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.

Bibliographic Details
Main Author: Tall, David Orme
Language:English
Published: Cambridge : Cambridge University Press, 2013.
Series:Learning in doing.
Subjects:
Mathematics > Philosophy.
Mathematics > Psychological aspects.
Mathematics > Study and teaching.
Thought and thinking.
Knowledge, Theory of.
Cognition.
Cognition in children.
Physical Description:xxi, 457 pages : illustrations ; 24 cm.
Format: Book
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.