Thinking and Comprehending in the Mathematics Classroom

Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Foreword: Recreational Mathematics xi
4. Introduction xvii
5. What is Mathematics For? 1
6. A Tisket, a Tasket, an Apollonian Gasket 13
7. The Quest for God’s Number 27
8. Meta-morphism: From Graduate Student to Networked Mathematician 35
9. One, Two, Many: Individuality and Collectivity in Mathematics 43
10. Reflections on the Decline of Mathematical Tables 51
11. Under-Represented Then Over-Represented: 55
12. Did Over-Reliance on Mathematical Models for Risk Assessment Create the Financial Crisis? 67
13. Fill in the Blanks: 75
14. The Great Principles of Computing 82
15. Computer Generation of Ribbed Sculptures 93
16. Lorenz System Offers Manifold Possibilities for Art 115
17. Celebrating Mathematics in Stone and Bronze 150
18. Mathematics Education 169
19. Thinking and Comprehending in the Mathematics Classroom 188
20. Teaching Research: Encouraging Discoveries 203
21. Reflections of an Accidental Theorist 219
22. The Conjoint Origin of Proof and Theoretical Physics 236
23. What Makes Mathematics Mathematics? 257
24. What Anti-realism in Philosophy of Mathematics Must Offer 286
25. Seeing Numbers 312
26. Autism and Mathematical Talent 330
27. How Much Math is Too Much Math? 336
28. Hidden Dimensions 347
29. Playing with Matches 356
30. Notable Texts 367
31. Contributors 371
32. Acknowledgments 379
33. Credits 381