A notable example is found in Galison’s (1997) study of twentieth-century high-energy physics, where he demonstrated that physicists in different research traditions use different forms of arguments to support their claims. These complexities suggest that similarities and differences should be a central theme for understanding and describing “epistemic nature” of STEM in schools (Broggy, O’Reilly, & Erduran, 2017; Hodson, 2014; Irzik & Nola, 2014; Park & Song, 2019). In what follows, we suggest the Family Resemblance Approach (FRA) as a conceptual lens to view the diverse epistemic nature of the STEM disciplines, and we utilise it to examine two science curriculum documents from the USA.

8.3  T  heoretical Framework: Family Resemblance Approach (FRA) The concept of family resemblance has its origin in the German philosopher Ludwig Wittgenstein’s linguistic philosophy (Wittgenstein, 1953/2009). Using the example of the word “game”, Wittgenstein argued that a concept cannot be defined by a certain set of necessary and sufficient conditions—some games are not competitive, some are not entertaining, and some are without rules. Instead, a word is “a complicated network of similarities overlapping and criss-crossing” (Wittgenstein, 1953/2009, p. 36). A decade later, Thomas Kuhn took up the family resemblance concept in his seminal work The Structure of Scientific Revolutions (Kuhn, 1962/2012) to describe the scientific practice. An established scientific tradition, Kuhn explained, can be identified: … by resemblance and by modelling to one or another part of the scientific corpus which the community in question already recognises as among its established achievements [but not by] some explicit or even some fully discoverable set of rules and assumptions that gives the tradition its character and its hold upon the scientific mind. (Kuhn, 1962/2012, p. 45)

In the 2010s, FRA has drawn attention in the field of science education as a tool to conceptualise and portray NOS. Irzik and Nola (2014) understand science in terms of its cognitive-epistemic (aims and values, methods and methodological rules, process of inquiry, knowledge) and social-institutional characteristics (professional activities, social certification and dissemination, social values, scientific ethos). Irzik and Nola’s framework is based on the idea that these eight categories can be used as a lens to understand the similarities and differences among scientific domains such as astronomy, experimental physics and molecular biology (Irzik & Nola, 2014). They described science as: a cognitive and social system whose investigative activities have a number of aims that it tries to achieve with the help of its methodologies, methodological rules, system of knowledge certification and dissemination in line with its institutional social-ethical norms, and when successful, ultimately produces knowledge and serves society. (Irzik & Nola, 2014, p. 1014)

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Defining science this way allows revealing both the domain-general and domainspecific aspects of science in a holistic and coherent manner. FRA as an approach to NOS is gaining increasing attention among science educators (e.g. Alsop & Gardner, 2017; Hodson & Wong, 2017). Recently, Erduran and Dagher (2014a) significantly extended the original account of FRA and added three new categories—political power structures, financial systems and social values—which are becoming more significant in the contemporary scientific practice (see Table 8.1).

Table 8.1  Descriptions of the 11 FRA categories Category Aims and values

Description The key cognitive and epistemic objectives of STEM, such as accuracy and objectivity The manipulative as well as non-­ manipulative techniques that underpin STEM research The set of epistemic and cognitive practices that lead to STEM knowledge through social certification

Keywords Aim, value, goal, accuracy, objectivity

Method, scientific method, inquiry, process, hypothesis, manipulation of variables Observation, experimentation, Practices data, explanation, model, argumentation, classification, prediction Knowledge Theories, laws and explanations that Knowledge, scientific knowledge, underpin the outcomes of STEM inquiry formulation of knowledge, theory, law, model Peer review, validate, evaluate, The social mechanisms through which Social certification, dissemination, certification and STEM professionals review, evaluate collaboration and validate knowledge, for instance, dissemination through the peer review systems of journals Scientific norms, ethics, bias, Ethos The norms that STEM professionals being sceptical, caution against employ in their work as well as in bias interaction with colleagues Social values Values such as freedom, respect for the Culture, cultural, social values, environment and social utility society, beliefs, freedom, respect Conference, article, presentation, How STEM professionals engage in Professional writing, publishing, publication activities professional settings such as attending conferences and doing publication reviews University, research centre, How STEM is arranged in institutional Social organisations and settings such as universities and research institution, organisation institutes interactions Financial systems The underlying financial dimensions of Financial, funding, finance, STEM, including funding mechanisms economy, economical, budget Political power, research team, Political power The dynamics of power that exist structures between STEM professionals and within team leader, team members, researcher, gender, ethnicity, disciplinary cultures race, nationality Methods

Adapted from (Erduran & Dagher, 2014a)

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Fig. 8.1  FRA wheel: science as a cognitive-epistemic and social-institutional system (Reprinted with permission from Erduran & Dagher, 2014a, p. 28)

An aspect of Erduran and Dagher’s work is that it includes visual images as well as other pedagogical adaptations of FRA ideas to make the approach more relevant and applicable to science education (Erduran, 2017; Erduran & Kaya, 2018). There is now considerable number of studies that have used FRA in science education, for example in the context of science teacher education (e.g. Erduran, Kaya, Cilekrenkli, Akgun & Aksoz, 2020; Petersen, Herzog, Path & FleiBner, 2020), undergraduate education (Akgun & Kaya, 2020) as well as textbook (Park, Seinguran & Song, 2020) and curriculum (Cheung, 2020) analysis. As an example, the FRA wheel (see Fig. 8.1) provides a visual and holistic model to capture diverse NOS aspects, instead of a set of specific NOS statements to be transmitted to students. FRA itself does not provide, for example, some universally valid tenets about scientific methods or practices. Instead, FRA offers “a broader and more inclusive framework to capture various aspects of NOS, rather than discrete ideas about NOS tenets” (Kaya & Erduran, 2016). This characteristic of FRA as a “heuristic” makes it particularly suitable for comparing and contrasting diverse areas of human knowledge such as STEM. In the following, we use FRA to analyse SfAA and NGSS as examples of science curriculum documents to exemplify the potential of FRA in informing curriculum policy and practice.

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8.4  E  pistemic Nature of STEM Disciplines in SfAA and NGSS Curriculum documents as the guidelines for designing curriculum materials, planning instruction and assessing student performance are important to be studied, because they reflect not only the core interest of the curriculum makers but also their potential impact on teaching practice in schools (Olson, 2018). Olson (2018) examined nine science curriculum documents and found that NOS was insufficiently stated in these countries’ documents. Previous studies have demonstrated the contribution of the FRA framework as an analytical tool not only in facilitating science curriculum analysis but also in determining the gaps related to the NOS in the curriculum, such as NGSS in the USA (Erduran & Dagher, 2014a), the Junior Cycle Draft Specifications in Ireland (Erduran & Dagher, 2014b; Kelly & Erduran, 2018) and Turkish national science curricula from 2006 and 2013 (Kaya & Erduran, 2016). The findings of Kaya and Erduran (2016) indicated that the Turkish curricula underemphasise the social-institutional aspects of science, suggesting a need for further efforts. More recently, Park, Wu and Erduran (2020) used FRA to compare how recent science education standards documents from the USA, Korea and Taiwan portray the aims, values and practices of STEM disciplines. Their analysis showed a general lack of mathematics-related features in the documents and the variations across the three countries.

8.4.1  Curriculum Documents To demonstrate the potential of the FRA framework in revealing and informing the representation of the nature of STEM, SfAA and NGSS were selected for analysis. SfAA was published as an early-stage outcome of Project 2061 of the American Association for the Advancement of Science in an effort to initiate significant and lasting improvements in science education. Setting out what constitutes scientific literacy for the next generation, SfAA has since functioned as a basis for a number of science curriculum documents in the USA. In 2013, NGSS came out as the result of a multi-state effort to develop new standards that are “rich in content and practice, arranged in a coherent manner across disciplines and grades to provide all students an internationally benchmarked science education” (NGSS Lead States, 2013, p. xiii). Since its release, NGSS has been widely influencing the science curricula and classroom practices both in the USA and internationally (Sadler & Brown, 2018). We selected these two documents because they reflect what US ­science curriculum makers thought to be most important things to know in 1989 and 2013, respectively. Besides, since SfAA sets out the visions for science education, while NGSS represents the standards for ideas and practices that scientifically literate citizens should know, comparing the two can show how the emphasis has changed (or not) over time between the two distinct types of curriculum documents.

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Table  8.2 shows the structure of SfAA and NGSS. The table shows that both documents include sections that connect science to its neighbour disciplines and the ones that address the epistemic nature of these d­ isciplines, although neither SfAA nor NGSS explicitly mentions “STEM integration” anywhere in the documents. In SfAA, references to the nature of STEM disciplines are concentrated in Chapters 1 through 3, while in NGSS, references are made in both the standards and the appendixes. To get a holistic understanding of each document in terms of the nature of STEM disciplines, we included the entire document for analysis, including the appendixes, and front and back matters.

Table 8.2  Structure of SfAA and NGSS SfAA Front matter Recommendations for science literacy    1. The nature of science    2. The nature of mathematics    3. The nature of technology    4. The physical setting    5. The living environment    6. The human organism    7. Human society    8. The designed world    9. The mathematical world    10. Historical perspectives    11. Common themes    12. Habits of mind Bridges to the future    13. Effective learning and teaching    14. Reforming education    15. Next steps Back matter

NGSS Volume 1: The standards—arranged by disciplinary core ideas and by topics   Front matter    NGSS arranged by disciplinary core ideas    NGSS arranged by topics Volume 2: Appendixes   Front matter     A. Conceptual shifts in NGSS     B. Responses to the public drafts     C. College and career readiness    D. “All standards, all students”: Making NGSS accessible to all students    E. Disciplinary core idea progressions in NGSS    F. Science and engineering practices in NGSS     G. Crosscutting concepts in NGSS    H. Understanding the scientific enterprise: The nature of science in NGSS     I. Engineering design in NGSS    J. Science, technology, society and the environment    K. Model course mapping in middle and high school for NGSS    L. Connections to the common core state standards for mathematics    M. Connections to the common core state standards for literacy in science and technical subjects

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8.4.2  Content Analysis In line with similar studies (Erduran & Dagher, 2014a, 2014b; Kaya & Erduran, 2016), we used the descriptions of each category and a set of keywords to identify indicative statements of NOS, NOT, NOE and NOM in the two documents (Table 8.1). When the statements contained the keywords or similar words to imply the relationships between the performance expectations and the nature of features in the FRA categories, they were coded to the corresponding category. For example, the statement “Science investigations are guided by a set of values to ensure accuracy of measurements, observations and objectivity of findings” in NGSS (Appendix H, p. 98) was identified as a reference to aims and values of science. However, statements that did not conform to the FRA definitions were not coded, even if they included some of the keywords. Instead of counting how many times each category is addressed in the documents, we looked at whether the respective categories are being addressed at least once and, if so, what are the salient features being represented. This was because we were interested in the qualitative representation of each epistemic category rather than the frequency of references made to the categories. The analysis was conducted by two coders. Each coder coded SfAA and NGSS individually and selected the exemplary statements that showed each document’s description of the epistemic aspects of STEM. Any disagreements in coding were resolved through discussion between the coders.

8.4.3  Findings The results of the analysis on SfAA and NGSS are shown in Tables 8.3 and 8.4. The existence of at least one instance of a category is noted in the tables. As the tables indicate, most categories have instances except for practices of technology and methods of mathematics in NGSS. The following paragraphs illustrate example excerpts to provide a qualitative indication of how the documents address each category. First, in the case of NOS, “accuracy” appears in both SfAA and NGSS as an epistemic aim of science (see Table 8.5). With respect to methods, SfAA is more nuanced in terms of the kind of methodological approaches science utilises. For instance, SfAA makes reference to hypothesis as well as quantitative and qualitative methods, while NGSS is fairly broad in its depiction of methods in terms of measurements and observations. In terms of scientific practices, both documents refer to similar concepts such as evidence, explanations and predictions, all of which were suggested as important practices of science in Erduran and Dagher (2014a). While SfAA refers to scientific knowledge in a fairly generic sense and describes its tentativeness, limitation and universality, NGSS details the kinds of scientific knowledge in terms of theories and laws and explains what they are. Despite these minor varia-

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Table 8.3  Distribution of epistemic categories in SfAA Epistemic category Aims and values Methods Practices Knowledge

NOS + + + +

NOT + + + +

NOE + + + +

NOM + + + +

NOE + + + +

NOM +

Table 8.4  Distribution of epistemic categories in NGSS Epistemic category Aims and values Methods Practices Knowledge

NOS + + + +

NOT + + +

+ +

tions, NOS is generally well represented in SfAA and NGSS, which is unsurprising given the richness of the discussion on NOS in science education community during the past three decades (Hodson, 2014; Lederman, 2007). In the case of NOT, both SfAA and NGSS refer to the utility of technology in society as its core value (see Table 8.6). While SfAA focuses on the role of probability and risk in the context of aims and values of technology, NGSS emphasises the role of engineering design. NGSS does not refer to particular practices in relation to technology, whereas SfAA refers to mathematical models in the context of computer technology. The focus on materials in the development of knowledge in technology is evident in NGSS, whereas the emphasis in the case of SfAA seems to be primarily on scientific knowledge. The epistemic features of engineering are covered in both SfAA and NGSS, although NGSS has much more detail and nuance to how engineering practices work in all categories except for methods (see Table 8.7). When describing the aims of engineering, both documents stressed finding solutions to practical problems as its main goal, as opposed to science being primarily interested in providing explanations. Also, they both highlighted that engineers rely on science and technology to accomplish their aims. A significant variation between the two documents is the reference to practices such as argumentation and modelling. In parallel with NGSS’s emphasis on scientific and engineering practices (NGSS Lead States, 2013, Appendix F), it delineates the centrality of argumentation and reasoning in engineering as well as in science and also explicitly states that these practices are shared between the two disciplines. Such an emphasis reflects science educators’ ­increasing interest in argumentation as a core practice across school subjects (Erduran, Guilfoyle, Park, Chan, & Fancourt, 2019; Fischer, Chinn, Engelmann, & Osborne, 2018). On the contrary, SfAA refers to several steps of engineering design such as constructing problems and testing without comparing them to practices in other disciplines. Finally, in the case of NOM, a significant observation is that NGSS does not explicitly refer to the methods of mathematics (i.e. how mathematical inquiry is carried out), while there is some reference to them in SfAA (see Table 8.8). When it

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Table 8.5  Examples of NOS in SfAA versus NGSS Epistemic category Aims and values

Methods

Practices

Knowledge

SfAA Scientists try to identify and avoid bias. (p. 6) Scientists assume that even if there is no way to secure complete and absolute truth, increasingly accurate approximations can be made to account for the world and how it works (p. 2) Fundamentally, the various scientific disciplines are alike in their reliance on evidence, the use of hypothesis and theories, the kinds of logic used and much more. (p. 3) … they place on historical data or on experimental findings and on qualitative or quantitative methods There simply is no fixed set of steps … (p. 4) Science demands evidence. (p. 4) Science is a blend of logic and imagination. (p. 5) Science explains and predicts. (p. 6) Scientists see patterns in phenomena as making the world understandable. (p. 27)

Scientific ideas are subject to change. (p. 29) Scientific knowledge is durable. (p. 3) Science cannot provide complete answers to all questions. (p. 3) Science also assumes that the universe is, as its name implies, a vast single system in which the basic rules are everywhere the same. Knowledge gained from studying one part of the universe is applicable to other parts. (p. 2)

NGSS Science investigations are guided by a set of values to ensure accuracy of measurements, observations and objectivity of findings. (Appendix H, p. 98) Science investigations use a variety of methods and tools to make measurements and observations. (Appendix H, p. 98)

Science is both a body of knowledge and the processes and practices used to add to that body of knowledge. (Appendix H, p. 100) A scientific theory is a substantiated explanation of some aspect of the natural world, based on a body of facts that has been repeatedly confirmed through observation and experiment. (Appendix H, p. 99) Science knowledge is based upon logical and conceptual connections between evidence and explanations. (Appendix H, p. 98) Scientific theories are based on a body of evidence developed over time. (Appendix H, p. 99) Laws are regularities or mathematical descriptions of natural phenomena. (Appendix H, p. 99)

comes to the aims and values, SfAA describes at several places what mathematics is, what mathematicians seek to discover and both the intrinsic values (e.g. “its beauty and its intellectual challenge” [p. 15] and “the greatest economy and simplicity” [p. 16]) and its utility in the context of other disciplines such as science and engineering. On the contrary, NGSS only provides a limited account of what math-

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Table 8.6  Examples of NOT in SfAA versus NGSS Epistemic category Aims and values

SfAA In the broadest sense, technology extends our abilities to change the world: to cut, shape, or put together materials; to move things from one place to another; to reach farther with our hands, voices, and senses (p. 25)

NGSS The uses of technologies and any limitations on their use are driven by individual or societal needs, desires and values; by the findings of scientific research; and by differences in such factors as climate, natural resources and economic conditions. Thus technology use varies from region to region and over time. (p. 57) Methods Analysis of risk, therefore, involves Scientific discoveries about the natural world can often lead to new and improved estimating a probability of technologies, which are developed through occurrence for every undesirable outcome that can be foreseen—and the engineering design process. (p. 25) also estimating a measure of the harm that would be done if it did occur. (p. 32) None found Practices Using mathematical models of wave behavior, computers are able to process information from these probes to produce moving, three-dimensional images. (p. 124) Every human-made product is designed by Knowledge But just as important as accumulated practical knowledge is applying some knowledge of the natural the contribution to technology that world and is built using materials derived from the natural world. (p. 174) comes from understanding the principles that underlie how things behave—that is, from scientific understanding. (p. 26)

ematics is for by describing it as a “fundamental tool” for representing variables and relationships in science and engineering (Appendix F, p.  68). Similarly, there is much more coverage of types of mathematical knowledge such as theories in the case of SfAA, while NGSS is fairly limited in its discussion of the nature of ­mathematical knowledge, particularly how knowledge is generated and relates to other knowledge in mathematics. In summary, NGSS includes much less descriptions of mathematics as an academic discipline, although it acknowledges the close relationship between science and mathematics (NGSS Lead States, 2013, p. 138).

