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.

Format:

Book

Author/Creator:

Tall, David Orme.

Contributor:

Cambridge University Press.

Christine Hikawa Fund.

Series:

Learning in doing

Learning in doing : social, cognitive and computational perspectives

Language:

English

Subjects (All):

Mathematics--Philosophy.

Mathematics.

Mathematics--Study and teaching--Psychological aspects.

Mathematics--Study and teaching.

Thought and thinking.

Knowledge, Theory of.

Cognition.

Cognition in children.

Physical Description:

1 online resource (xxi, 457 pages) : illustrations.

Place of Publication:

Cambridge : Cambridge University Press, 2013.

System Details:

text file

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.

Notes:

Description based on print version record.

Includes bibliographical references (pages 433-445) and index.

Electronic reproduction. Cambridge Available via World Wide Web.

Local Notes:

Acquired for the Penn Libraries with assistance from the Christine Hikawa Fund.

ISBN:

1139565206

9781139565202

Publisher Number:

99959126368

Access Restriction:

Restricted for use by site license.