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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	How humans learn to think mathematically :/ David Tall, emeritus professor in mathematical thinking, University of Warwick, visiting professor, Mathematics Education Centre, Loughborough University.
Reminder of title:	exploring the three worlds of mathematics /
Author:	Tall, David Orme,
Description:	1 online resource (xix, 457 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Mathematics - Philosophy. -
Online resource:	https://doi.org/10.1017/CBO9781139565202
ISBN:	9781139565202 (ebook)

How humans learn to think mathematically : = exploring the three worlds of mathematics /
Tall, David Orme,

How humans learn to think mathematically :exploring the three worlds of mathematics /David Tall, emeritus professor in mathematical thinking, University of Warwick, visiting professor, Mathematics Education Centre, Loughborough University. - 1 online resource (xix, 457 pages) :digital, PDF file(s). - Learning in doing : social, cognitive and computational perspectives. - Learning in doing..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.

ISBN: 9781139565202 (ebook)Subjects--Topical Terms:

575254
Mathematics
--Philosophy.

LC Class. No.: QA8.4 / .T33 2013

Dewey Class. No.: 510.1

How humans learn to think mathematically : = exploring the three worlds of mathematics /
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505 0 $a 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.
520 $a 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, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
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