8.5  Implications for Curriculum Policy in STEM Education While numerous arguments have been advanced for the inclusion of an integrated STEM in school curricula worldwide, the precise nature of these inclusions needs further articulation. In this chapter, we addressed the epistemic dimension of technology, engineering and mathematics to be included in the science curriculum. A

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Table 8.7  Examples of NOE in SfAA versus NGSS Epistemic category Aims and values

Methods

Practices

SfAA Engineers use knowledge of science and technology, together with strategies of design, to solve practical problems. (p. 26) Engineering combines scientific inquiry and practical values. (p. 27) One goal in the design of such devices is to make them as efficient as possible—that is, to maximise the useful output for a given input (p. 117)

The basic method is to first devise a general approach and then work out the technical details of the construction of requisite objects (such as an automobile engine, a computer chip, or a mechanical toy) or processes (such as irrigation, opinion polling, or product testing). (p. 27) In its broadest sense, engineering consists of construing a problem and designing a solution for it. (p. 27) Designs almost always require testing, especially when the design is unusual or complicated, when the final product or process is likely to be expensive or dangerous, or when failure has a very high cost. (p. 29)

NGSS The end-products of science are explanations and the end-products of engineering are solutions. (Appendix F, p. 74)

The goal of engineering design is to find a systematic solution to problems that is based on scientific knowledge and models of the material world. Each proposed solution results from a process of balancing competing criteria of desired functions, technical feasibility, cost, safety, aesthetics and compliance with legal requirements. The optimal choice depends on how well the proposed solutions meet criteria and constraints. (Appendix F, p. 75) Scientific discoveries about the natural world can often lead to new and improved technologies, which are developed through the engineering design process. (p. 25)

In science and engineering, reasoning and argument based on evidence are essential to identifying the best explanation for a natural phenomenon or the best solution to a design problem. (Appendix F, p. 62) Scientists and engineers engage in argumentation when investigating a phenomenon, testing a design solution, resolving questions about measurements, building data models and using evidence to evaluate claims. (Appendix F, p. 62) Like scientists, engineers require a range of tools to identify patterns within data and interpret the results. Advances in science make analysis of proposed solutions more efficient and effective. (Appendix F, p. 72) (continued)

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Table 8.7 (continued) Epistemic category SfAA Knowledge Engineers use knowledge of science and technology, together with strategies of design, to solve practical problems. (p. 26)

NGSS Modelling tools are used to develop questions, predictions and explanations; analyse and identify flaws in systems; and communicate ideas. Models are used to build and revise scientific explanations and proposed engineered systems. Measurements and observations are used to revise models and designs. (Appendix F, p. 68)

recent framework to the nature of science in science education concerns the so-­ called Family Resemblance Approach which inherently places an emphasis on the epistemic categories of science. Hence, we capitalised on this framework to explore the epistemic aims, values, methods, practices and knowledge accounts in relation to nature of science, technology, engineering and mathematics as advanced in high-­ profile and influential science curriculum documents of SfAA and NGSS. In general, our result indicates that both documents have some references to most epistemic categories of STEM disciplines. However, several curricular omissions including the neglect of NOM suggest that the documents have limitation in addressing the epistemic aspects in a balanced and coherent manner. While there are many similarities between SfAA and NGSS (e.g. advocating the epistemic aim of “accuracy” in science), SfAA seems more nuanced in some aspect while NGSS in others. For example, while SfAA is more nuanced in terms of the kind of methodological approaches science utilises (e.g. reference to hypothesis as well as quantitative and qualitative methods), NGSS details the kinds of scientific knowledge in terms of theories and laws in a more thorough manner. With respect to a contrast of the reference to technology and engineering, NGSS seems to place more emphasis on engineering design, and extensive reference is devoted to engineering practices. A significant variation between the two documents is the reference to practices such as argumentation and modelling. Finally, in the case of NOM, a significant observation is that NGSS does not explicitly refer to the methods of mathematics, while there is some reference to this category in SfAA (see Table 8.8). There is much more coverage of types of mathematical knowledge such as theories in the case of SfAA, while NGSS is fairly limited in its discussion of the nature of mathematical knowledge. Part of the differences between SfAA and NGSS can be explained in terms of the different purposes of the two documents, the former being the statement of higher-­ level visions for science education and the latter a set of concrete standards for curriculum development and classroom practice. However, the comparison also tells us much about how the focus of the US science curriculum documents has changed over the two decades with regard to the nature of STEM disciplines, while the abstract ideals and visions were translated into more concrete curriculum standards. Our analysis shows that there are many places where NGSS elaborates on the visions set out in SfAA (e.g. the relationship between science and engineering), but it also suggests that several important ideas of SfAA has been lost in NGSS (e.g. the

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Table 8.8  Examples of NOM in SfAA versus NGSS Epistemic category Aims and values

Methods

Practices

Knowledge

SfAA Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. For others, including many scientists and engineers, the chief value of mathematics is how it applies to their own work. (p. 15) Part of the sense of beauty that many people have perceived in mathematics lies … in finding the greatest economy and simplicity of representation and proof. (p. 16) Mathematical thinking often begins with the process of abstraction—that is, noticing a similarity between two or more objects or events. (p. 19) Mathematical processes can lead to a kind of model of a thing, from which insights can be gained about the thing itself. (p. 20) Using mathematics to express ideas or to solve problems involves at least three phases: (1) representing some aspects of things abstractly, (2) manipulating the abstractions by rules of logic to find new relationships between them and (3) seeing whether the new relationships say something useful about the original things. (p. 19) As a theoretical discipline, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world. (p. 16) Mathematicians, like other scientists, are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory. (p. 16) A central line of investigation in theoretical mathematics is identifying in each field of study a small set of basic ideas and rules from which all other interesting ideas and rules in that field can be logically deduced. (p. 16)

NGSS In both science and engineering, mathematics and computation are fundamental tools for representing physical variables and their relationships. (Appendix F, p. 68)

None found

Mathematical and computational approaches enable scientists and engineers to predict the behaviour of systems and test the validity of such predictions. (Appendix F, p. 73)

Laws are regularities or mathematical descriptions of natural phenomena. (Appendix H, p. 99)

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nature of mathematics as a discipline and the interdependence of science, technology, engineering and mathematics). Given the rise of STEM education and the increasing interest in teaching the nature of the disciplines, more explicit consideration of the nature of STEM would be crucial in developing future curricula. In this chapter, we drew on the recent discourse on the nature of science to shed light on the epistemic aspects of STEM disciplines and their potential importance in integrated approaches to STEM education. More specifically, we highlighted how the FRA can point to specific curriculum emphases and omissions with respect to the epistemic nature of STEM. This way, FRA allowed us to illustrate what were the epistemic aspects of each discipline being highlighted in the curriculum document. Such information can be used for effective curriculum development and eventual implementation of STEM in teaching and learning such that there is coherence in how STEM domains are represented (Yeh, Erduran & Hsu, 2019). FRA not only provides a useful analytical tool for tracing curriculum content but also has the potential to clarify the epistemic foundations of STEM. While we focused on two key curriculum documents for K-12 science in this chapter, FRA would be a useful tool for analysing mathematics, technology and engineering curricula as well. For example, given that understanding the mathematical practice has emerged as one key goal of school mathematics (Ernest, 1989b; François & van Bendegem, 2007), it would be necessary for K-12 mathematics curricula to include how mathematics as a discipline operates in a broader enterprise of STEM and how it relates to the other three disciplines in terms of each epistemic categories of FRA. In this sense, FRA provides a useful lens for incorporating the rich discussion in the philosophy of mathematics (Ernest, 1989b), and of technology (Waight, 2014; Waight & AbdEl-Khalick, 2012) and engineering (Antink-Meyer & Brown, 2019; Pleasants & Olson, 2018) into curricular content that is suitable for students.

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Armstrong, H.  E. (1910). The teaching of scientific method and other papers on education. London: Macmillan. Bell, R. L., Mulvey, B. K., & Maeng, J. L. (2016). Outcomes of nature of science instruction along a context continuum: Preservice secondary science teachers’ conceptions and instructional intentions. International Journal of Science Education, 38(3), 493–520. Black, P. (1990). Science—The past and the future. School Science Review, 72(258), 13–28. Broggy, J., O’Reilly, J., & Erduran, S. (2017). Interdisciplinarity and science education. In K. Taber & B.  Akpan (Eds.), Science education: An international course companion (pp.  81–90). Dordrecht, The Netherlands: Springer. Brown, B. R., Brown, J., Reardon, K., & Merrill, C. (2011). Understanding STEM: Current perceptions. Technology and Engineering Teacher, 70(6), 5–9. Bybee, R. W. (2010). Advancing STEM education: A 2020 vision. Technology and Engineering Teacher, 70(1), 30–35. Chesky, N.  Z., & Wolfmeyer, M.  R. (2015). Philosophy of STEM education. New  York, NY: Palgrave Macmillan. Cheung, Kason Ka Ching. (2020). Exploring the Inclusion of Nature of Science in Biology Curriculum and High-Stakes Assessments in Hong Kong. Science & Education, 29(3), 491–512. Clough, M.  P., Olson, J.  K., & Niederhauser, D.  S. (Eds.). (2013). The nature of technology: Implications for teaching and learning. Rotterdam, The Netherlands: Sense Publishers. Collier, C. P. (1972). Prospective elementary teachers’ intensity and ambivalence of beliefs about mathematics and mathematics instruction. Journal for Research in Mathematics Education, 3(3), 155–163. De Vries, M.  J. (2005). The nature of technological knowledge: Philosophical reflections and educational consequences. International Journal of Technology and Design Education, 15(2), 149–154. DiGironimo, N. (2011). What is technology? Investigating student conceptions about the nature of technology. International Journal of Science Education, 33(10), 1337–1352. Driver, R., Leach, J., Millar, R., & Scott, P. (1997). A study of progression in learning about “the nature of science”: Issues of conceptualisation and methodology. International Journal of Science Education, 19(2), 147–166. Erduran, S., & Dagher, Z. R. (2014a). Reconceptualizing nature of science for science education: Scientific knowledge, practices and other family categories. Dordrecht: Springer. Erduran, S., & Dagher, Z. R. (2014b). Regaining focus in Irish junior cycle science: Potential new directions for curriculum and assessment on Nature of Science. Irish Educational Studies, 33(4), 335–350. Erduran, S., Kaya, E., Cilekrenkli, A., Akgun, S., & Aksoz, B. (2020). Perceptions of Nature of Science Emerging in Group Discussions: a Comparative Account of Pre-service Teachers from Turkey and England. International Journal of Science and Mathematics Education. https://doi. org/10.1007/s10763-020-10110-9 Erduran, S., Dagher, Z. R., & McDonald, C. V. (2019). Contributions of the family resemblance approach to nature of science in science education: A review of emergent research and development. Science & Education, 28(3–5), 311–328. Erduran, S., Guilfoyle, L., Park, W., Chan, J., & Fancourt, N. (2019). Argumentation and interdisciplinarity: Reflections from the Oxford argumentation in religion and Science project. Disciplinary and Interdisciplinary Science Education Research, 1, 8. https://doi.org/10.1186/ s43031-019-0006-9 Erduran, S., & Kaya, E. (2018). Drawing nature of science in pre-service science teacher education: Epistemic insight through visual representations. Research in Science Education, 48(6), 1133–1149. Ernest, P. (1989a). The impact of beliefs on the teaching of mathematics. In P.  Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249–253). New York, NY: Falmer.

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Chapter 9

Approaches to Effecting an iSTEM Education in Southern Africa: The Role of Indigenous Knowledges Judah Makonye and Reuben Dlamini

Contents 9.1  Introduction 9.1.1  Approaches to STEM Curriculum 9.1.2  Why Some STEM Approaches May Not Work in Developing Countries 9.1.3  Research Problem 9.1.4  Literature Review on iSTEM Frameworks 9.1.5  Theoretical Framework 9.1.6  Methodology 9.1.7  Data Analysis 9.1.8  Coding of Interview with Participants 9.1.9  An iSTEM Framework for Developing Countries 9.2  Conclusion References

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9.1  Introduction Science, technology, engineering and mathematics (STEM) education in developing countries offers new challenges since it requires a vision of what the curriculum should look like to address local issues. Taking into account local knowledge and understandings of the separate STEM subjects as well as how they are linked appears to be crucial and is often overlooked by policy makers and practitioners. Two examples are offered here involving medicine and weather forecasting to set the context and highlight the issues faced by people in developing countries. The first example refers to indigenous knowledge about the topic of inoculation, immunisation and vaccination. A participant in our research, Anneline, a Life Science educator, shared this story. She referred to a custom of the Shona people

J. Makonye (*) · R. Dlamini University of the Witwatersrand, Johannesburg, South Africa e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_9

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in Zimbabwe, Southern Africa. When children visited grandparents who lived far from their usual home, their grandmother would, on arrival, give the children some clay from an anthill to eat. Even older people visiting faraway places were advised to eat some soil from the new area on arrival. The Shona elders knew that it prevented the children from getting sick. From a Western science perspective, it was a very good thing to do because clay from a new place helped the children to build antibodies against the pathogens of the new place that their systems had not yet encountered. So, the powerful scientific notion of immunisation attributed to Louis Pasteur and Edward Jenner was discovered independently in Africa long ago. Anneline felt that an iSTEM curriculum could include some forms of indigenous knowledge, such as this example, to improve ownership of ideas. The African indigenous people had a deep knowledge of science, but they did not have the language of description that Western science provides. A second example is taken from indigenous weather forecasting. Old people have been able to forecast rain by the direction the wind was blowing. The rain winds were called “nhurura” meaning “causing to fall”. When the winds blew in another direction, they would tell the people that this year there would be no or little rain. This indigenous knowledge needs to be used and combined with canonical science knowledge to develop a suitable iSTEM curriculum relevant to children in developing countries. International comparisons show governments’ universal pre-occupation with STEM education, buoyed by a shared assumption that STEM education promotes innovation and economic competitiveness (see, e.g. English, 2016; the US National Science & Technology Council, 2013; The Royal Society Science Policy Centre, 2014). To begin these innovations, particularly in developing countries, we need to motivate and inspire our school students so that they can aspire to a future in STEM. Research into STEM curriculum has been around for some time (e.g. Stains et al., 2018; Williams, 2011), yet (Charette, 2013), among others, regards the STEM crisis as a myth. We strongly disagree with Charette, because in our quest to gain knowledge to solve new problems and find better solutions for old problems, curriculum reform must be never ending. In many countries, particularly in Africa, iSTEM education is still in its infancy. Traditional approaches that teach the sciences and mathematics separately as if they are not related are still the norm.

9.1.1  Approaches to STEM Curriculum STEM education is an integrative approach to the organisation and instruction of science, technology, engineering and mathematics in school. Roberts (2012) envisages a situation where STEM can be taught as one subject at primary school. Kelley and Knowles (2016) regard an iSTEM education as an approach to teaching the

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content of two or more STEM subjects in the realm of STEM practices centred on authentic problems to deepen the understanding of the domains. On the other hand, Vasquez (2015) argues that “STEM education is a range of strategies that help students apply concepts and skills from different disciplines to meaningful problems” (p. 10). The key is to apply what has been learnt where relevant. Many approaches have been proposed for iSTEM. Some argue for separate specialist STEM schools, inclusive STEM schools and schools with STEM-focussed career and technical education (Timms, Moyle, Weldon & Mitchell, 2018). Honey, Pearson and Schweingruber (2014) highlight that STEM integration should be made explicit. They note “that integration across representations and materials, as well as over the arc of multi-day units, is not spontaneously made by students and therefore cannot be assumed to take place” (p. 5). Thus, practitioners need to take advantage of any contexts that can make inter- and multidisciplinary STEM connections explicit to both students and educators. The general view is that STEM integration must be a gradual process and that this integration can be problematic if students’ basic knowledge in the separate disciplines is weak. Honey et al. (2014) argue that strong disciplinary knowledge correlated with real STEM integration and remarked that the expertise of educators in STEM settings was a critical factor in determining the success of iSTEM education. They cautioned that evidence gathered so far does not rule out continued separate teaching of distinct disciplines in favour of their integration. In many countries, integrated STEM education has been introduced in the face of falling interest in STEM subjects in the hope that it will improve motivation towards STEM subjects and uptake of STEM careers (Anderson, 2017). Also Tytler, Osborne, Williams, Tytler and Cripps Clark (2008) observed that young people generally form their career aspirations before the age of 14. They thus recommended that introducing learners to STEM careers must start with teaching them STEM subjects in upper primary and lower secondary school. It was observed that current approaches to teaching mathematics and science failed to engage learners. English (2017) and Jho, Hong and Song (2016) suggest that marrying art to science to create STEAM could be a useful way to attract young learners which appears to be already happening in South Korea. English and King (2015) argue that good examples of STEM tasks can involve aerospace design to cater for mathematical physics and geometric forces. They also argue that problem scoping is very important and that the more time learners spend on this, the better they become at solving problems. Problem scoping (Atman et al., 2007) involves identifying the boundaries of a problem, including pertinent issues to be addressed, and constraints to be met which then leads to idea creation. In particular, they warned that past experiences and the first ideas that come to mind can limit thinking.

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9.1.2  W  hy Some STEM Approaches May Not Work in Developing Countries Since learning is situated (Brown, Collins, & Duguid, 1989), and learning contexts are so different, an integrated STEM curriculum cannot be readily adopted from another context, particularly for developing countries. While the suggested iSTEM approaches in developed countries are varied (Marginson, Tytler, Freeman, & Roberts, 2013), it will still be necessary for developing countries to develop their own iSTEM curriculum. Further, developed countries typically have highly developed technologies that may not be available in developing countries. Therefore, it is important to start with STEM education that takes into account local resources and epistemologies. It is always questionable to import knowledge wholesale without attempting to adapt it to local contexts. Integrated curriculum is not new to South Africa. In 1998, South Africa introduced an outcome-based curriculum. One of the keystones of that curriculum was the philosophy that knowledge does not exist in isolation and that in the real world the best solutions for problems call for the application of diverse knowledge bases. It was argued that “the principle of integrated learning is integral to outcomes-based education … integration ensures that learners experience the Learning Areas as linked and related” (Department of Basic Education, 2010, p. 5). The curriculum also stated that learners must be able to “identify and solve problems and make decisions using critical and creative thinking” (p. 1). These goals and objectives showed that in general learners were expected to apply their knowledge in solving open-­ ended real-world problems connected to the workplace and daily life. Even though successive South African curricula argued for the integration of subject disciplines, in practice, no specific action plan had been proposed to facilitate that subject integration. This became an important criticism of the outcome-based curriculum of South Africa. The curriculum adopted in 2011 was the opposite and emphasised the teaching and assessment of the atomised distinct and separate subjects in a prescriptive manner. This suggested that even though education policy advocated learners experience and integration of the subjects they learnt, in practice this was not done. A potential way forward is to develop a framework such as iSTEM to guide and support implementation. For a long time in South Africa, the teaching of the sciences was done with strong framing and classification of discrete subject disciplines (Bernstein, 1975, 2018). Biology, Physics, Chemistry and Mathematics were taught as separate subjects by specialist teachers during the final years of schooling. It was hoped that learners would eventually see the connections between the subjects (Timms et al., 2018). In the earlier years at school, the science subjects were studied as General Science, but the scenario of teaching and learning these subjects in silos in the final years of schooling as if they are not related to each other is now being challenged by iSTEM researchers.

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9.1.3  Research Problem Developing countries, particularly in Africa, are late-stage importers and implementers of technology. Africa has many valuable resources such as minerals, good climate and fertile soils. It is a net exporter of unprocessed minerals such platinum, iron and chrome, yet it imports finished products made from them at higher prices. African nations face great economic challenges, and her people are poor compared to other continents. This is largely because of a lack of technological understanding and innovation. Africa needs to develop its own industries to process her raw materials so that they can develop products that can be traded with the international community. Therefore, it is important to develop an iSTEM education to motivate this development. In this, community involvement and harnessing indigenous knowledge are important. Like Singapore, it needs to marry Western science and traditional science in order to prosper (Jho et al., 2016). Because of economic challenges, African schools and higher education institutions are mostly underresourced to participate in the inquiry that STEM education brings. Further, some Western-­trained scientists do not find suitable jobs when they return to their African homes, so they return to the West. If these scientists are trained to use local knowledge for local contexts, but not excluding worldwide scientific systems in this, they are likely to remain in their countries and contribute to local industrial growth. Integrating STEM in education places new demands on teachers. Bursal and Paznokas (2006) report that teachers who are not sure of teaching a topic, such as with many STEM themes, are prone to skip that topic or teach it procedurally rather than conceptually. They note that such teacher incapacity damages both student learning and students’ attitude towards the subject. Teachers might undermine the program because of their lack of knowledge and understanding. Many teachers have learnt STEM subjects separately at school and have often specialised to teach one of the subjects such as Mathematics or Life Sciences. Therefore, it is a challenge for them to teach a connected and integrated curriculum. They have never seen this discipline taught so they do not have experience of how it is done. Therefore, the pedagogical framework and methodology of teaching iSTEM needs to be visible for teachers just as STEM integration must be explicit to learners. If an integrated STEM curriculum is to be taken seriously in South Africa, there is a need for teachers to be supported to design and implement iSTEM in their classrooms, and to do that, a pedagogical framework is needed from which to design effective professional development. The research question that is considered in this chapter is: What pedagogical framework can be proposed for an iSTEM curriculum for developing countries?

