I. Prelude
About this Book
II. School Mathematics and Its Consequences
The Foundations of Mathematical Thinking
Compression, Connection and Blending of Mathematical Ideas
Set-befores, Met-befores and Long-term Learning
Mathematics and the Emotions
The Three Worlds of Mathematics
Journeys through Embodiment and Symbolism
Problem-Solving and Proof
III. Interlude
The Historical Evolution of Mathematics
IV. University Mathematics and Beyond
The Transition to Formal Knowledge
Blending Knowledge Structures in the Calculus
Expert Thinking and Structure Theorems
Contemplating the Infinitely Large and the Infinitely Small
Expanding the Frontiers through Mathematical Research
Reflections
Appendix: Where the Ideas Came From.
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How humans learn to think mathematically : exploring the three worlds of mathematics by David Orme Tall. ISBN 9781107668546. Published by Cambridge University Press in 2013. Publication and catalogue information, links to buy online and reader comments.
