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How Humans Learn to Think Mathematically

David Tall
Publisher: 
Cambridge University Press
Publication Date: 
2013
Number of Pages: 
457
Format: 
Paperback
Series: 
Learning in Doing: Social, Cognitive and Computational Perspectives
Price: 
39.99
ISBN: 
9781107668546
Category: 
Monograph
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Part I. Prelude:
1. About this book
Part II. School Mathematics and its Consequences:
2. The foundations of mathematical thinking
3. Compression, connection and blending of mathematical ideas
4. Set-befores, met-befores and long-term learning
5. Mathematics and the emotions
6. The three worlds of mathematics
7. Journeys through embodiment and symbolism
8. Problem-solving and proof
Part III. Interlude:
9. The historical evolution of mathematics
Part IV. University Mathematics and Beyond:
10. The transition to formal knowledge
11. Blending knowledge structures in calculus
12. Expert thinking and structure theorems
13. Contemplating the infinitely large and the infinitely small
14. Expanding frontiers through mathematical research
15. Reflections
Appendix: where the ideas came from.

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