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9.1.4  Literature Review on iSTEM Frameworks To inform the development of an iSTEM framework for a developing country, a literature review was undertaken which examined a range of integrated STEM frameworks from a variety of other countries. To begin, Vasquez (2015) proposed the inclined plane model for STEM integration. The scale starts with learning concepts and skills in separate STEM subjects (Disciplinary—Level 1) and then moves on to learning concepts and skills in different subjects all of which focus on a common theme (Multidisciplinary—Level 2), to learning concepts and skills from two or more STEM subjects in which learning is tightly connected (Interdisciplinary— Level 3) and finally to solving real-world problems where the STEM subjects become less of a focus (Transdisciplinary—Level 4). “This happens when students apply skills from math and science seamlessly without asking ‘is this math or is this science?’” (Vasquez, 2015, p. 14). Based on a situated theory of learning (Brown et al., 1989), another model was proposed by Kelley and Knowles (2016) that used pulleys to connect the STEM discipline practices. The model has four components, science enquiry, technological literacy, mathematical thinking and engineering design, as pulleys connected by a rope, which is the community of practice. The model from Timms et al. (2018) of STEM integration regards the different roles of the subjects in supporting each other in problem contexts. The sciences are seen as helping to understand the universe, whereas mathematics provides models and representations to the sciences. Preliminary research found that STEM approaches improve learner outcomes in the sciences but not necessarily in mathematics. Engineering is seen as providing technology, which is enabled by the sciences and mathematics to solve real-world problems that people encounter. This framework by nature is integrative from the start as it describes the different roles of each discipline in the learning situation, but remains challenging to implement. Another framework is suited to specialised STEM schools (Erdogan & Stuessy, 2015). The learners at these schools are selected based on capability and interest (Pfeiffer, Overstreet, & Park, 2010). Erdogan and Stuessy’s (2015) ecological-­ collaborative model for specialised STEM acknowledges that STEM teaching does not occur in a vacuum. All stakeholders within the school, particularly highly trained teachers, and outside the school, such as community leaders and experts, work together to support learners. The framework proposes that participants’ efforts succeed based on rigorous disciplinary knowledge the learners must acquire. While this framework situates STEM curriculum, the issue of specialised STEM schools means that many learners are excluded. This raises social justice issues in education. Stohlmann, Moore and Roehrig’s (2012) framework considers inter-­ institutional collaboration in teaching STEM.  Furthermore, it emphasises professional development which is crucial in integrating STEM in developing countries. This is because knowledge is developing so rapidly that content and methodology must be frequently shared between teachers to increase their capability to teach

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the subject and increase their confidence in the subject. This hedges against poor-­ quality teaching that can have unproductive effects on student learning. Other elements are contextual factors relating to learning environments. In particular, the boundaries between formal and informal learning are removed. Gerber, Marek and Cavallo (2001) regard formal learning as learning that occurs in schools, is directed by the teacher and is usually discipline specific. On the other hand, informal learning is regarded as less structured, often occurring outside school with little teacher direction. Finally, Stohlmann et al. (2012) suggested a framework of support, teaching, efficacy and materials (s.t.e.m). The support included inter- and intra-institutional partnerships and professional development. The teaching incorporates lesson planning and classroom practices such as conjecturing and justifying one’s thinking as well as finding patterns, inquiry and collaborative learning. Lesson planning includes understanding students’ misconceptions and focussing on big ideas. Efficacy is related to positive disposition to STEM and dedication, while the materials included, among others, kit for use in activities as well as laboratories. The challenge is to consider key recommendations from these models and to determine how they could be adapted and developed for the South African context. For STEM integration to be possible, it will be necessary to remove the traditional barriers between the STEM domains (Kelley & Knowles, 2016). Teachers will need substantial support and will need to learn to work together in collaborative teams to develop integrated STEM tasks and lessons. Collaborative actions will be an important part of the framework where all actors act in symbiosis for a common goal, whether in teaching or carrying out investigations in pursuing an objective. But what is the role of the learner when introducing such change in curriculum and pedagogy?

9.1.5  Theoretical Framework To develop a theoretical framework for iSTEM in South Africa, the work of Bybee (2010, 2013) helped to provide an approach to support teachers and school leaders. Bybee (2013) proposed the 4Ps as a way of providing for all dimensions of STEM education. These dimensions are purpose, policy, programs and practice, for which the questions asked were: What is the Purpose of STEM education? What Policies will support STEM education? What Programs are needed to implement STEM education? and What Practices are most appropriate for STEM Education? (p. 92)

The study discussed in this chapter is focussed on the practices that support iSTEM for a developing country. To Bybee, “practices are the specific strategies and methods used by STEM teachers” (p. 92). However, practices do not exist in isolation of the other three Ps; they are closely related to the purpose, the policies and the programs.

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In addition to recommending the 4Ps, Bybee (2010) proposed a framework for implementing STEM. His model is grade based and emphasises core competencies in science, mathematics, engineering and technology. Central to the model are STEM contexts based on life and work situations encompassing environment, resources, health and other current authentic problems. This model is useful but needs to also have a social dimension, in particular the indigenous and cultural knowledge of the locality of the school. That way there is less “cultural conflict” (Bishop, 1988). Such practice dispels the notion within some communities that the curriculum and Western knowledge are imposed on them at the expense of indigenous knowledge. However, since learning is situated and inseparable from the context in which it occurs (Brown et al., 1989), classroom-based learning may not be readily transferred to out-of-school contexts and problems. Solving real-world problems is important for individuals as well as society in general. It is presumed that one of the most important roles of education is to promote a country’s sustainable development. Education is regarded as an investment that must give a return to the individual and society. The argument is that if education cannot make people’s lives better through helping solve problems of national development, it is ineffective and needs to be revamped. In particular, education is seen as apprenticeship in learning to solve real problems (Brown et al., 1989). This is because it cannot be always assumed that transferring learning from one situation to another is possible. In Southern Africa, situated learning of necessity needs to link to local indigenous knowledge systems. Africa is resource rich but has poor local communities, and iSTEM can help to reverse this. Horsthemke (2004) calls for the valorisation and legitimising of indigenous knowledge. This creates a healthy interface between Western science and indigenous knowledge systems that enables iSTEM to prosper. Thus Western exogenous knowledge needs to work together with local endogenous knowledge for iSTEM to have a viable base. We argue that the valorisation of universal knowledge needs to occur together with indigenous knowledge (Horsthemke, 2004). As Horsthemke (2004) argues, the dualisms of “indigenous knowledge” and “science” are not helpful in advancing understanding. What is required is to embrace knowledge diversity because every epistemology has its limits.

9.1.6  Methodology This qualitative study aimed to investigate possibilities rather than prove and hypothesis (Yin, 2011). Data were collected through interviews with mathematics, science, engineering and technology teacher educators from teacher education institutions in South Africa catering for undergraduate and postgraduate students. These participants  were familiar to the authors and were willing to openly share their views on STEM education. All the participants had doctorates in education in their specialist areas and came from five different teacher education institutions in South

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Table 9.1  Participant backgrounds Participant (pseudonyms) Anneline, 45 Bernard, 41 Charles, 47 Chikede, 51 Denise, 44 Ephraim, 57 Felistus, 52 Grace, 43 Happy, 58

Education specialisation Life Science Environmental Science Physical Science Life Science Mathematics Physical Science ICT and Engineering Design Life Science Mathematics

Qualifications BSc, Dip Ed, PhD BSc, MSc (Physics), Dip Ed, PhD BEd, MEd, PhD BSc, MSc, Dip Ed, PhD BSc, MSc (Maths), Dip Ed, PhD BSc, MSc (Chemistry), Dip Ed, PhD BEd, MEd, PhD BEd, MEd, PhD BSc, MSc (Maths), Dip Ed, PhD

Africa. There were three life science educators, two mathematics educators, one educational technology and engineering educator, one environmental science educator and two physical science educators. Their teaching experiences ranged from 8 to 30 years (Table 9.1). In Southern Africa, more capable school leavers opt to study Science degrees such as BSc or better. In general, those who just pass high school examinations study education not because it is their first choice, but because it may be the “only” option available to them. After graduating many of the “science” students will come back to teaching if they are unable to secure employment in a science field. The “education” students soon find that education was not a bad choice after all. Therefore the participants in this study were highly qualified and dedicated professionals who had pursued many years of study and teaching experience. Face-to-face interviews were conducted with each of the teacher educators to determine what they considered to be the most important elements of an iSTEM framework, how this could be implemented in schools in South Africa, what were the challenges to implementing this framework and how these challenges might be overcome. They were also asked: 1 . What is your understanding of indigenous science and mathematics knowledge? 2. Can you provide me with some examples of indigenous science? 3. To what extent do you think indigenous science and mathematics knowledge is important in education? 4. What role if any can indigenous science and mathematics knowledge play in the development and implementation of an ISTEM curriculum in this part of the world? 5. Suggest ways to implement a quality STEM integration program in the school system in South Africa. Interviews were audio-recorded and transcribed verbatim for analysis.

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9.1.7  Data Analysis Data analysis focussed on interview transcriptions with the nine teacher educators. The method used in analysing data is that of thematic content analysis (Roberts & Pettigrew, 2007). There were three levels of analysis—the first level involved identifying common ideas and coding descriptions of what each participant said concerning the question: What pedagogical framework can be proposed for an iSTEM curriculum for developing countries?

The second level involved linking and classifying themes from the codes. The themes helped to pull the broader patterns of meaning suggested by the codes. Thirdly, the emerging themes were compared with the theoretical framework and other research. In the presentation of data which follows, the second and third level analyses were combined followed by a summary about the suggested factors in the iSTEM pedagogical framework for developing countries.

9.1.8  Coding of Interview with Participants In this section, key ideas from the interviews are presented. Anneline strongly disagreed with the notion of projects as a way of infusing iSTEM although she acknowledged that the separate STEM subjects could be linked to show connections. She perceived an iSTEM education as instrumental only to furthering the understanding of separate STEM disciplines and that iSTEM is useful for cross-disciplinary investigations with the end being the development of disciplinary knowledge. To Anneline, the iSTEM curriculum is important because it helps learners to experience the strong relationships between concepts from different STEM subjects, and its advantage is the strengthening of concepts and skills in as far as learners will, for example, realise that biology concepts can be enhanced when taught alongside mathematical concepts. For example, in heredity biology, Mendelian heredity on dominant and recessive genes can be better understood if the biological topic is taught alongside the related mathematical topics. These are permutations and combinations alongside probability theory and probability distributions such as Bernoulli, binomial, hypergeometric and others. These topics can  illuminate the topic of heredity and offspring  with much deeper understanding. Similarly, the topic of movement in biology can be linked to the physics concepts of lever, fulcrum, load and work. If muscle energy is also taken into consideration, the ideas of metabolism come into play, so bio-­ chemistry ideas become explicit. There are also mechanics or applied mathematics concepts when one studies movement caused by a joint. Nerves also pass synapses to control muscle movement, so the study of electric currents (physics) comes into play.

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Anneline’s views have bearing on curriculum policy and planning. She argued that for co-teaching to happen, there needs to be political support. The curriculum must be designed so that when the topic of heredity or movement in the skeleton is taught, specialist mathematics, physics and chemistry teachers must also be there so that each teacher teaches requisite specialist concepts on that topic. That way, STEM integration takes place, and students get a more powerful grasp of the subject matter from interdisciplinary points of view. Anneline believed that it is not possible for STEM to be taught by one teacher particularly at the high school level and that it is only at primary school that a single teacher could teach an iSTEM curriculum. At high school one teacher cannot be expected to do that because the disciplines are more challenging. Therefore team-teaching involving cooperation and collaboration might work although it would have curriculum implications for textbooks and examinations. Anneline also gave an example of the dichotomy between theory and practice in some cases. She said rural tomato farmers know how to successfully grow tomatoes, but do not understand the scientific concepts and principles behind it. They know very well the tomato pests and the pesticides to treat them or the amount of fertiliser for each plant to get the best crop. Yet, when agricultural graduates try to grow tomatoes using their scientific knowledge, they are not as successful. They have superior theoretical knowledge but practically they fail. These comments suggest scientific knowledge alone is not sufficient to solve real problems, hence, the need for iSTEM, which aims to bridge this gap between theory and practice. Chikede talked about making connections in the curriculum through investigating and monitoring weather. He suggested learners might use a rain gauge to measure the rainfall in an area over a month, draw statistical tables and graphs to represent the data and then analyse the data to find out the quantity of rain per day. In particular, they can also observe the wind, the clouds and the temperature before, during and after the rain and measure the acidity of the water. He stated “These investigations help learners to integrate STEM and realise that it helps them to understand and adapt if not control the environment to their advantage”. Bernard was of the opinion that culture, politics and language are important in iSTEM education. He argued that we cannot separate people’s humanity and their indigenous knowledge from successful iSTEM education, particularly in developing countries. For example, there is the phenomenon of distillation  – the Shona people have been making alcoholic spirits in their homes for a long time. Another example is that of smelting iron from iron ore. These technologies were there before the arrival of Western science. What is required is to build from there. Another example given was on environmental management. Bernard suggested: Ask learners to collect materials from dustbins from two or three different areas of a city … ask children to classify the materials into different classes as to what they are made of and what was their purpose. In doing so they learn statistical skills of sorting. Further they try to find out how the material was made, this leads to engineering technology. When they look at what constitutes the waste, they enter into the field of chemistry and chemical engineering say if they are plastics. If metal it’s still chemical engineering and mechanical engineering.

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While these activities might not really give learners hands-on experience, it helps them to learn the importance of science, technology, engineering and mathematics, particularly as they are applied to produce goods that people need in society. It is important to remember that traditionally indigenous science was not separated into different disciplines. All knowledge, whether social, philosophical, mathematical and scientific, was an integrated whole, passed orally from one generation to the next through narratives. Therefore, it is a good example of what we are trying to build as an integrated knowledge structure. Charles argued that there are some topics across two or more disciplines whose concepts can overlap. For example, vectors in mathematics readily connect with the physics concepts of displacement, velocity and gravity, or geometric transformations connect to reflection, rotation and shears. Once the mathematics basics have been taught, then learners could write algorithms for making those transformations. He argued that collaboration and cooperation between teachers of different disciplines must be done in teaching. Like Anneline, he thought that one teacher alone cannot teach a topic in an iSTEM curriculum. A physics teacher would teach vectors for another end not necessarily pursued by a mathematics teacher. Similarly a mathematics teacher might pursue the notion of vectors for other purposes such as geometrical proofs. Thus it would be important for teacher to collaborate, identify topics and plan what can be taught simultaneously. The assumption being that when STEM subjects are taught that way, it helps to deepen learner understanding within and across disciplines. He argued that basic disciplinary concepts and skills are necessary to learn before integration is possible. Charles argued that particularly in Africa there are other variables that affect uptake of iSTEM, such as too much political interference so that the iSTEM curriculum initiatives are thwarted because they are never prioritised. In fact, governments do not understand iSTEM. It is the academics who recognise the need for iSTEM education for countries to capitalise on their resources to make consumer goods and thus raise the quality of life. Charles argued that academics can be intimidated and because of perceived corruption there is no one who stands for these important ideas of curriculum innovation. It is not uncommon in African countries that academics such as doctors and professors dabble in politics and are given political appointments, such as ministerial positions. Such scenarios are not common in developed countries where academics concentrate on academia and politicians concentrate on politics. There is separation and mutual respect for each other’s professions. Therefore, it is important to come up with strategies to convince politicians of the importance of the uptake of STEM curriculum in schools. Governments must enable innovative curriculum developments. Denise, Ephraim and Felistus’ responses were somewhat similar. They argued that for successful iSTEM curriculum implementation, young children must be apprenticed to certain industries so that they grow and develop certain interests from a young age. “This helps them to grow to be specialists in their chosen trade”, said Denise. They gave the example of young children in Japan who take up electronics as a hobby. In her interview, Grace exclaimed:

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In Africa the education is too bookish and not linked to the practical world … graduate engineers must start working at the shop floor with technicians to appreciate the need to marry theory and practice … those graduates who take up management positions without practical experience do not make good managers.

She also said “a good builder must start by learning how to dig a foundation, and not just start at the top … for a strong industry, theory and practice need to have symbiotic relationship”. Happy observed that “in some countries such as Nigeria, Science and Technology are taught from grade 1 as a single subject. Mathematics is compulsory for all stages of education including undergraduate. The integrated STEM curriculum proper does not exist”. Themes Emerging from the Data The interviews in general show different views on iSTEM.  One group regards iSTEM as a means of improving school grades in STEM subjects. They regard iSTEM as a way of making subject disciplines visible. Even though integration was supported, the main message was to return to the original discipline. This interpretation could be referred to as Stage 1 level of iSTEM because it is still focussed on the acquisition of concepts and skills inside the classroom. However, this stage is important for an iSTEM curriculum to build basic disciplinary knowledge, which can be called upon when learners solve the open-ended problems that drive iSTEM. Anneline and Bernard could have been influenced by their educational background. Before Anneline became an educator, she trained as a science specialist studying the sciences as her majors. She studied education as a postgraduate diploma to become an educator. Her basic academic training seemed to influence her view that STEM education must aim to strengthen the canonical knowledge of the separate disciplines, probably in a way that she studied them herself. Other academics started as education majors, with science and mathematics being education components. These practitioners seemed to have a strong pedagogic orientation and were not worried about the subjects being taught in an integrated way. In contrast, Anneline held that the disciplines themselves need to be the focus of STEM and not their application to problem-solving outside the classroom. This group of participants hold a traditional view of education, where STEM education activities are regarded as instrumental in strengthening the learning of the separate science, technology, engineering and mathematics disciplines. These participants do not see STEM education as an end in itself but as a way to for learners to see how these disciplinary knowledges are closely connected to each other. Vasquez (2015) regarded this teaching as interdisciplinary where students “learn concepts and skills from two or more disciplines tightly linked to a common theme so as to deepen their knowledge” (p. 13). It is clear that the primary focus here is the theoretical and disciplinary knowledge with the aim of passing examinations. Under this theme was the argument that it would be difficult for learners to do the STEM

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tasks without strong content knowledge in each of the disciplines. Similarly Erdogan and Stuessy (2015) argued for rigorous disciplinary knowledge for STEM education. The other group interviewed (see Bernard, e.g.) recognised that more can be done than in the traditional mathematics and science curriculums characterised by visible pedagogy, strong classification and framing. They argued that science is part of society and cannot be divorced from it. There is the argument that science has to be human and has to incorporate the human elements such as learners’ environment, language and culture; that is, education must be situated in the contexts in which it occurs. This group argued that for iSTEM to be relevant, it needs to particularly take stock of the indigenous knowledge of African societies. They argued that this mesh with textbook science will strengthen the acceptance of iSTEM. Then there will be home-grown solutions that respect indigenous knowledge. This group also referred to the political factor. They argued that very little can be done in developing countries without the express support of politicians. Most politicians focussed on winning and maintaining political power for its own sake. Many politicians are also uneducated and largely unaware of the importance of iSTEM in developing their countries. This group of participants argued that STEM education must be based on realistic problems that learners and their communities confront in their living contexts - a view similar to Bybee (2010) who argued that STEM must address “Environment, Resources, Health, Hazards, Frontiers” problems. Also Bybee (2013) argued “one must consider the use and application of that knowledge, not just the acquisition of knowledge as a primary purpose of STEM education” (p. 64). According to some participants, there is a lot of cultural knowledge that exists within local communities that is not capitalised on when teaching STEM subjects in schools. There is a strong feeling that this is a key factor in the success of STEM education in developing countries as learning is situated in the contexts it takes place (Brown et al., 1989; Lave & Wenger, 1991). In addition, Bishop (1988) argued that mathematics and hence science cannot be culture-free or value-free. For example, in some societies, girls are not expected to do well in mathematics or sciences because those are regarded as male domains. These are issue of culture and values and affect the learning of these STEM subjects. Another theme that emerged was the need for political and social support for success. If there is no strong political and financial support, very good ideas about improving the curriculum may not be realised. Kelly and Knowles’s (2016) argued that a sustainable STEM education framework must have a strong social base. Similarly, Erdogan and Stuessy (2015) argued for an ecological-collaborative framework where community leaders and experts from industry are participating stakeholders for STEM programs. Participants raised the concern that many educators do not understand what STEM is. Indeed there are variants of STEM. In this sample participants held different interpretations of STEM. This indicates that professional development is an important factor for integrating STEM in education so that the purposes, policies, programs and processes of STEM (Bybee, 2013) are shared among professionals.

