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2 - The Foundations of Mathematical Thinking

from II - School Mathematics and Its Consequences

Published online by Cambridge University Press:  05 June 2014

David Tall
David Tall
Affiliation:
University of Warwick
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Summary

This chapter begins the quest to seek the origins of mathematical thinking by asking the fundamental question:

How does a species like Homo sapiens learn to think mathematically?

In particular, how do young children build ideas about space and shape on the one hand and number on the other?

Mathematical thinking occurs within a biological brain that has evolved over the millennia to enable the human species to survive and prosper in the material world. The brain is not carefully designed like a computer. Francis Crick expressed this eloquently, saying:

Evolution is not a clean designer. … It builds, mainly in a series of smallish steps, on what was there before. It is opportunistic. If a new device works, in however odd a manner, evolution will try to promote it. This means that changes and improvements that can be added to the existing structures with relative ease are more likely to be selected, so the final design may not be a clean one, but rather a messy accumulation of interacting gadgets. Surprisingly, such a system often works better than a more straight-forward mechanism that is designed to do the job in a more direct manner.

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Chapter
Information
How Humans Learn to Think Mathematically
Exploring the Three Worlds of Mathematics
 , pp. 33 - 49
Publisher: Cambridge University Press
Print publication year: 2013

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