Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving [Combined Edition] [Combined] 0471089753, 9780471089759
A unique, heuristic approach to mathematical discovery and problem solving This combined edition of Mathematical Discov
116 2 4MB
English Pages 432 [458] Year 1981
Table of contents :
Cover
Title
Foreword
Preface
Hints to the Reader
Contents
Part I: Patterns
1. The Pattern of Two Loci
2. The Cartesian Pattern
3. Recursion
4. Superposition
Part II: Toward a General Method
5. Problems
6. Widening the Scope
Solutions 1-6
Appendix
7. Geometric Representation of the Progress of the Solution
8. Plans and Programs
9. Problems within Problems
10. The Coming of the Idea
11. The Working of the Mind
12. The Discipline of the Mind
13. Rules of Discovery
14. On Learning, Teaching, and Learning Teaching
15. Guessing and Scientific Method
Solutions 7-15
Appendix
Bibliography
Index
Cover
Title
Foreword
Preface
Hints to the Reader
Contents
Part I: Patterns
1. The Pattern of Two Loci
2. The Cartesian Pattern
3. Recursion
4. Superposition
Part II: Toward a General Method
5. Problems
6. Widening the Scope
Solutions 1-6
Appendix
7. Geometric Representation of the Progress of the Solution
8. Plans and Programs
9. Problems within Problems
10. The Coming of the Idea
11. The Working of the Mind
12. The Discipline of the Mind
13. Rules of Discovery
14. On Learning, Teaching, and Learning Teaching
15. Guessing and Scientific Method
Solutions 7-15
Appendix
Bibliography
Index
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