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9.1.9  An iSTEM Framework for Developing Countries The suggested framework for an iSTEM curriculum is influenced by a review of the relevant literature and STEM education as well as the interviews with mathematics, science and technology teacher educators. The most distinctive features of this pedagogical framework are the infusing of STEM in indigenous knowledge alongside political support and professional development. It is composed of the following elements: 1. Strong indigenous knowledge and connections with local communities Schools do not exist in a vacuum but belong to their local community. Southern Africa has a long history with considerable local knowledge about the environment within indigenous communities. These knowledges should be recognised and shared along with the knowledge from the school STEM curriculum. Also, teaching and learning are situated in the contexts in which they happen (Brown et al., 1989). English and King’s (2015) examples of aerospace STEM tasks are not suitable for developing countries where resources are scarce and earthquake problems are not relevant. African societies are full of their own indigenous technologies that enabled African societies to survive and flourish before the arrival of Western science. There is great danger of the epistemicide of African indigenous science and technology. This indigenous knowledge needs to be the starting point of an iSTEM curriculum in conjunction with universal knowledge (Horsthemke, 2004; Kelley & Knowles, 2016). Teaching and learning must use local contexts in an iSTEM curriculum (Timms et al., 2018); for example, schools near ports can encourage students to study the technology and science for managing the sea, such as marine ecology and shipping. Schools near airports, manufacturing industries, agricultural areas and so on need to study those contexts. They need to visit and familiarise themselves with local industry. At the same time, experts from these industries must visit schools to initiate learners about their work. This removes the boundaries between formal and informal schooling (Erdogan & Stuessy, 2015). This is an apprenticeship situation linked to Legitimate Peripheral Participation to bring school into society and society into school (Lave & Wenger, 1991). 2. Problem-based and authentic learning Atman et al. (2007) argue that a key element of iSTEM is problem scoping, a process in which learners determine the parameters and limitations of the problem, before actually setting out to solve it. Vasquez (2015) argues that the application of transdisciplinary knowledge to problem-solving “shape learning experience” (p.  13). In particular, iSTEM must be based on solving authentic problems, however small. This acclimatises learners to the fact that problems are a fact of life and that it is possible to solve problems through positive initiatives and creativity by using iSTEM methods (Timms et al., 2018). 3. Strong content base This was argued as important because without it learners will not make headway in solving context-based problems as this requires clear thinking. Strong

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content ensures that learners have and know the tools to use when faced with solving unfamiliar problems. 4. Teacher capacity It is important that new curriculum initiatives in developing countries, such as iSTEM, be supported by intensive and continued professional development of teachers (Stohlmann et al., 2012). To that end, it is also important that these teachers must be paid well. This will help to attract and retain the most talented iSTEM teachers. Continued professional development is important to increase teacher capacity to teach the new STEM content in innovative and progressive ways and to hedge against poor-quality teaching that are deleterious to learner outcomes and attitudes to iSTEM (Nadelson, Seifert, Moll, & Coats, 2012). 5. Supportive political environment Successful iSTEM initiatives require political will to make continued efforts (Stohlmann et  al., 2012). Erdogan and Stuessy’s (2015) ecological framework supports situated STEM by involving all stakeholders. Government needs to be convinced that iSTEM education is an imperative for economic development. The government can support it through appropriate education policy. Funding must be available for research and development and for iSTEM kits and associated resources. Open iSTEM competitions at local, regional, national and international levels need to be supported along with science exhibitions. Academics must be supported, particularly to do practice informed STEM research. Benchmarking of countries with successful iSTEM initiatives and programs must be encouraged, although local initiatives are also very important.

9.2  Conclusion In this chapter, we have explored different facets of STEM curriculum integration. We aimed to develop a pedagogical framework for STEM integration in Southern Africa. We argued that such a pedagogical framework must take into account the varying local contexts such as indigenous knowledge bases. From data gleaned from the literature and study participants, a framework that combines the indigenous knowledge bases with Western science was suggested. This is key because traditional science existed in Africa  before the arrival of Western science, but it lacks  recognition and legitimation at school  compared to Western science. Incorporating local knowledge from local communities within schools makes STEM education relevant and meaningful to the manpower to harness local African resources for sustainable development.

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References Anderson, J. (2017). The STEM teacher enrichment academy: Evaluating teachers’ approaches to implementing STEM education in secondary school contexts. ACER Research Conference Proceedings, 2016, 18–22. Atman, C.  J., Adams, R.  S., Cardella, M.  E., Turns, J., Mosborg, S., & Saleem, J. (2007). Engineering design processes: A comparison of students and expert practitioners. Journal of Engineering Education, 96(4), 359–379. https://doi.org/10.1002/j.2168-9830.2007.tb00945.x Bernstein, B. (1975). Class and pedagogies: Visible and invisible. Educational Studies, 1(1), 23–41. https://doi.org/10.1080/0305569750010105 Bernstein, B. (2018). On the classification and framing of educational knowledge. In Knowledge, education, and cultural change (pp. 365–392). Chicago: Routledge. Bishop, A.  J. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19(2), 179–191. Brown, J.  S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32–42. https://doi.org/10.3102/0013189X018001032 Bursal, M., & Paznokas, L. (2006). Mathematics anxiety and preservice elementary teachers’ confidence to teach mathematics and science. School Science and Mathematics, 106(4), 173–180. https://doi.org/10.1111/j.1949-8594.2006.tb18073.x Bybee, R. W. (2010). Advancing STEM education: A 2020 vision. Technology and Engineering Teacher, 70(1), 30–35. https://doi.org/10.4236/ce.2014.514141 Bybee, R. W. (2013). The case for STEM education: Challenges and opportunities. Arlington, VA: National Science Teachers Association. Charette, R.  N. (2013). The STEM crisis is a myth. IEEE Spectrum, 50(9), 44–59. https://doi. org/10.1109/MSPEC.2013.6587189 Department of Basic Education. (2010). Education for all, 2009 country report: South Africa. Pretoria, South Africa: DBE. English, L. (2017). Advancing elementary and middle school STEM education. International Journal of Science and Maths Education, 15(1), 5–24. https://doi.org/10.1007/ s10763-017-9802-x English, L. D. (2016). STEM education K-12: Perspectives on integration. International Journal of STEM Education, 3(1), 3. https://doi.org/10.1186/s40594-016-0036-1 English, L. D., & King, D. T. (2015). STEM learning through engineering design: Fourth-grade students’ investigations in aerospace. International Journal of STEM Education, 2(1), 14. https://doi.org/10.1186/2196-7822-1-6 Erdogan, N., & Stuessy, C.  L. (2015). Modelling successful STEM high schools in the United States: An ecology framework. International Journal of Education in Mathematics, Science and Technology, 3(1), 77–92. https://doi.org/10.18404/ijemst.85245 Gerber, B. L., Marek, E. A., & Cavallo, A. M. (2001). Development of an informal learning opportunities essay. International Journal of Science Education, 23(6), 569–583. Honey, M., Pearson, G., & Schweingruber, H. (2014). STEM integration in K-12 education: Status, prospects and an agenda for research. Washington, DC: National Academies Press. https://doi. org/10.17226/18612 Horsthemke, K. (2004). Knowledge, education and the limits of Africanisation. Journal of Philosophy of Education, 38(4), 571–587. https://doi.org/10.1111/j.0309-8249.2004.00405.x Jho, H., Hong, O., & Song, J. (2016). An analysis of STEM/STEAM teacher education in Korea with a case study of two schools from a community of practice perspective. Eurasia Journal of Mathematics, Science & Technology Education, 12(7), 1843–1862. Kelley, T. R., & Knowles, J. G. (2016). A conceptual framework for iSTEM education. International Journal of STEM Education, 3(11), 1–11. https://doi.org/10.1186/s40594-016-0046-z Lave, J., & Wenger, E. (1991). Situated learning. Legitimate peripheral participation (Vol. 21, p.  918). Cambridge: Cambridge University Press. https://doi.org/10.1525/ ae.1994.21.4.02a00340

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Marginson, S., Tytler, R., Freeman, B., & Roberts, K. (2013). STEM: Country comparisons: International comparisons of science, technology, engineering and mathematics (STEM) education. Australian Council of Learned Academies (ACOLA): Sydney, Australia. Nadelson, L. S., Seifert, A., Moll, A. J., & Coats, B. (2012). I-STEM summer institute: An integrated approach to teacher professional development in STEM. Journal of STEM Education: Innovation and Outreach, 13(2), 69–83. National Science and Technology Council. (2013). A report from the committee on STEM education. Washington, DC: National Science and Technology Council. Pfeiffer, A. I., Overstreet, J. M., & Park, A. (2010). The state of science and mathematics education in state-supported residential academies: A nationwide survey. Roeper Review, 32(1), 25–31. https://doi.org/10.1080/02783190903386579 Roberts, A. (2012). A justification for STEM education. Technology and Engineering Teacher, 71(8), 1–4. Roberts, M., & Pettigrew, S. (2007). A thematic content analysis of children’s food advertising. International Journal of Advertising, 26(3), 357–367. Stains, M., Harshman, J., Barker, M. K., Chasteen, S. V., Cole, R., DeChenneeters, S. E., et al. (2018). Anatomy of STEM teaching in north American universities. Science, 359(6383), 1468–1470. https://doi.org/10.1126/science.aap8892 Stohlmann, M., Moore, T. J., & Roehrig, G. H. (2012). Considerations for teaching iSTEM education. Journal of Pre-College Engineering Education Research (J-PEER), 2(1), 28–34. https:// doi.org/10.5703/1288284314653 The Royal Society Science Policy Centre. (2014). Vision for science and mathematics education. London: The Royal Society. Timms, M., Moyle, K., Weldon, P., & Mitchell, P. (2018). Challenges in STEM learning in Australian schools. In Policy insights Issue 7. Camberwell, VIC, Australia: ACER. Tytler, R., Osborne, J., Williams, G., Tytler, K., & Cripps Clark, J. (2008). Opening up pathways: Engagement in STEM across the primary-secondary school transition. Sydney, Australia: Australian Department of Education, Employment and Workplace Relations. Vasquez, J. A. (2015). STEM—Beyond the acronym. Educational Leadership, 72(4), 10–15. Williams, J. (2011). STEM education: Proceed with caution. Design and Technology Education: An International Journal, 16(1), 26–54. Yin, R.  K. (2011). Qualitative research from start to finish (Vol. 44, p.  324). New  York: The Guilford Press. https://doi.org/10.1111/fcsr.12144

Part II

Designing Integrated STEM Approaches for Students

Chapter 10

Focusing on Students and Their Experiences in and Through Integrated STEM Education Yeping Li and Judy Anderson

Contents 10.1  L  earning About Students’ Learning and Experience in and Through Integrated STEM Education 10.1.1  Students’ Learning and Experience in and Through Specifically Designed Activities with STEM Integration 10.1.2  Getting to Learn More About STEM/STEAM Integration for Students 10.2  Expecting More to Develop and Learn in this Rich Topic Area References

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The movement of emphasizing science, technology, mathematics, and engineering (STEM) education has long been focusing on students’ experience and preparation for the future. Students’ acquisition of disciplinary knowledge and skills as isolated and “given” through school education needs to be problematized and changed (e.g., Li & Schoenfeld, 2019). In contrast to traditional discipline-based education, STEM education has been perceived to provide great opportunities for transforming school education as we discussed in our introductory chapter (Chap. 2) for Part 1 (Li & Anderson, 2020). With a focus on different models of STEM integration in Part 1, we read about a wide spectrum of possibilities of integrating STEM to meet diverse needs (Li & Anderson, 2020). At the same time, we realize that how to turn those possibilities into reality would require tremendous efforts from multiple stakeholders, community, and the entire system. Those possibilities are opportunities that come

Y. Li (*) Texas A&M University, College Station, TX, USA e-mail: [email protected] J. Anderson Sydney School of Education and Social Work, The University of Sydney, Camperdown, NSW, Australia e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_10

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with great challenges. Indeed, there is no easy and ready path for making changes for quick success. The encouraging fact is that numerous educators, researchers, and teachers are fascinated by those opportunities and willing to face those challenges. It is in this spirit that readers can find in this part a collection of chapters that document and share possible successes and challenges in transforming students’ learning in and through integrated STEM education. Before we go further to discuss chapters included in this part, we would like to provide a broader context about scholarship development in this topic area. Although STEM education has experienced tremendous development over the past decade, scholarship development is still in its early stage in STEM education (Li, 2014), especially in integrated STEM education (Li, 2018). Recent reviews of journal publications revealed that the research community had a broad interest in both teaching and learning in K–12 STEM education. Both “K–12 teaching, teacher, and teacher education” and “K–12 learner, learning, and learning environment” are in the top three topic areas in terms of publication counts in the International Journal of STEM Education from 2014 to 2018 (Li, Froyd, & Wang, 2019) and in 36 journals from 2000 to 2018 (Li, Wang, Xiao, & Froyd, 2020). At the same time, however, if we check specific numbers of publications about students’ learning and experience, both cognitive and noncognitive aspects, in education involving more than one discipline of STEM, we find few publications. For example, in the International Journal of STEM Education, the first STEM education journal being accepted in Social Sciences Citation Index (SSCI) in 2019 (Li, 2019), there are only 10 publications (out of 142 publications from 2014 to the end of 2018) about students’ learning and experience in education involving more than one discipline of STEM. Out of these 10 publications, only four (2.8% of 142 publications) focus on cognitive issues and the remaining six (4.2% of 142 publications) on noncognitive issues. The results clearly suggest that scholarship on students’ learning and experience in integrated STEM education is still in an initial stage and needs considerable research development. With this broader context, we are grateful to all authors of chapters in Part 2 for being willing to share with us their pioneering efforts in this important topic area.

10.1  L  earning About Students’ Learning and Experience in and Through Integrated STEM Education Part 2 includes eight chapters, excluding this chapter. There are two features that we would like to share with readers first about this part. First, this is a book subtitled with an international perspective. Readers can certainly expect to find scholarly contributions from different education systems around the world. Indeed, chapters in this part are contributed by researchers from six education systems (Australia, Norway, South Korea, Turkey, UK, and USA) about students’ learning and thinking development in and through integrated STEM education. Although authors of each chapter had no intention of making possible

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comparisons and connections across different STEM integrations or education ­systems, readers shall have the privilege of appreciating possible differences and connections about students’ learning across different STEM activities in specific social–cultural contexts. Reading across the chapters, we encourage readers to critically identify what can be learned or possibly connected to what is happening in your own system and social–cultural context. Second, we know that it is difficult to make absolute and clear separation between curriculum design and students’ experience in education, including integrated STEM education. So readers won’t be surprised when reading chapters in Part 1 to find out a lot of discussions about providing students with important experience and preparation needed for the future. Students and their experiences are the focus of all educational efforts and changes. Likewise, readers can expect to read chapters in this part about ways of integrating STEM to facilitate students’ learning and thinking development at different grade levels. What makes chapters in this part different from those in Part 1 mainly resides in the focal consideration of research work and associated efforts to examine and document students’ experiences in and through integrated STEM education. With this note, it occurs to us that five (Chaps. 11, 12, 14, 15, and 17) out of these eight chapters in this part provide information about ways of integrating STEM and then documenting students’ learning experience in and through those specifically designed STEM activities. The remaining three chapters (Chaps. 13, 16, and 18) focus on students’ learning and thinking with a literature review, experience with an existing course, or assessment. The second feature helps to frame our summary of these eight chapters as follows.

10.1.1  S  tudents’ Learning and Experience in and Through Specifically Designed Activities with STEM Integration Among these five chapters, researchers and educators designed different STEM integration activities with two closely related to science. In particular, Miller, Severance, and Krajcik (2020) in Chap. 11 present an approach of integrating computational thinking as a practice that can support understanding across disciplines. They demonstrate its feasibility and benefits through a case study of a group of U.S. students in a fifth-grade project-based learning in science. Their case study provides qualitative analyses of how various practices associated with computational thinking helped these students in developing a shared understanding of the particle nature of matter. In Chap. 17, Touitou, Schneider, and Krajcik (2020) present a case study of developing and testing an NGSS (next-generation science standards) aligned curriculum unit (and associated assessment tasks) using a project-based learning framework. It is a high school physics unit with a focus on mathematical thinking and engineering design with disciplinary core ideas and crosscutting concepts. The results show that a carefully designed curriculum unit

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can help students to increase mastery of using science ideas and mathematical thinking. The remaining three chapters include more blended STEM integration. Wang et al. (2020) in Chap. 12 set to explore how an integrated STEM inquiry, “Is there life on Mars” (i.e., designing a robot to detect life on Mars), may afford opportunities and challenges for U.S. elementary school students’ learning. Their study revealed not only opportunities for students’ learning of merging concepts through analyzing students’ scientific–mathematics discourse but also the complexity and challenge in specifying “STEM concepts” in activity design and the lack of assessment tools for documenting students’ learning in integrated STEM education. In Chap. 14, Skilling (2020) reports her findings about UK secondary school students’ experience and beliefs as STEM learners through participating in a transdisciplinary STEM project, robot design, and construction. The findings provide support for advocating integrated STEM education with evidence of students’ building knowledge connections and thinking development. In Chap. 15, Steffensen (2020) examines tenth-grade Norwegian students’ classroom debates and group discussions on climate change. With a focus on students’ critical mathematical competencies, Steffensen demonstrated that students’ participation in dialogues and debates allowed them to develop critical competencies through mathematical, technological, and reflective argumentation with multiple perspectives.

10.1.2  G  etting to Learn More About STEM/STEAM Integration for Students Chapter 13 is a literature review together with a survey study. In particular, Kang (2020) presents integrated STEAM movement in South Korea with a meta-analysis of effects on student learning and a survey of students’ perceptions. The results indicate positive effects of integrated STEAM approach on students’ learning in general and some aspects in specific. For example, self-directed problem-solving and team collaboration were identified by students as the most salient positive features of STEAM activities to generate their confidence and sense of identity and achievement. At the same time, Kang also points out the need for further research to make specific links between program designs and students’ learning outcomes. Ubuz (2020) in Chap. 16 examines the relationship between the intended curriculum and implemented the curriculum for the seventh-grade technology and design course in Turkey. In particular, Ubuz focuses on identifying and analyzing the engineering design process for integrating mathematics and science in the intended curriculum and how the course teacher perceives and implements the intended curriculum. The study shows not only possible opportunities in the intended curriculum but also great challenges in the implementation process for the integration associated with contextual and cognitive factors. Ubuz also points out

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that much more professional support and training are needed for effective implementation. Bartholomew and Williams (2020) in Chap. 18 present and discuss the application of adaptive comparative judgment (ACJ) for assessing procedural skill and declarative knowledge embedded in open-ended STEM problems. Based on previous research, they share several different cases to illustrate how students’ STEM skills can be assessed with the use of ACJ, such as identifying student communication competencies and design ability.

