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How humans learn to think mathematically : exploring the three worlds of mathematics

Author: David Orme Tall
Publisher: Cambridge : Cambridge University Press, 2013.
Series: Learning in doing.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers,  Read more...
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Document Type: Book
All Authors / Contributors: David Orme Tall
ISBN: 9781107035706 1107035708 9781107668546 1107668549
OCLC Number: 838192705
Awards: Short-listed for PROSE Award for Psychology 2013
Description: xix, 457 pages : illustrations ; 24 cm.
Contents: 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.
Series Title: Learning in doing.
Responsibility: David Tall, emeritus professor in mathematical thinking, University of Warwick, visiting professor, Mathematics Education Centre, Loughborough University.

Abstract:

How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult.  Read more...

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