David Tall : Mathematical Growth |
MATHEMATICAL GROWTH: from Child to Mathematician
Journeys through Three Worlds of Mathematics
The book on Mathematical Growth is more than two thirds finished. Chapters in black are in final draft, those in blue are in an advanced draft and those in red are short outlines or old versions needing much rewriting.
1. The Nature of Mathematical Growth (17 pp) [Nov 4th 2004 revised] comments welcome
PART I Evolution and Cognitive Growth
2. Object and Action – The Evolution of Mathematics, 32pp [Sept 26th revisions]
3. Biological Brain and Mathematical Mind, 21 pp [Sept 12th minor revisions]
4. Local Focus of Attention and Global Awareness, 26 pp [Oct 13th 2004 minor revisions]
5. Excitation and Inhibition: Pleasure and Fear, 14 pp [Oct 13th 2004]
6. Three Worlds of Mathematics and the Role of Language, 29 pp [Nov 4th 2004] comments welcome
PART II Elementary Mathematics
7. Geometric Objects: from Doodles to Deductions, 20 pp [October 13th 2004 minor revisions.]
8. Children Counting – a Study in Compression, 34 pp, [Oct 13th 2004]
9. Number Symbols as Process and Concept – The Theory of Procepts, 25 pp [Sept 26th 2004 revised]
10. More Procepts – Algebra 22 pp – [Aug 12th 2004 revised]. comments welcome
11. Functions and Graphs 18pp – [Sept 26th 2004 latest draft].
PART III Interlude: Global Issues
12. Versatile links between the embodied and the symbolic [33 pp draft, November 4th 2004] comments welcome
13. The Role of the Computer, [37pp draft, Sept 26th 2004, I am still working on this]
14. Encouraging Mathematical Thinking [13 page draft, not yet in any good shape. October 23rd]
PARTIV Towards Proof and Formal Thinking
15. The process of deduction and the concept of proof, c. 10 pp [7 pp draft]
16. Contemplating the Infinite, 18 pp
17 Visualising and Symbolising the Calculus, c. 20 pp [18 pp draft]
18. Transition to the Formal World [1 page draft]
19. Natural and Formal Thinking [1 page draft]
20. Creativity and Formalism: embodiment and axiomatics c. 10 pp [1 page draft]
PART V Reflections
21. A Simple Theory c. 20 pp [16 pp draft]