10.2  E  xpecting More to Develop and Learn in this Rich Topic Area The eight chapters provide us a glimpse of the complexity, excitement, and challenge in this topic area on students and their experience. Indeed, it is a rich topic area that, we can be sure, contains many more questions than answers. In fact, the Journal for STEM Education Research (https://www.springer.com/journal/41979), established at the end of 2018, is dedicated to promote the development of interdisciplinary research in STEM education (Li, 2018). Students’ learning and psychological development in integrated STEM education are key topics for this journal (e.g., Barth-Cohen, Jiang, Shen, Chen, & Eltoukhy, 2018; Chen & Lo, 2019; Talafian, Moy, Woodard, & Foster, 2019). Interested readers may want to visit the journal for keeping up-to-date about relevant studies. Since scholarship development on integrated STEM education is relatively new, readers may notice that existing research in traditional discipline-based education can’t simply be used directly in STEM education. New development needs to take place, including not only curriculum models as we learned from Part 1 but also students’ learning, pedagogy, assessment, and even research methodology and theoretical perspectives. For example, several articles recently published in the International Journal of STEM Education focus on assessment (e.g., Gamage, Ayres, Behrend, & Smith, 2019; Herro, Quigley, Andrews, & Delacruz, 2017; Reynders, Lantz, Ruder, Stanford, & Cole, 2020) and the development of research methods and instruments (e.g., Morris, Owens, Ellenbogen, Erduran, & Dunlosky, 2019; Rowland, Dounas-Frazer, Rios, Lewandowski, & Corwin, 2019; Scanlon, Roman, Ibadlit, & Chini, 2019). If the chapters in this part can inspire readers to further discussion and research on relevant issues on students’ learning and thinking development, it can well be taken as a sign of success of putting these chapters together as a special collection.

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References Barth-Cohen, L. A., Jiang, S., Shen, J., Chen, G., & Eltoukhy, M. (2018). Interpreting and navigating multiple representations for computational thinking in a robotics programming environment. Journal for STEM Education Research, 1(1), 119–147. Bartholomew, S. R., & Williams, P. J. (2020). STEM skill assessment: An application for adaptive comparative judgement. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Chen, C.  W. J., & Lo, K. (2019). From teacher-designer to student-researcher: a study of attitude change regarding creativity in STEAM education by using Makey Makey as platform for human-centered design instrument. Journal for STEM Education Research, 2(1), 75–91. Gamage, S.  H. P.  W., Ayres, J.  R., Behrend, M.  B., & Smith, E.  J. (2019). Optimising moodle quizzes for online assessments. International Journal of STEM Education, 6, 27. https://doi. org/10.1186/s40594-019-0181-4 Herro, D., Quigley, C., Andrews, J., & Delacruz, G. (2017). Co-measure: developing an assessment for student collaboration in STEAM activities. International Journal of STEM Education, 4, 26. https://doi.org/10.1186/s40594-017-0094-z Kang, N. H. (2020). What can integrated STEAM (Science, Technology, Engineering, Arts and Mathematics) education achieve? A South Korea case. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Li, Y. (2014). International journal of STEM education – A platform to promote STEM education and research worldwide. International Journal of STEM Education, 1, 1. https://doi. org/10.1186/2196-7822-1-1 Li, Y. (2018). Journal for STEM Education Research—Promoting the development of interdisciplinary research in STEM education. Journal for STEM Education Research, 1(1–2), 1–6. https://doi.org/10.1007/s41979-018-0009-z Li, Y. (2019). Five years of development in pursuing excellence in quality and global impact to become the first journal in STEM education covered in SSCI. International Journal of STEM Education, 6, 42. https://doi.org/10.1186/s40594-019-0198-8 Li, Y., & Anderson, J. (2020). STEM integration: Diverse approaches to meet diverse needs. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Li, Y., Froyd, J.  E., & Wang, K. (2019). Learning about research and readership development in STEM education: a systematic analysis of the journal’s publications from 2014 to 2018. International Journal of STEM Education, 6, 19. https://doi.org/10.1186/s40594-019-0176-1 Li, Y., & Schoenfeld, A. H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6, 44. https://doi.org/10.1186/ s40594-019-0197-9 Li, Y., Wang, K., Xiao, Y., & Froyd, J. E. (2020). Research and trends in STEM education: A systematic review of journal publications. International Journal of STEM Education, 7, 11. https:// doi.org/10.1186/s40594-020-00207-6 Miller, E., Severance, S., & Krajcik, J. (2020). Connecting computational thinking and science in U.S. elementary classroom. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Morris, B. J., Owens, W., Ellenbogen, K., Erduran, S., & Dunlosky, J. (2019). Measuring informal STEM learning support across contexts and time. International Journal of STEM Education, 6, 40. https://doi.org/10.1186/s40594-019-0195-y Reynders, G., Lantz, J., Ruder, S. M., Stanford, C. L., & Cole, R. S. (2020). Rubrics to assess critical thinking and information processing in undergraduate STEM courses. International Journal of STEM Education, 7, 9. https://doi.org/10.1186/s40594-020-00208-5 Rowland, A. A., Dounas-Frazer, D. R., Rios, L., Lewandowski, H. J., & Corwin, L. A. (2019). Using the life grid interview technique in STEM education research. International Journal of STEM Education, 6, 32. https://doi.org/10.1186/s40594-019-0186-z

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Scanlon, E., Roman, B. Z., Ibadlit, E., & Chini, J. J. (2019). A method for analysing instructors’ purposeful modifications to research-based instructional strategies. International Journal of STEM Education, 6, 12. https://doi.org/10.1186/s40594-019-0167-2 Skilling, K. (2020). Student STEM beliefs and engagement in the U.K.: How they shift and are shaped through integrated projects. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Steffensen, L. (2020). Climate change and students’ critical competences: A Norwegian study. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Talafian, H., Moy, M. K., Woodard, M. A., & Foster, A. N. (2019). STEM identity exploration through an immersive learning environment. Journal for STEM Education Research, 2(2), 105–127. Touitou, I., & Krajcik, J. (2020). Incorporating mathematical thinking into high school STEM physics – A case study in the USA. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Ubuz, B. (2020). Examining a technology and design course in middle school in Turkey for opportunities to engage in STEM practices. In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer. Wang, S., Swanson, S., Ching, Y., Baek, Y., Yang, D., & Chittoori, B. (2020). Developing U.S. elementary students’ STEM practices and concepts in an after school integrated STEM project. In J.  Anderson & Y.  Li (Eds.), Integrated approaches to STEM education: An international perspective. Cham, Switzerland: Springer.

Chapter 11

Connecting Computational Thinking and Science in a US Elementary Classroom Emily C. Miller, Samuel Severance, and Joe Krajcik

Contents 11.1  I ntroduction 11.2  D  isciplinary Core Ideas (DCIs), Science and Engineering Practices (SEPs), and Crosscutting Concepts (CCCs) Work Together 11.3  Using Project-Based Learning Toward Integrated Learning 11.4  Conceptualizing Computational Thinking 11.5  Conceptualizing Learning of the Particle Nature of Matter 11.6  Description of the ML-PBL Unit: How Can I Design a New Taste? 11.7  Description of Learning Set 1 11.8  Data Collection and Analysis 11.9  Results 11.9.1  Lesson One: Using the Practice of Scientific Questioning While Engaging with a Phenomenon to get at the Particle Nature of Matter 11.9.2  Lesson Two: Using the Practice of Conducting an Investigation for Explaining and Predicting Phenomenon to Get at the Particle Nature of Matter 11.9.3  Lessons Three and Four: Using the Practice of Investigation and Revising Models for Explaining and Predicting Phenomenon to Get at the Particle Nature of Matter 11.9.4  Lesson Five: Using the Practice of Computational Thinking for Explaining and Predicting Phenomenon to Get at Particle Nature of Matter 11.10  Discussion and Conclusion References

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11.1  Introduction The latest science education reform documents in the USA—A Framework for K-12 Science Education (Framework; NRC, 2012) and the Next Generation of Science Standards (NGSS; NGSS Lead States, 2013)—present a conception of science learning as consisting of three dimensions, where core ideas, practices, and overarching concepts for viewing the world work together and are developed synergistically. But this idea of three dimensions working in tandem has proven difficult for teachers to implement (Penuel, Harris, & DeBarger, 2015). Teachers are often seen as falling short of implementing the vision and theory expressed in the Framework (Haag & Megowan, 2015; Trygstad, Smith, Banilower, & Nelson, 2013). A viable solution to this challenge is professional learning, new curriculum that aligns with the Framework, and a focus on assessment to drive change in practice and teacher beliefs (NRC, 2015). Key questions include “Are practices taught in the service of developing a core idea or do students apply a science idea in the service of developing scientific practices?” and “How do the three dimensions work together to support students in explaining phenomena?”. We explore how project-based learning offers an approach that meets three-dimensional performance expectations through project-based learning where students make sense of a science phenomenon (Blumenfeld et al., 1991; Krajcik & Shin, 2014). The Framework and NGSS standards shift the conception of science learning, yet there remains discussion in the field about the ideal way to combine and integrate the three dimensions of disciplinary core ideas (DCIs), science and engineering practices (SEPs), and crosscutting concepts (CCCs) to support three-dimensional learning for students (NRC, 2012). The disciplinary core ideas are the three or four generative and explanatory overarching ideas in the disciplines of life science, earth and space, physical science, and engineering. For example, ESS2.C: The Roles of Water in Earth’s Surface Processes is a component idea of the larger DCI Earth’s Systems. The crosscutting concepts (CCCs) describe “lenses” that can be applied across disciplines to ask questions of a natural event. For instance, the CCC Patterns can be applied to explain aspects of an ecological system to ask questions about plant and animal lifecycles, or the lens Cause and Effect can be used to ask about the loss of a species from a habitat. Finally, the scientific practices have overlapping features involved in scientific inquiry, including planning and carrying out investigations, developing models, or arguing from evidence. The NGSS are performance standards that focus on doing science. Students develop a deeper sophistication in the science and engineering practices, disciplinary core ideas, and crosscutting concepts over time (NRC, 2012), and each dimension mutually reinforces the others. This approach is authentic, mirroring how scientists and engineers engage in practices (Engle & Conant, 2002; NRC, 2012). In this chapter, we explore the integration of the dimensions through project-­ based learning. We address how the crosscutting concept Patterns and the disciplinary core idea Particle Nature of Matter can inform and be informed by the development of the science and engineering practice of Computational Thinking.

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11.2  D  isciplinary Core Ideas (DCIs), Science and Engineering Practices (SEPs), and Crosscutting Concepts (CCCs) Work Together Unlike the work of practicing scientists who use DCIs, SEPs, and CCCs together to explain and predict phenomena and solve problems, “school science” has traditionally focused on explicating a science concept or completing a science unit or activity based on specific content (NRC, 2012). The emphasis in a traditional science classroom has been to acquire science knowledge. Sometimes an inquiry activity or investigation accompanies the acquisition of knowledge, but the activity or investigation is designed so that a student goes through steps to elicit the desired concept (Duran & Duran, 2004; Windschitl, Thompson, & Braaten, 2008). This prioritizes learning of science concepts with science practices subordinated to this end (Bartholomew, Osborne, & Ratcliffe, 2004; Shepardson, 2005). There is a parallel trend in the post-NGSS literature to focus only on one practice at a time. Here, the science concept seems to be almost inconsequential (see Grooms, Enderle, & Sampson, 2015). In this literature, the pairing of science ideas with a practice occurs only after the practice is fully understood and conceptualized, suggesting a partially understood practice may offer little purchase for gaining science knowledge (Manz, 2012, 2015; Miller, Manz, Russ, Stroupe, & Berland, 2018). This approach positions practices as the primary focus. Researchers have examined the usefulness of several SEPs, such as modeling (see Schwarz et al., 2009), explanation building (see McNeill & Krajcik, 2012), and argumentation (see Osborne, Erduran, & Simon, 2004), and how such practices with ideas work together to build knowledge (Pellegrino & Hilton, 2012). However, less is known about three important topics: (1) how to support elementary students in computational thinking—one of the eight scientific practices of NGSS; (2) how computational thinking can support elementary students in building scientific DCIs and CCCs over time; and (3) how deepening the practice of computational thinking enables students to work toward a more sophisticated capacity to use DCIs and CCCs. This case study focuses on the question “What does the practice of computational thinking afford students in making sense of phenomena related to the core idea of the Particle Nature of Matter?”. We add to the relatively nascent body of understanding around computational thinking, in terms of both how the practice develops and how its development informs thinking about phenomena using DCIs and CCCs. Different practices offer specific advantages in terms of helping students make scientific sense of their world. For example, the practice of modeling amplifies the relationships between components in a scientific event and can force thinking about mechanisms (Schwarz et al., 2009). Argumentation is concerned with soliciting the most compelling evidence and reasoning to evaluate competing explanations (Osborne et  al., 2004). Scientific investigation is ideal when an important

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understanding will become apparent with changing conditions, allowing students to question prior thinking (Miller, Lauffer, & Messina, 2014). Individual practices, in short, offer distinct perspectives and advantages or “affordances” for figuring out a phenomenon (Miller et al., 2014).

11.3  U  sing Project-Based Learning Toward Integrated Learning Project-based learning (PBL) draws on several major theoretical ideas regarding learning, chiefly (1) active construction, (2) situated learning, (3) social interactions, and (4) cognitive tools (Bransford, Brown, & Cocking, 1999; NRC, 2007). PBL environments revolve around and focus on a driving question that children find meaningful, promoting a sense of wonderment and a “need to know” that propels learning. Because of PBL’s focus on making sense of a meaningful question, its design principles reflect the vision of three-dimensional learning put forth in the Framework and the NGSS. Table 11.1 presents the various design principles of PBL. We draw upon ongoing work in elementary science from the Multiple Literacies in Project-Based Learning (ML-PBL) project (Krajcik, Palincsar, & Miller, 2015). ML-PBL is a design-based project, using features of project-based learning (Blumenfeld et al., 1991; Krajcik & Shin, 2014), to create, develop, and test elementary curriculum to promote student learning of the big ideas of science and social emotional learning. Our approach integrates the development of teacher and student materials with long-term professional learning and assessments. ML-PBL is unique in that it integrates multiple literacies (i.e., reading, writing, math, and discourse) with the NGSS to support children in developing useable science knowledge. This case study follows students as they explore phenomena of taste and smell to promote a “need to know” and engage in relevant contexts to build useable knowledge of the three dimensions. These phenomena elicit the SEP of Computational

Table 11.1  Design principles of project-based learning Meet important three-dimensional learning goals based upon the NGSS performance 1 expectations 2 Pursue solutions to meaningful questions anchored in the lives of learners 3 Explore questions by participating in authentic, situated science experiences using various science practices to “figure out” why phenomena occur 4 Engage in collaborative activities to make sense of phenomena through discourse 5 Use learning tools and other scaffolds to support students’ participation in activities normally beyond their ability 6 Create artifacts—tangible products—that address the driving question and show students’ emerging understandings

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Thinking, the DCI of Particle Nature of Matter, and CCC of Patterns, to answer the driving question “How can I design a new taste?”. The setting for this case study is a fifth grade classroom. The following sections provide a brief review of research on the practice of Computational Thinking and the core idea of the Particle Nature of Matter.

11.4  Conceptualizing Computational Thinking The initial conception of computational thinking (Wing, 2006)—that it “involves solving problems, designing systems, and understanding human behavior, by drawing on the concepts fundamental to computer science” (p. 33)—galvanized education researchers in computer science and other domains to move beyond a focus on student programming to fostering the actual thinking computer scientists employ. Given our focus on developing innovative science curriculum materials, we gravitated toward conceptions of computational thinking that work well with a project-­ based learning approach and the vision of science education put forth in the Framework (NRC, 2012). The Framework specifies eight science and engineering practices students should use with DCIs and CCCs to figure out phenomena and solve problems. Computational thinking comprises part of a practice: using mathematics and computational thinking (NGSS Lead States, 2013). In the Framework, computational thinking refers to the capacity to use computational tools—including computers—and computational methods, such as constructing simulations, statistically analyzing data, applying quantitative relationships, and mathematically testing design solutions (NRC, 2012). Wilkerson and Fenwick’s (2017) discussion of computational thinking provides useful ideas from an NGSS perspective, noting a need to focus on examining the properties and relationships within systems and discerning patterns, often through engaging with—or creating—computer models of systems. We see this emphasis on understanding systems—like a given phenomenon—and the construction of computational models, an artifact, as working well with a PBL perspective that places final artifacts as the culmination of learning (Blumenfeld et al., 1991; Krajcik & Shin, 2014). Grover and Pea (2013) note how computational thinking has become more associated with a set of computational practices, rather than constrained to computer usage and programming (diSessa, 2000). Grover and Pea (2018) provide a set of concepts and practices that in their view encompass computational thinking (see Table 11.2). In our design of the fifth grade ML-PBL units, we make use of many of the concepts and practices of computational thinking delineated by Grover and Pea (2013, 2018).

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Table 11.2  Computational thinking concepts and practices (Grover & Pea, 2018) Concepts Logic and Logical Thinking: the use of conditional logic to reach a conclusion about a problem (e.g., IF…THEN statements) Algorithms and Algorithmic Thinking: precise step-by-step processes for a solution Patterns and Pattern Recognition: identifying repetitions to help solve a problem Abstraction and Generalization: the hiding of complex elements to create simpler representations Evaluation: the assessment of how well an approach meets criteria within specified constraints Automation: implementing a solution on a machine

Practices Problem Decomposition: the breaking down of a problem into more manageable sub-problems Creating Computational Artifacts: the development of a solution or model governed by computation (not necessarily digital) Testing and Debugging: the detection of flaws or inefficiencies in an approach Iterative Refinement: the revision of an approach over time to better fit desired outcomes Collaboration and Creativity: sharing labor and responsibilities and developing innovative and/or expressive solutions

11.5  C  onceptualizing Learning of the Particle Nature of Matter There is robust research on student thinking about the particle nature of matter. Andersson (1991) grouped students’ developing understanding of conceptions of matter into four categories wherein each category is fundamental to deeper learning. Andersson’s work in this area forms the basis of current thinking (Hadenfeldt, Liu, & Neumann, 2014; Merritt, Krajcik, & Shwartz, 2008). The categories are (1) particle nature of matter, (2) chemical reactions, (3) physical states and their changes, and (4) conservation of matter. The categories represent equally important aspects of matter and need to be developed as connected ideas in order for students to be able to explain related phenomenon (Liu & Lesniak, 2006). In this case study, students are tasked to describe a mechanism for why the tastes in foods differ, based on the food being comprised of different particles, causing different perceptions of smell and taste. Students must recognize that foods are made of something that is experienced when the particles come into contact with a tongue mixed with saliva or by having invisible particles traveling to contact receptors in the nose. Through successfully explaining these related phenomena, students must be able to apply ideas from each of Andersson’s categories. Finally, students recognize that there are some common compositions of particles in similar tasting foods. The NGSS is organized so that one DCI is reiterated at each grade band—K-2, 3–5, middle school, and high school—but with increasing sophistication. The NGSS learning progression for science ideas introduces ideas and experiences at the

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earlier levels that are necessary to advance to the next level. For instance, for learners to develop the science idea of PS1.B at the middle school level, that properties at the macroscale change as a result of rearrangement of atoms at the micro level, they need to understand science ideas from PS1.A and PS1.B at the grade 3–5 and K-2 level. The idea that substances have properties is introduced at the K-2 level, but the learning progression does not show how students actually learn these ideas. We see PBL as an ideal method to engage students in “figuring out” phenomena using DCIs with CCCs and SEPs. Learning progressions provide tools for teachers to support students in building future understandings. We build from Johnson’s (1998) work on learning progressions discussed earlier. Johnson’s (1998) third classification, that matter consists of particles, aligns with the ideas in the NGSS that learners should develop by the end of fifth grade. His fourth classification, that matter is composed of particles and the properties of matter depend on the interaction between particles, aligns with the level of understanding that students should develop by the end of middle school and which is necessary for more advanced DCIs at the high school level.

11.6  D  escription of the ML-PBL Unit: How Can I Design a New Taste? Below is an overview of the five key lessons in this case study. The lessons come from the set of lessons (i.e., “learning set”) for a PBL unit centered around the driving question “How can I design a new taste?”. The learning set was designed to support students primarily in building their capacity to meet the physical science performance expectation 5-PS1-1 Develop a model to describe that matter is made of particles too small to be seen. The unit, the second of four comprising a full year of curriculum, contains five learning sets with five lessons each. The five learning sets work together to answer the driving question and build across 5 weeks of instruction to address the following enduring understanding: Students will explain that foods may look similar but taste or smell different because they consist of specific and too-small-to-see particles. Foods such and salt and sugar are substances that have properties that can be described and used to identify them. Such substances behave differently when heated, cooled or mixed with other materials, which is also because of the particles that they are comprised of. In these conditions, the substances sometimes form a new substance with different properties, although the weight -- the total number of particles-- will not change. Some substances are made through nature-based processes, including the formation of the new substance, sugar, by plants.

In this case study, we are interested in how students build understanding of the focus performance expectation (PE) for Learning Set 1 through multiple practices, but particularly through computational thinking. These five lessons spanned 2 weeks.

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11.7  Description of Learning Set 1 Lesson 1. The students engaged in the phenomenon that foods have different tastes. They developed related questions in small groups to share with the class. The class organized the questions and placed them on a “driving question board” for later use. Lesson 2. The teacher presented the students with two foods, carob powder and cumin powder, with very similar visible properties but very different tastes. Students answered the question “Can you tell how a food tastes by the way it looks?” and then developed a model to explain the mechanism by which we taste foods. This lesson was designed to elicit initial ideas related to food being comprised of matter and particles which are too small to see. Lesson 3. The students engaged in the practice of conducting an investigation and collecting and analyzing data. They predicted taste with their noses plugged in one trial and then without their noses plugged. The students developed a claim that smell and taste are related and smell adds to the ability to sense taste, although smell may be an “invisible” mechanism. Lesson 4. Students returned to their models to revise, now needing to include smell and “invisible” particles. They presented their models to their peers. Lesson 5. In the final lesson, students are guided in the practice of computational thinking through working on decomposing the phenomenon, recognizing and describing patterns, and engaging in iteration. They classify the taste of sweetness into three categories, categorize foods into them, and try to figure out how different foods can belong in the same category of sweetness.

11.8  Data Collection and Analysis This case study took place within an elementary school in a lower middle-class neighborhood on the outskirts of a large urban area in the upper Midwest of the USA. The school has a student population in which 46% of students are classified as economically disadvantaged, 20.1% are English language learners, 42% are White, and the majority of the students of color are Latino (21.3%) and Black/ African-American (17.9%). The remaining students are Asian and mixed race. Across grades K-5, 39% of students are considered “proficient or above” in English language arts according to the state reading proficiency assessment. One fifth grade classroom with 25 students (with attrition of one student) served as the focus classroom for this study. The classroom typically was divided into collaborative groups with four students within each group. The classroom teacher, Ann (pseudonym), was in her first year of teaching the fifth grade ML-PBL science curriculum. This was also her first year teaching fifth grade; however, she had 15 years of teaching experience, primarily in fourth grade.

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Data collection consisted of video recording student and teacher activity for the five lessons. The video camera and microphone captured the activity of a focus group as well as the teacher’s words and instruction. The artifacts developed by the focus group during each lesson—questions, model, list of data, and computational graph—were also photographed. Student and teacher discourse and visible actions were transcribed verbatim in field notes. This case study used an ethnographic approach to follow one group of four students within the classroom. The focus group was selected immediately after the first lesson in the unit, How can I design a new taste? The first lesson is designed to immerse students in an anchoring phenomenon: foods taste different. Our team collected questions developed by each group, aiming to find one group to follow based on their initial level of understanding. Our team used purposeful sampling based on the questions generated in this first lesson (Coyne, 1997), as questions that students ask can provide information about what students understand and care about in science (Chin & Brown, 2002). We gave each of the six groups an average score for the three to five questions they asked. Group 5 had the fourth highest score of the six groups, and their average progression number fell in the middle between the highest scoring group and the lowest scoring group. For this reason, we selected Group 5 as our focus group. Group 5 had four students: one boy (White) and three girls (White, African-­ American, and Latina). All four students—Shay, Valencia, Ava, and Jacob—showed an interest in science, had consistent attendance and work completion, but, on average, tended to speak less often in class. In analyzing the data, our approach involved both deductive and inductive coding of transcribed excerpts. We developed potential coding bins prior to analyzing the data and coded the data according to these bins, followed by a second round of analysis where we allowed for patterns to emerge from the data to serve as additional coding bins. Deductive coding bins fell along aspects of computational thinking put forth by Grover and Pea (2018), aspects of a progression for understanding the particle nature of matter put forth by Johnson (1998), as well as general bins for other aspects of DCIs, use of SEPs, or CCCs from the NGSS.  Coding bins that emerged from the data included a focus on identifying productive learning moments and noting where students built on previous ideas.

11.9  Results Below is an overview of what occurred during each lesson, interspersed with analysis relevant to our research question: What does the practice of computational thinking afford students making sense of phenomena related to the core idea of the particle nature of matter?

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11.9.1  L  esson One: Using the Practice of Scientific Questioning While Engaging with a Phenomenon to get at the Particle Nature of Matter The first lesson of five in the learning set introduced the larger learning set driving question, What makes food taste the way it does?, as well as the lesson driving question, How can we best describe tastes? The lesson involved engaging students in the phenomenon of different tastes. Each group sampled different foods and described their taste, focusing on differences in the properties of foods (i.e., color, shape, texture, and rigidity) and whether the properties are related or unrelated to the tastes. The foods included dried apricot, lemon slices, arugula, raisins, celery, tomato paste, fresh hot peppers, olives, and garbanzo beans. After being introduced to the lesson Driving Questions, each small group sampled the foods and described the tastes. Then they discussed how the tastes were different or similar in a small group for share-out. The students then wrote questions on sentence strips. Group 5, Shay, Jacob, Valencia, and Ava, tried all the foods and were highly motivated to ask questions. Group 5 engaged in collaboration (a key element of PBL) to develop the following questions: Is a bean mostly made up of water? Can some foods make your saliva poisonous? Can we taste things that aren’t food? Why do we taste things? People have different taste buds. Are we tasting what the food actually tastes like? Is there sugar in dried fruit? Are the nose and the mouth connected?

What purchase does the practice of asking questions provide for understanding taste in terms of the particle nature of matter? The practice of asking exploratory questions brings to the forefront various experiential resources that students have from their own lived experiences for making sense of a phenomenon. Group 5’s questions include some useful ideas about the mechanism of taste (e.g., the notion that beans may be made of mostly water surfaces; ideas that there are different substances with different properties) and show they are beginning to think about how taste may be related to chemical change (e.g., that an interaction with food can make saliva change its properties). The students in this group are already considering what the foods they eat might have in them, but appear to be thinking of taste as having to do with something extra that is in the matter (sugar, water) rather than matter consisting of particles. Some of the questions show that students may be viewing foods as being comprised of smaller units (e.g., Is there sugar in dried fruit?; Can some foods make your saliva poisonous?; Is a bean mostly made up of water?) but note these units are smaller than a given unit of sugar, water, or poison.

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11.9.2  L  esson Two: Using the Practice of Conducting an Investigation for Explaining and Predicting Phenomenon to Get at the Particle Nature of Matter Ann wrote the new lesson driving question on the chart paper: Can you tell how a food will taste by the way it looks? The students carefully observed two brown-­ colored powders which were almost identical in appearance on two plates that Ann put in the middle of the circle on the carpet. One powder was cumin, and the other was carob powder, but the students did not know that. The teacher had the students call out “visible” properties of the foods, and she rapidly recorded what they said. Ann explained that the powders were not the same and asked the class “Can you make a guess about what the powders are and how they will taste based on these visible properties?”. Most of the students guessed that one of the powders was cinnamon and will taste “cinnamon-y” and the other was chocolate and will taste “chocolatey.” After making predictions about which powder is which, the students taste a tiny sample of each. The students were surprised that two substances that looked so much alike tasted different, one sweet and earthy, while the other was bitter. Shay seizes on the idea that taste buds are responsible for this. Shay: (Explanation) Think about raisins. Ava loved them and now she hates them. I used to love strawberries, I loved them. Now, yech. My taste buds changed.”

Initially Group 5 follows Shay’s thinking and is mostly interested in how the taste buds are picking up tastes that get translated in the brain. They describe different interactions with taste buds. Shay recorded the groups’ ideas in her notebook page, drawing the taste buds and the brain. She served as the scribe throughout most of their time working together. Shay wrote: Your taste buds change over the years. A lot of them die and a lot of them regrow and have you taste diff things.

Ann comes by the group. She goes over what the students have written so far, reading out loud, “The model shows that it is the brain picking up different messages from taste buds that causes the different tastes.” She asks them, “Is it that the foods are basically the same stuff?”. In posing this question, Ann pressed the group to show why the messages the brain receives might be so different between the two foods, moving them toward considering unseen characteristics. This led to an exchange in the group, where they collaborate on building their ideas: Jacob: I had for lunch chicken taco salad. There’s meat in there and some lettuce. So does meat taste different from lettuce? Shay: Yes! Valencia: Yes! Ava: Yes! Jacob: Why? What’s happening? Ava: Meat comes from animals and the leaves come from trees and God and they wash them. They are grown differently, and they also grow differently.

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Shay wants to go back to taste buds, and the group engages in the question of food being a homologous substance versus a substance that contains particles of matter (level 2 in Johnson’s (1998) progression). Shay: Skittles let’s do skittles … grapes and lemon. So, if you want to your mouth would detect what kind of food it is, so it gives you that kind of taste in your mouth. Valencia : Grape skittles tastes nice, but it doesn't taste like a grape! You taste the flavor. If there wasn’t any flavor then your mouth would be Yeach. Jacob: Flavor is something that you taste that you might like or not like. Ava: Minerals is the flavor. (The group agrees) They have flavor, tomato, chicken teriyaki, raisins.”

Ann leans over and asks the group, “So what’s happening here? There’s one food and it tastes like something and then the other food and it tastes different?” “How can you show that they taste different, and why they taste different in your model?” Ann watches the group as they consider her words, and she says, “Keep thinking, you are doing great here!” Ava asks the group to think about how the two substances came to be, using the word minerals again to explain taste. Ava: You know how the food grows makes it taste. Like … if the soil has minerals in it, or if there are pesticides, then it gets in the food and makes the taste. (Shay looks to Jacob and then Valencia) Valencia: This one, (points to the carob powder) tastes like it has minerals!

Shay has the pencil and records minerals in the page by placing dots and squiggly lines next to the tongue. In doing so, Group 5 demonstrates level 2 in Johnson’s (1998) progression that matter contains particles: The taste buds react to minerals and send a message to the brain then something happens in the brain. What purchase does modeling provide for understanding taste in terms of the particle nature of matter? The practice of modeling pushed the students’ sensemaking to include invisible mechanisms. The students used simple aspects of computational thinking to debate the idea that foods have something in them, or added to them, that may be different across various foods (e.g., If there wasn’t any flavor then your mouth would be Yeach). Specifically, students engaged in decomposing the phenomena of taste, developing a beginning understanding that smaller units with distinct properties contribute to the sensation of a given taste. However, they also hold the contradictory idea that something responsible for taste is an added but perhaps not essential component of the food. The students also have not ruled out the idea that taste buds and the brain cause the sensation of different tastes. While the modeling practice was useful for mechanistic reasoning, in this case it did not surface the contradiction. However, modeling promoted more discussion by forcing the students to concretely break down and represent abstract ideas. The students needed to make clear the interaction between components that result in taste.

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11.9.3  L  essons Three and Four: Using the Practice of Investigation and Revising Models for Explaining and Predicting Phenomenon to Get at the Particle Nature of Matter Instead of using the driving question in the materials, How do we smell different tastes?, Ann introduced this investigation based on one of the student questions asked in lesson one, Can we taste with our nose plugged?, which the class liked. They predicted smell would influence their ability to differentiate taste. Ann distributed skittles and had the students use blindfolds to conduct taste trials with their noses plugged and unplugged. Group 5 tried to explain why they were more accurate when their noses were unplugged. Shay: Well I was thinking I have this theory. There is the taste that goes to the roof of your mouth. And when you taste something … (she trailed off) Well I don’t know what I am talking about … Something about … It’s like connected … Ava: Your nose and your mouth. It’s connected. In your mouth there is a passageway up to your mouth. Shay: Then there is another passageway up to your brain! Ava: Yeah. It goes up to your nose and there is like holes and so yeah. Valencia: That is when you smell. Shay: Yeah goes up to your brain.

Jacob pushes the students toward the invisible mechanism of smell, which prompts Shay to go back to taste buds: Jacob: It goes up the aroma maybe. The things in your nose like if you have your nose plugged you can taste it like the back of your nose. Ava: By it we mean food, it is food. Jacob: Aroma. Some foods taste different than others right? Shay: Cause there’s taste buds on your tongue and on the roof of your mouth. (She pauses) And in the roof of your nose. Valencia: The roof of your nose? (Laughs. All of the students laugh)

Ann comes by and asks the students how smell is working to help the taste. Ava responds, “The aroma maybe?”. The students in Group 5 agreed that aroma is the same thing as food. The group added a nose and the same symbol for taste (the squiggly lines with dots for minerals) reaching toward the nose to their model. What purchase does data analysis of an investigation provide for understanding taste in terms of the particle nature of matter? For Group 5, the investigation and data analysis made apparent that smell is a phenomenon that needs to be included in an explanation of different tastes. Yet, the intention of the lesson—to push students toward the need to explain “invisible” matter—did not occur. Using Johnson’s progression between categories 2 and 3, the students are still in the gray area between matter contains particles and matter is composed of particles. They also seem to continue to hold onto the idea that particles could be comprised of a homogeneous substance (see Fig. 11.1).

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(2) matter contains particles, Particles are homogeneous substances

(3) matter is composed of particles

(4) matter is composed of particles and the properties of matter depend on the interaction between particles

Fig. 11.1  Students progression toward understanding particle nature of matter. Darker areas indicate more understanding achieved

11.9.4  L  esson Five: Using the Practice of Computational Thinking for Explaining and Predicting Phenomenon to Get at Particle Nature of Matter Ann began class by going over with the class some of the questions they are still working on. She told the class: We have really been thinking a lot about taste and how we are tasting and smelling foods. But we need to think about patterns in tastes and foods. How is that foods have some tastes that are similar? We need to figure out patterns and describe what is happening when we encounter a pattern. That is something that scientists do.

Following the actions outlined in the curriculum, Ann had the students come up with a definition of pattern to refine later. The students came up with the following definition: Pattern: A pattern is the same sequence that repeats indefinitely. If something is in a pattern, you can use the pattern to predict what might happen. A pattern might not go on forever, but it could.

Ann told the students that they would refine the definition later on in the unit. She presented the task for the lesson while distributing plates of goji berries, dried apricot, tomato, orange, apple, and raisins: I am putting the foods out here and you have to figure out three categories to describe sweetness. I don’t want you to describe the food. I want you to make three different categories for the experience of the taste of sweetness.

Ann sketched lines for three distinct categories on the whiteboard and continues: Like intensity, maybe, really strong sweet taste. Or, what sweetness also has with it, like another taste that accompanies the taste in different foods. For example, does sweetness come with sour in one food, and not in another. You have to describe the sweetness in three different ways, and then place the foods in the three categories. Can you do it? Do you need more examples?

The students in Group 5 sampled the food and quickly refined or engaged in iterating (a computational thinking practice) how to break up the way they tasted sweetness into three categories: (1) sweet now, (2) sweet later, and (3) sweet the

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Fig. 11.2  Patterns of taste described by Group 5

whole time. The categories were based on trying the goji berries, which started out sweet and then tasted “bad.” After figuring out the categories—essentially decomposing (a computational thinking practice) the phenomenon problem into smaller elements based on patterns (a computational thinking concept)—the group was able to categorize the different foods into the three categories, essentially recognizing patterns in the similarities and differences among the foods. As seen in Fig. 11.2, the three patterns the students found across the foods are labeled: sweet now; sweet later; and sweet the whole time. In revising or iterating how to sort tastes in these categories, students re-engaged with the notion of matter being composed of particles. Ann asked each student group to denote one of their groups as the most courageous taster. She told the kids that they were going to taste a mystery food, and the taster would write one of the categories in their table. Then based on the table, the others would try to figure out how that taste could be described. The students in Group 5 selected Ava to be the taster, who tasted a date. Her group studied her face while she tasted the date. Ava made the most of the moment, swishing the food around in her mouth like a sommelier. After the teacher’s cue, Ava wrote “Dates” down in the first category and “Sweet now.” Ann asked each group to see if they could try to identify what the mystery taste had been. The students discuss how to identify the mystery taste below: Shay: So what I am thinking that you are tasting it. You first took a bite and it was like … she likes it. Before it was sweet and then it turned nasty. Valencia: I know! Because you didn’t put it in sweet the whole time! Jacob: When I saw her facial expression it was kind of disgusting I think it was sweet when she first took the first bite and I saw her like … she did this (He makes a sweet face) that like she liked it. And then she took another bite and ah um (He changed his face to indicate that it stopped being sweet. The students all looked to Ava for assent. She gave them a thumbs up.)

Ann asked the groups to consider their charts: Is there something the same about how you taste the things on one side of your chart compared to the other categories? How you tasted the sweetness in different categories? I want

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you to discuss with your groups and be ready to share. Is how you are tasting one group actually different from how you are tasting the other food in the other? What is the same in some foods that is different or the same in the other foods?

This line of questioning worked to spark discussion in Group 5. Jacob started with the idea of the taster physically moving the food to a particular taste bud purposefully, because they expect a certain taste, but Ava disagrees with Jacob: Jacob: Um. It was like some time there was a lot of things that were sweet the whole time because sometimes you know where the taste is gonna go. When you don’t know where it's gonna go you taste it and see what it tastes like. Ava: How are these different from tasting those? He (Jacob) said that but there are so many things that weren’t sweet the whole time. Not the whole thing, maybe part of the food is not sweet Jacob: I didn’t really say about the later part!

Shay thinks the foods react at different times, alluding to chemical reaction again, though Jacob questions this idea: Shay: The sweet now, I feel like the process happened faster than sweet later. Sweet now … like your brain goes faster your taste buds are sending up the food to your brain to figure out that sweet. Jacob: If it is sweet later, then the process happens the same? Why? And then it takes longer to taste the sweet, Why? Shay: Because of your taste buds, that is why! Jacob: (shakes his head) Ava said it happened quicker and slower.

Valencia suggests that there is something different in the actual foods that results in the patterns of faster or quicker sensation of sweet tastes, an idea that interests Ava: Valencia: It happens how the food grow in the ground, on the bush in or on the bush. The food grow different and then they are different places where the sweet is in them. Or sometimes the people, they put like chemical in it and it tastes different in the, the chemical that they add. Ava: Why are you tasting these the same? (She indicated the foods in the sweet all the time column) and then these taste different?

Jacob continues, building on Valencia’s idea, and Shay finally comes around too: Jacob: I think that because you probably want to know how it’s something sweet at first and then it fades always how they are grown faster or slower makes that food different. They food had stuff in it that makes the sweet taste quicker or slower. Not sweet the whole time because everything that like because I mean everything is organic so there is not chemical stuff in it, it is a natural way of it how it is grown. Shay: OK, yes, I tried an apple from an apple tree there is not chemical in it, like they grow on the tree. Also these (indicates the sweet whole time column) would taste the whole time because it was without anything extra.

Ava was listening intently, now she speaks, summing up the group’s ideas about how to categorize tastes—the process they have been iterating on—she presses on the idea that matter is composed of particles too small to see: Everything that was sweet the whole time, and some things on that list this was like sweet then it goes yummy and then a few minutes later, yuck! … The flavor that the ingredient of

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sweet, and the flavor was the same at different times, is a similar ingredient that is in all of them. It is part of what was in the growing in there is some things the same and different because they were grown. But the similar ingredient is in the food … somewhere in the food and different in the food. Jacob: (points to the word “Pattern” on the notebook) “That’s the pattern!” (He leans back, triumphant) “The minerals inside the food, that is the same in every one of them.”

What purchase does computational thinking provide learners for using the particle nature of matter to understand taste? This final lesson in the set forwarded the practice of computational thinking. The use of the patterns promoted an iteration of ideas around the phenomenon of taste and discussion about how this phenomenon has patterns that can be applied to determine similar and different compositions across foods. Here we see students making use of computational thinking to iteratively develop beginning ideas around the phenomenon of taste being the chemical reaction to various compositions of particles that make up foods, a deepened understanding arrived at through engaging in the decomposition of the phenomenon into smaller parts. In lessons 1–4, the variance of taste seemed to be an experience that they were not able to deeply refine or iterate their understanding. Instead, the students understood taste as an encompassing experience: a food was good, or it was spicy, or lemony, causing them to consider foods as homologous substances. Computational thinking, especially the practices of decomposition and iteration, enabled the group to rework the phenomenon of taste and smell as being a phenomena with multiple steps, deepening the idea of the particle nature of matter.

11.10  Discussion and Conclusion The promise of computational thinking for supporting science instruction has begun to receive more attention (Grover & Pea, 2013, 2018), but additional exploration is needed on how to productively integrate the practices and concepts of computational thinking to support the building of useable knowledge. Little is known about how to support elementary children in computational thinking. In this case study, we explored how elements of computational thinking were critical in supporting a group of learners in developing knowledge of the particle nature of matter. Like Grover and Pea (2013, 2018), we like to think of computational thinking as several reinforcing practices, and we do not restrict the practice to computer programming. As this study shows, when supported by carefully designed instruction, students can productively engage in various associated practices of computational thinking without having to rely on technology-laden approaches that emphasize programming or coding. This particularly comes through in lesson five. When teachers explicitly support computational thinking practices such as decomposition and iterative refinement, young learners do engage in these practices. For this case study, we asked What does the practice of computational thinking afford students making sense of phenomena related to the core idea of the particle

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nature of matter? Our work offers insights into the value of computational thinking for supporting students in sensemaking. The students had already engaged in the practices of asking questions, developing a model, and conducting an investigation with data analysis. However, they had reached a point of relative immobility, alternating between Johnson’s (1998) levels of matter being homologous (i.e., “The aroma is the food”) and matter containing particles (i.e., “There are minerals in the food”). After using various practices associated with computational thinking, students made progress in their shared understanding of particle nature of matter (i.e., “The flavor that the ingredient of sweet, and the flavor was the same at different times, is a similar ingredient that is in all of them”). The students did not have the language yet to express the idea scientifically, that indeed goji berries and dates contain sugars (fructose and glucose) and that these chemicals form part of the matter that makes up these foods. These ideas are beyond what is expected at the fifth grade level. However, our work shows that the groups were wading into the territory of the third level in Johnson’s (1998) progression, matter is composed of particles, and also the fourth level—that this composition is related to the properties of that matter, specifically taste. This is an appropriate level of understanding for students to develop at this grade level as suggested by the Framework and the NGSS. In this case, computational thinking was particularly helpful in moving the focus group students squarely along the progression of understanding. Group 5’s interactions show the beginning of a trajectory to using computational thinking, but significant challenges remain in terms of how to sequence student engagement in building on early experiences while also leveraging DCIs. Aspects of computational thinking may prove more useful for some sets of science ideas (DCIs and CCCs) than others. Further, the appropriate progression for computational thinking may depend on purposeful integration with a specific set of science ideas. Given the limited scope of this work, our results only suggest limited insights, but they do offer a glimpse of the value of computational thinking in supporting learners in making sense of phenomena. In STEM careers, professionals must be adept in iteratively using their science knowledge and in refining practices to accomplish goals, reflecting a knowledge-in-­ use perspective (Harris, Krajcik, Pellegrino, & DeBarger, 2019; Pellegrino & Hilton, 2012). To accomplish a scientific aim, such as answering a question about a natural phenomenon, the three dimensions must be practiced and honed together. Project-based learning provides teachers a way to more authentically integrate this into the classroom and can be used to better inform teaching that can operationalize three-dimensional learning.

References Andersson, B. (1991). Pupils' conceptions of matter and its transformations (age 12-16). Studies in Science Education, 18, 53–85. Bartholomew, H., Osborne, J., & Ratcliffe, M. (2004). Teaching students “ideas-about-science”: Five dimensions of effective practice. Science Education, 88(5), 655–682.

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Blumenfeld, P. C., Soloway, E., Marx, R. W., Krajcik, J. S., Guzdial, M., & Palincsar, A. (1991). Motivating project-based learning: Sustaining the doing, supporting the learning. Educational Psychologist, 26(3-4), 369–398. Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (1999). How people learn: Brain, mind, experience, and school. Washington, DC: National Academies Press. Chin, C., & Brown, D. E. (2002). Student-generated questions: A meaningful aspect of learning in science. International Journal of Science Education, 24(5), 521–549. Coyne, I. T. (1997). Sampling in qualitative research. Purposeful and theoretical sampling; merging or clear boundaries? Journal of Advanced Nursing, 26(3), 623–630. diSessa, A. A. (2000). Changing minds: Computers, learning, and literacy. Cambridge: MIT Press. Duran, L.  B., & Duran, E. (2004). The 5E instructional model: A learning cycle approach for inquiry-based science teaching. Science Education Review, 3(2), 49–58. Engle, R.  A., & Conant, F.  R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20(4), 399–483. Grooms, J., Enderle, P., & Sampson, V. (2015). Coordinating scientific argumentation and the next generation science standards through argument driven inquiry. Science Educator, 24(1), 45–50. Grover, S., & Pea, R. (2013). Computational thinking in K-12: A review of the state of the field. Educational Researcher, 42(1), 38–43. Grover, S., & Pea, R. (2018). Computational Thinking: A competency whose time has come. In S. Sentance, E. Barendsen, & C. Schulte (Eds.), Computer Science Education: Perspectives on Teaching and Learning in School (pp. 19–38). London: Bloomsbury Academic. Haag, S., & Megowan, C. (2015). Next generation science standards: A national mixed-methods study on teacher readiness. School Science and Mathematics, 115(8), 416–426. Hadenfeldt, J. C., Liu, X., & Neumann, K. (2014). Framing students’ progression in understanding matter: A review of previous research. Studies in Science Education, 50(2), 181–208. Harris, C., Krajcik, J., Pellegrino, J., & DeBarger, A. (2019). Designing knowledge-in-use assessments to promote deeper learning. Educational Measurement: Issues and Practice, 38(2), 53–67. Johnson, P. (1998). Progression in children's understanding of a ‘basic’ particle theory: A longitudinal study. International Journal of Science Education, 20(4), 393–412. Krajcik, J.  S., Palincsar, A., & Miller, E. (2015). Multiple literacies in project-based learning. In Michigan State University in East Lansing. MI: Lucas Education Research/George Lucas Educational Foundation. Krajcik, J. S., & Shin, N. (2014). Project-based learning. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (2nd ed., pp. 275–297). New York: Cambridge. Liu, X., & Lesniak, K. (2006). Progression in children's understanding of the matter concept from elementary to high school. Journal of Research in Science Teaching, 43(3), 320–347. Manz, E. (2012). Understanding the codevelopment of modeling practice and ecological knowledge. Science Education, 96(6), 1071–1105. Manz, E. (2015). Representing student argumentation as functionally emergent from scientific activity. Review of Educational Research, 85(4), 553–590. McNeill, K. L., & Krajcik, J. (2012). Supporting grade 5—8 students in constructing explanations in science: The claim, evidence and reasoning framework for talk and writing. New  York: Allyn & Bacon. Merritt, J. D., Krajcik, J., & Shwartz, Y. (2008). Development of a learning progression for the particle model of matter. In Proceedings of the 8th International Conference for the Learning Sciences: Vol. 2 (pp. 75–81). Utrecht: International Society of the Learning Sciences. Miller, E., Lauffer, H. B., & Messina, P. (2014). NGSS for English language learners. Science and Children, 51(5), 55. Miller, E., Manz, E., Russ, R., Stroupe, D., & Berland, L. (2018). Addressing the epistemic elephant in the room: Epistemic agency and the next generation science standards. Journal of Research in Science Teaching, 55(7), 1053–1075.

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National Research Council. (2007). Taking science to school: Learning and teaching science in grades K-8. Washington, DC: National Academies Press. National Research Council. (2012). A framework for K-12 science education: Practices, crosscutting concepts, and core ideas. Washington, DC: National Academies Press. National Research Council. (2015). Guide to implementing the next generation science standards. Washington, DC: National Academies Press. NGSS Lead States. (2013). Next generation science standards: For states, by states. Washington, DC: National Academies Press. Osborne, J., Erduran, S., & Simon, S. (2004). Enhancing the quality of argumentation in school science. Journal of Research in Science Education, 41(10), 994–1020. Pellegrino, J. W., & Hilton, M. L. (Eds.). (2012). Education for life and work: Developing transferable knowledge and skills in the 21st century. Washington, DC: The National Academies Press. Penuel, W. R., Harris, C. J., & DeBarger, A. H. (2015). Implementing the next generation science standards. Phi Delta Kappan, 96(6), 45–49. Schwarz, C.  V., Reiser, B.  J., Davis, E.  A., Kenyon, L., Achér, A., Fortus, D., et  al. (2009). Developing a learning progression for scientific modeling: Making scientific modeling accessible and meaningful for learners. Journal of Research in Science Teaching, 46(6), 632–654. Shepardson, D. P. (2005). Student ideas: What is an environment? The Journal of Environmental Education, 36(4), 49. Trygstad, P. J., Smith, P. S., Banilower, E. R., & Nelson, M. M. (2013). The Status of Elementary Science Education: Are We Ready for the Next Generation Science Standards? Inc: Horizon Research. Wilkerson, M., & Fenwick, M. (2017). Using mathematics and computational thinking. In C.  V. Schwartz, C.  Passmore, & B.  J. Reiser (Eds.), Helping students make sense of the world using next generation science and engineering practices (pp. 181–204). Arlington, VA: National Science Teachers Association. Windschitl, M., Thompson, J., & Braaten, M. (2008). Beyond the scientific method: Model-based inquiry as a new paradigm of preference for school science investigations. Science Education, 92(5), 941–967. Wing, J. M. (2006). Computational thinking. Communications of the ACM, 49(3), 33–35.

Chapter 12

Developing US Elementary Students’ STEM Practices and Concepts in an Afterschool Integrated STEM Project Sasha Wang, Yu-hui Ching, Dazhi Yang, Steve Swanson, Youngkyun Baek, and Bhaskar Chittoori

Contents 12.1  R  eview of Integrated STEM Research in Primary School Grades 12.2  Our Perspective of Integrated STEM Approach 12.3  An Integrated STEM Inquiry Design 12.3.1  Inquiry Design 12.3.2  Implementation 12.3.3  Evaluation 12.4  Theoretical Framework 12.5  Method 12.5.1  Task: Finding Water on Mars 12.5.2  Data Source 12.5.3  Data Analysis 12.6  Results 12.6.1  Routines 12.6.2  Word Use 12.7  Discussion 12.7.1  Merging STEM Practices 12.7.2  Overlapping STEM Concepts 12.7.3  Learning Opportunities in Integrated STEM Approach 12.7.4  Challenges in an Integrated STEM Approach References

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In this chapter, we begin with a review of various STEM perspectives and research on STEM teaching and learning. We take on an integrated STEM approach to design and implement a robotics activity to engage primary school students’ interests in STEM learning. We expand Sfard’s discursive framework as an analytic tool to gain a better understanding of students’ scientific-mathematical thinking. The discursive framework sheds light on ways students communicate their thinking using words S. Wang (*) · Y.-h. Ching · D. Yang · S. Swanson · Y. Baek · B. Chittoori Boise State University, Boise, ID, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Anderson, Y. Li (eds.), Integrated Approaches to STEM Education, Advances in STEM Education, https://doi.org/10.1007/978-3-030-52229-2_12

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and their course of actions in completing tasks in a robotics activity. We identify some opportunities and challenges in this integrated approach to start a global dialogue to promote needed research in STEM education. STEM education has been gaining increasing national and international attention. As the US economy is becoming more diversified and reliant on innovation, STEM skills and proficiency are increasingly needed to build a STEM-literate society and a general workforce with twenty-first-century competencies (Bybee, 2013). While the STEM reform movement has ambitious goals in the USA, a lack of shared understanding exists in regard to what STEM is and how to start STEM education with students in primary schools. The term “STEM reform” encompasses a range of perspectives including disciplinary focus, curriculum design, student learning and achievement, identity and interests, and so on (Renninger, 2010; Sansone, 2009). In the USA, STEM curriculum in primary schools is predominately focused on mathematics and science (NAE & NRC, 2014). Technology in STEM is addressed in a variety of ways, and researchers refer to it as educational or instructional technology (ITEEA, 2000). The newest and least developed component of STEM is engineering. In presenting the connections between STEM disciplines, the term “integrated STEM” arose with the intent to teach STEM in a more connected manner in the context of real-life issues and to engage students in STEM learning (Bybee, 2013; NAE & NRC, 2014). Yet, despite these efforts to make the connections between STEM subjects, the “integrated STEM” approach is complicated by the curriculum that is introduced in K-12 in which learning is emphasized in discrete subject areas. Given these various perspectives of STEM education and the lack of connectedness between STEM subjects, English (2016) pointed out that “the challenge is how to achieve a more balanced content representation in STEM education” (p. 2).

12.1  R  eview of Integrated STEM Research in Primary School Grades Many studies claim the benefits of learning of integrating STEM education for students and how integrated approaches support a range of outcomes within and across disciplines. Among those studies, in integrating mathematics and science, Lehrer and Schauble (2006) conducted studies using mathematics to represent and model natural systems and found that enhanced development of scientific concepts was challenging for students in the primary grades. The effect of engineering content and practice on learning in science and mathematics was examined in engineering in K-12 education, and researchers found promising evidence of a positive impact (NRC, 2009). For example, English and King (2015) found that fourth-grade students showed varying levels of sophistications to design and redesign model planes through engineering design process using mathematics and science ideas and offered a framework of design process for younger learners as one way to approach early engineering education.

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Fostering the development of students’ interest in STEM is an important potential outcome of integrated STEM experiences. Most research reviews have shown that afterschool programs or experiences have emphasized interest and engagement outcomes, whereas school-based programs were more likely to focus on achievement outcomes (NAE & NRC, 2014). Interest is often characterized in terms of curiosity and persistence, and research findings show that the presence of interest positively affects learner attention, goals, and levels of learning and that learners of all ages can be supported to develop interest (Hidi & Renninger, 2006; Renninger, 2010). Calabrese-Barton et al. (2013) observed a sixth-grade African American student learning in both classroom and afterschool activities. They found that by attending an integrated STEM project in an afterschool program, the student’s interest in science increased and her identity in science developed into one of a confident and competent student of STEM.  In a study of an all-girl summer camp with a STEM focus, the girls’ self-reporting of the likelihood of pursuing a career in mathematics, science, or engineering rose from an average of 6.3 to 7.4 on a 10-point scale (Plotowski, Sheline, Dill, & Noble, 2008). Studies of robotics programs in afterschool learning showed mixed results on students’ attitude toward STEM. Some revealed no significant differences in attitude between program participants and a control group of non-participants in a 4-H robotics program, whereas others showed improvements in students’ attitudes toward science and technology by engaging them in computer programming using robotic kits (Barker, Nugent, Grandgenett, & Hampton, 2008; Martin et al., 2011). Research on integrated STEM experiences suggests that there are promising opportunities for supporting both learning in and across the STEM disciplines. The research base is limited in terms of the design of the studies, the populations of students involved, the outcome measures used, and the extent to which research examines the mechanisms underlying learning in integrated STEM contexts. The committee on integrated STEM education (NAE & NRC, 2014) defined integrated STEM as “integration to mean working in the context of complex phenomena situations on tasks that require students to use knowledge and skills from multiple disciplines” (p.  52). There is a need for more studies that measure or document students’ abilities to make connections across concepts and practices in STEM disciplines. Few studies focus on the development of interest and identity in primary grades, and even fewer address interest and identity development in the context of integrated STEM in afterschool settings.

12.2  Our Perspective of Integrated STEM Approach In most US primary schools, teachers are responsible for teaching multiple subject areas including mathematics, science, literacy, and social sciences. Therefore, a well-designed integrated STEM curriculum has a practical value that can assist

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primary school teachers to overcome some of the instructional challenges and engage primary school students in STEM learning in and outside of the classroom. This approach also aligns with practices emphasized in the Common Core State Standard in Mathematics (NGACPB, 2010) and the Next Generation of Science Standards (NRC, 2013). Thus, our perspective of integrated STEM approach reflects the goals of designing an integrated STEM curriculum that offers balanced content and practices across the STEM subjects and facilitates learning experiences that “require students to use knowledge and skills from multiple disciplines” (NAE & NRC, 2014, p. 52). Based on this perspective, our study set out to explore merging STEM concepts and practices and to identify the opportunities and challenges of implementing integrated STEM inquiry with the following research questions: 1. Which STEM concepts and practices did students use in an integrated STEM inquiry? 2. What were the learning opportunities and challenges in an integrated STEM inquiry? In the following section, we use a robotics activity to give a detailed description of an integrated STEM inquiry design process and introduce Sfards’ framework for analyzing merging concepts and practices to investigate learning opportunities and challenges.

12.3  An Integrated STEM Inquiry Design In designing a robotics activity, we modified an interactive model provided by the committee on integrated STEM education (NAE & NRC, 2014) that included goals, inquiry design, implementation, and evaluation.

12.3.1  Inquiry Design To have a well-balanced content and pedagogical design for an integrated STEM inquiry, the interdisciplinary research team included a retired NASA astronaut, a civil engineer, and mathematics education and educational technology faculty. The teachers were local primary schools teachers who implemented the inquiry and offered content and pedagogical advice. These efforts brought together a range of STEM experts which enabled students to participate in activities related to science, technology, engineering, and mathematics as constructive practices.

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STEM Concepts, Practices, and Activity Phases We chose to design a robotics activity, “Is there Life on Mars?”, because it reflects a current research program in US National Aeronautics and Space Administration (NASA), to engage students in exploring problems or conducting investigations that represented STEM disciplines as an integrated way (Bybee, 2013). Figure  12.1 illustrates the intended STEM concepts and practices in the robotics activity. The three circles represent categories of STEM content: Science, Engineering and Technology, and Mathematics. Engineering and Technology is combined into one category to avoid redundancy. Concepts such as distance, time, speed, angle, and direction appear in all three categories. The arrows indicate common practices of the STEM disciplines such as “quantitative reasoning and spatial reasoning” and “developing strategies.” The robotics activity was sequenced into three phases, each with specific learning goals: Preparation Phase: Explore motors, sensors, wires, software, and wheels using LEGO Mindstorms kits. Research information on Mars and apply knowledge in science about life, reproduction, organisms, and growth to understand the formation of life. Designing, Building, and Testing Phase: Design and build a robot using LEGO Mindstorms kits, determine input values for programs, and test the robot for its

Fig. 12.1  STEM concepts and practices presented in the robotics activity

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ability to move, turn, and detect objects (rocks and colors) using motors and sensors. Final Challenge Phase: Participating in a robotics challenge as a team. The robot should be designed to detect “life (a green slot) on Mars” in a simulated Mars environment. Problem-Based Learning (PBL) PBL provides a learning environment that engages students in loosely structured problems for which multiple solutions are possible. According to Barrows (1996), the central features of PBL include being student-centered; working in small groups, with teachers as facilitators; using problems as the focus and stimulus for learning; and acquiring new information through self-directed learning. In this robotics activity, students built a robot using LEGO Mindstorms kits, and in doing so, they investigated a wide range of STEM concepts such as how sensors work and how input values such as angles of turning and speed affect the performance of the robot. They used mathematics to determine angle measures and applied spatial reasoning to explore how a robot moves. Through the design-test-redesign cycles, they developed their own strategies.

12.3.2  Implementation The enactment of the robotics activity included the following: discourse practices, afterschool learning environment, and resources and support. Guided by the PBL approach, infusing discourse practices offered a useful tool for teachers during the implementation. For example, in facilitating a team of students to design a robot, a teacher asked questions such as “What is the plan?”, “How is it going to store the rocks?”, and “Why can’t it just go around the rock [instead of hitting the rock]?” to guide student thinking through the design-test-redesign process. The approach of PBL is widely applied in many afterschool STEM programs to spark, sustain, and extend students’ interest, as well as to develop understanding and commitment to STEM (Afterschool Alliance, 2013; NRC, 2009). Afterschool programs provide desirable learning environments for students to engage in complex projects or innovations (NRC, 2011). This setting also engages teachers to explore new curriculum materials in afterschool programs because the assessment of learning is usually not driven by standardized tests. So afterschool programs in  local communities were selected to implement the robotics activity. As facilitators, teachers were given the curriculum materials, and they attended professional development (PD) sessions prior to the implementation. During the PD sessions, teachers were introduced to the core STEM contents represented in the robotics activity and PBL curriculum design. During the implementation, a retired

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NASA astronaut and two interdisciplinary team members were there to assist teachers and students.

12.3.3  Evaluation Our goal in designing integrated STEM inquiry was to engage students and develop their interests in STEM learning, so we assessed students’ attitude toward STEM as a learning outcome. We also used Sfard’s (2008) discursive framework to investigate how students communicated their thinking through teamwork interactions, as well as to identify merging concepts and practices in STEM learning.

12.4  Theoretical Framework Sfard’s (2008) communicational approach defined the term discourse as “any act of communication made distinct by its repertoire of admissible actions and the way these actions are paired with re-actions” (p.  297). She also made a distinction between language and discourse, viewing language as a tool while discourse as an activity in which the tool is used or mediates. Sfard’s work focuses on mathematical discourse and argues that discourse counts as mathematical when it features mathematical vocabulary relating to numbers and shapes. According to Sfard (2008), discourses are distinguishable by their vocabularies, visual mediators, routines, and endorsed narratives. These four features of discourse interact with one another in a variety of ways. For example, endorsed narratives contain discourse-specific words and provide the context in which those words are used; routines are apparent in the use of visual mediators and produce narratives; visual mediators are used in the construction of endorsed narratives, etc. In an integrated STEM context, we refer to the discourse as scientific-­ mathematical discourse when it features vocabulary relating to identifiable STEM concepts. We expand Sfard’s discursive framework to investigate students’ scientific-­ mathematical discourse because it provides a lens through which to view thought processes at a higher resolution (Wang, 2016). In what follows, we use a robotics activity to illustrate each of these characteristics. Words use are scientific terms that signify objects, processes, or input values. In the robotic activity using LEGO, discipline-specific words used for programming such as motor, sensor, loop, switch, and parameter signify objects, whereas words such as save, drag, touch, move, detect, and turn indicate processes in programming. Words such as distance, angle, time, and speed are used to determine how a robot moves and as input values for programming. Routines are well-defined repetitive patterns characteristic of the given discourse. In the robotics activity, routine procedures can range from routines of designing, programming, and testing. Moreover, when students explore how to make a robot

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move, routine procedures also include routines of determining angles of turning, distances, or speed and routines of using sensors. Narratives are “A set of utterances spoken or written that is framed as a description of objects, of relations between objects, or of processes with or by objects, that is subject to endorsement or rejection, with the help of discourse-specific substantiation procedures” (Sfard, 2008, p. 134). In the robotics activity, endorsed narratives are evident as input values for coding, or mathematical statements. For example, after testing, students endorsed a narrative (verbal), “moving straight with a speed of 50 for 2.5 seconds,” to determine how a robot moves and then translate it into input values for coding (codes). Visual mediators provide the means through which objects of discourse are identified. In the robotics activity, visual mediators may include a diagram of a robot, gestures for communicating the directions of robot’s movements, and symbolic artifacts that are created specifically for coding/programming, such as the images of loops and blocks. In this chapter, we focus on what students said to communicate their ideas through dialogues (words use) and what they did (routines) collaboratively in a robotics activity.

12.5  Method The robotics activity, “Is there life on Mars?”, was implemented in an afterschool program in a Northwestern state in the USA during fall 2017. Three primary school teachers from the same school (but teaching at different grade levels) facilitated the robotics activity. Eighteen students aged between 10 and 12 years old (5 girls and 13 boys) from the same primary school participated in the 8-week-long robotics activity for two 90-minute sessions weekly, and the first 18 to express interest in attending were recruited. These students were divided into three groups of six (led by one teacher), and then each group was divided into two subgroups of three students to form teams. Students worked in teams for the robotics activity. In this chapter, we introduce two teams (six students): the “Mars Z” Team and the “Einstein” Team (student named). The “Mars Z” team included Caleb, Mateo, and Owen (all pseudonyms). According to the demographic survey, Mateo had never built a robot using LEGO, nor had he any programming experience. He signed up for the robotics activity because he wanted to learn about space and science and how to make a robot. Both Caleb and Owen had built robots using LEGO before and had some experience with programming. They signed up for the robotics activity because “I love science so much” (Caleb) and “I like robots” (Owen). The “Einstein” Team included Sara, Lucy, and Dory (all pseudonyms). Sara, Lucy, and Dory had never built a robot using LEGO, nor had any programming experience. They signed up for the robotics activity because “I want to learn about science” (Sara) and “[I] love science and space” (Dory).

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Table 12.1  Finding water on Mars task

Image of the Mars simulation

Task: finding water on Mars • Robot will be placed in Location 1 with a specific heading or orientation. The “water” (green paper) is placed in a known location, somewhere near the middle • The robot will make a sound (whatever each team wants) when the robot finds “water” • The maximum time for the robot to find water is 3 minutes • If the robot doesn’t cooperate for whatever reason, the team can pick it up, move it back to the starting position, and try again. Repeat this until the 3 minutes is up. The time will keep running until the robot finds “water”

12.5.1  Task: Finding Water on Mars A retired NASA astronaut designed the Mars simulation (see Table 12.1). After 6 weeks of learning how to use the LEGO Mindstorms kits, students were given the task of programming their robots to detect “water” in the simulated Mars environment from a specific location. To complete the task, students needed to apply what they learned about the LEGO kits (e.g., sensors, motors, etc.) and to use their mathematics knowledge and skills to determine directions and angles of turning, as well as distance and speed for how far and fast the robot should move.

12.5.2  Data Source The entire “Finding Water on Mars” task was recorded. Video recordings captured students’ social interactions (what they said) and the strategies they used to solve problems during the activity (what they did). All video recordings (n = 120 minutes for each team) were transcribed for analysis. During our video analyses, we also used students’ computer codes that were produced as a team to augment our video analyses.

12.5.3  Data Analysis We focused our analyses on the task, Finding Water on Mars, because it offered students the opportunity to apply their knowledge and skills in mathematics along with what they learned about LEGO Mindstorms Programming Basics to build a robot that can move. In analyzing the task, there was a large amount of overlap in terms of the various STEM practices and concepts used. Some practices used concepts such as loops, sensors, blocks, and input values for programming the different mechanisms involved and are quite complex to explain. In this chapter, in order to

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Fig. 12.2  LEGO Mindstorms Programming blocks. 2a. Action Block. 2b. Gyro sensor

explore merging STEM concepts and practices, we only report aspects of the most frequently used words by the six students and their routines of determining angles, distance, direction, time, speed, and rotation as “Input Values” for programming the robot (see Fig. 12.2). Figure 12.2 provides an example of an Action Block and a Wait Block (e.g., wait until input from the Gyro sensor) that students used in LEGO Mindstorms for programming. The Input Values vary according to the Mode type that is selected. In Fig. 12.2a, the Mode is set to “Number of Rotations.” This sets the Input Values (from left to right) to be Direction, Power, Rotations, and Brake. More specifically: Direction: By entering a plus or minus value of up to 100, the robot will either turn left or right, and the arrow icon will also change to reflect those values. In Fig.  12.2, with a value of zero (neither plus nor minus), the robot will travel straight forward as indicated by the arrow icon above it. Power (or speed): The speedometer icon will change to reflect those values. In Fig. 12.2, the robot will travel straight forward with a speed of 50. Rotations: For this field, no icons will change to reflect the field entry. An alternative for Rotations is to use “Time” by switching it to “the clock icon.” In Fig. 12.2, the robot will travel straight forward with a speed of 50 with 1 rotation. Brake: This field is strictly a select field. A “Stop” or a “Coast” action can be selected. In this example, the Stop action is selected for a quicker stop. In Fig. 12.2b, an Action Block (left) is connected with a Wait Block (right) to turn the robot a certain number of degrees. The example in Fig. 12.2b shows the Wait Block Mode, with the Input Values set to “Greater Than, or Equal To” (≥) with a direction of −90°. In determining the input values to program the robot, students had different ways to communicate these concepts such as distance, speed, time, direction, and rotation. To explore further, we aim to show how these concepts are discussed and what STEM practices are observed in this scientific-mathematics discourse through the lens of routines and word use. In analyzing student team interactions, we utilized Sfard’s (2008) discursive framework as an analytical tool to investigate what students said (Word use) and what they did (Routines). Word use in scientific-mathematical discourse is usually about STEM objects, number words, comparison words (e.g., more/less, fast/slow), and so on that appear in utterances. In the task, students used words such as “distance” and “angle” to

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communicate the ways they estimated angle and distance measurements in order to program their robots. Early in our analyses, we noticed that students used terms such as “go forward,” “go up,” “turn left,” or “negative degree” to communicate directions; they used the word “turn” to indicate the angle of turning or rotation and used the word “fast” to describe speed; the word “centimeters” was mentioned as a measurement of estimated distance between the starting point and Rock 1. We identified the words “distance,” “speed,” “angle,” “rotation,” “time,” and “direction” that occurred in the video recordings. For instance, Example 1 was coded as “distance,” Example 2 was coded as “angle,” and Examples 3 and 4 were coded as “directions.” Example 1  What was it, sixty centimeters (“distance”)? Example 2  Make it 75 degree (“angle”). Example 3  Go straight (direction) and turn (“rotation”). Example 4  Working on negative 90 degrees (“direction”). Routines are repetitive patterns in forms of estimating, devising means for testing them, validating procedures, or negotiating ideas to endorse narratives. For this task, routine procedures are the course of actions in estimating time or determining angle and distance measurements and in negotiating ideas to program a robot. For example, some students used the routine of estimating time to determine the distance between two objects by setting speed as a constant, whereas some students used sensors to determine the robot’s motion. From noticeable patterns that appeared in the video recordings, we analyzed students’ routine procedures when identifying which sensors/blocks to use, or determining the directions for the robot to move, as well as the differences in the routine procedures used among the teams.

12.6  Results The findings are reported in two sections: Routines reveal details of students’ repetitive patterns to complete the task and students’ Words Use to communicate their scientific ideas related to the task.

12.6.1  Routines The Mars team (Mateo, Caleb, and Owen) aimed to make the robot move fast because the task, Finding Water on Mars, had a time limit of 3 minutes. In completing the task, they estimated the time the robot needed to travel between the starting point and Rock 1 and tried to determine the angle to turn the robot and then used the color sensor to detect the color green. The Einstein team (Sara, Lucy, and Dory)

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explored the task by using the Action Blocks to make the robot move forward, the Gyro sensor to determine the angle of turning, and the color sensor to detect the color green. It took each team a total of two sessions of approximately 60 minutes per session to figure out the necessary input values using various routines. Tables 12.2 summarizes Mars Z teams’ routine of estimating the robot’s travel time, as well as the routine of devising testing means, with selected transcripts. Caleb, Mateo, and Owen first estimated the robot’s travel time from Start to Rock 1. They started with 20 seconds and then changed the value to 5 seconds and then ultimately 3 seconds. After testing the robot five times in the Mars simulation using these input values, they reached an agreement that the time was 2.5 seconds. The codes they produced confirmed their declared narrative of “Moving straight with a speed of 50 for 2.5 seconds” (see Action Block A in Table 12.2b). When determining the angles of turning before the robot hit Rock 1, they tried to devise different testing methods because their first attempt did not work. The following dialogue took place after the first attempt: Caleb: It should’ve turned this way [←], but it turned in a circle. Wait, I want to see how it’s turning on the carpet. [They watched the robot as it kept turning in circles]. Owen: We should just make it turn, do another program. Say, go forward for 3 seconds. Caleb: I started at 50 [degree], which should turn this way [←], but it didn’t. I’m trying to do a different [angle] degree to see if it would stop [turning in circles]. Caleb: [Mateo] get your computer and make a program that you think will work, and let’s see who make a program that you think will work, okay? Mateo: I think I got mine to work, mine 25 [degree], minus 45[degree].

After the first attempt, the team tried to derive different methods such as changing the angle measure of turning and/or changing the time to stop the robot from turning in circles before it hits the rock. This cycle of comparing and testing the results repeated 12 times until Owen figured it out: Owen: Wait, it 65[degree], no, it’s negative 65 [degree]. [After this attempted failed] Caleb: Get it to turn more. Owen: 85°? We’re pretty close. I want to try 95°, negative 95°. Caleb: Watch this. [Turn on the robot, it’s not going] Owen: It’s not 95 [degree], is negative 90 [degree].

The team agreed that they should put a “negative” sign before 90° as an input value to make the robot turn left and declared narrative, “Turning with an angle of -90 with speed of 25 for one second” (see Action Block B in Table 12.2b). It is important to note that Caleb, Owen, and Mateo spent a lot of time trying to figure out the measurements for the angle of turning for the robot before it hits Rock 1. The team then estimated the speed and used the robot’s color sensor to detect the color green (see Action Block C & D in Table 12.2b). Table 12.3 summarizes Einstein team’s routines with selected transcripts.

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Table 12.2  Summary of Mars Z team’s routines

a. An illustration of the path of the robot to detect color green

Routine procedure 1. Estimate the “time” for robot to travel between “Start” and Rock 1.

Selected transcripts Caleb: We should go on for a certain amount of time Mateo: It’ll take 20 seconds to get there [hit the rock] Caleb: If I can get it to run into the rock in 5 seconds Owen: Try 3 seconds

2. Declared narrative

Input values: Moving straight with a speed of 50 for 2.5 seconds Caleb: It should’ve turned this way [←], but it turned in a circle Owen: I started at 50 [degree], which would turn it this way [←] Caleb: I got minus 25. I did mine as 45. Owen: Oh, not six, five. Sixty-five, wait. Negative 65 [degree] Caleb: Negative 95 [degree]. Get it to turn more…eight-five? Input values: Turning with an angle of − 90° with a speed of 25 for one second

3. Devise means to test the “angle” of turning after the robot hit the rock 4. Declared narrative

5. Estimate the “speed” and use the color sensor to detect color green

Caleb: It’s supposed to sense green… use the wait block? Mateo: How long is this [to the green spot], put it for 5 seconds? 6. Declared narrative

Moving straight with a speed of 50 until (orange wait block) detects with sensor “color green”

b. Mars Z team’s codes

As noted in Table 12.3, the Einstein team incorporated the Gyro sensor to turn the robot for a certain number of degrees with Action Blocks to determine which directions the robot should move and turn. Finally, they used the color sensor to detect the color green. The codes in Table 12.3b were a snapshot of their partial work. We focused on their routines of determining input values instead of the completeness and correctness of the codes. This team also had issues with determining the angle of turning. The following dialogue highlighted their frustrations:

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After the team tested (n = 8) their “educated guess” about the angles of turning, Lucy figured out, “I have the Gyro sensor to go left. Put the negative 90 degrees so it turns the whole robot. It turns the wheels that direction.” The team reached a Table 12.3  Summary of Einstein team’s routines Routine procedure 1. Select Gyro sensor 2. Declared narrative

Selected transcripts Sara: If that [use distance] doesn’t work, we can use “touch” [sensor] Dory: Here is the deal. If it runs into rock and it tries to turn Lucy: Gyro [sensor], and you want reset before that even happens Input values: Reset Gyro sensor Lucy: Go straight, going at the speed of five 3. Determine the a. An illustration of the direction for the robot Sara: Are you sure you want speed of five? path of the robot to and the angle of turning Dory: You want it less than or equal to [≤]? detect color green Lucy: You want it always greater than or equal using Gyro sensor to [≥] 4. Declared narrative Input values: Moving straight with a speed of 5 continue while it is greater than or equal − 90° per second 5. Determine “angle” of Dory: It will turn, go 60 degree, it will have it turning after the robot go straight Sara: It’s still doing that thing where it spins detects Rock 1 around and around 6. Declared narrative Lucy: I have the gyro sensor to go left. The negative 90 degrees so it turns the whole robot. It turns the wheels that direction 7. Keep the same speed Input values: Turning with an angle of − 90° and use color sensor to with a speed of 5 detect color green 8. Declared narrative Dory: I wanna make sure the color sensor sees at the end Lucy: So I want it [color senor] to hit the green Input values: Moving straight with a speed of 5 until (orange wait block) detects with sensor “color green”

b. Einstein team’s codes

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common declared narrative, “Turning with an angle of -90° with speed of 5” (see Action Block D in Table 12.3b). When selecting the icons (i.e., >,