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How Humans Learn to Think Mathematically
Exploring the Three Worlds of Mathematics

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Part of Learning in Doing: Social, Cognitive and Computational Perspectives

  • Date Published: September 2013
  • availability: Available
  • format: Paperback
  • isbn: 9781107668546

$ 47.99 (P)

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About the Authors
  • 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.

    • Traces mathematical development from child to adult
    • Encourages a common framework useful for researchers across different fields
    • Looks at teaching, curriculum, and cognitive development in elementary school through postgraduate research
    Read more


    • Honourable Mention, 2013 PROSE Award for Psychology

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    Product details

    • Date Published: September 2013
    • format: Paperback
    • isbn: 9781107668546
    • length: 484 pages
    • dimensions: 229 x 152 x 28 mm
    • weight: 0.64kg
    • contains: 175 b/w illus. 4 tables
    • availability: Available
  • Table of Contents

    Part I. Prelude:
    1. About this book
    Part II. School Mathematics and its Consequences:
    2. The foundations of mathematical thinking
    3. Compression, connection and blending of mathematical ideas
    4. Set-befores, met-befores and long-term learning
    5. Mathematics and the emotions
    6. The three worlds of mathematics
    7. Journeys through embodiment and symbolism
    8. Problem-solving and proof
    Part III. Interlude:
    9. The historical evolution of mathematics
    Part IV. University Mathematics and Beyond:
    10. The transition to formal knowledge
    11. Blending knowledge structures in calculus
    12. Expert thinking and structure theorems
    13. Contemplating the infinitely large and the infinitely small
    14. Expanding frontiers through mathematical research
    15. Reflections
    Appendix: where the ideas came from.

  • Author

    David Tall, University of Warwick
    David Tall is Emeritus Professor of Mathematical Thinking at the University of Warwick. He is internationally known for his research into long-term mathematical development at all levels, from preschool to the frontiers of research, including in-depth studies explaining mathematical success and failure.


    • Honourable Mention, 2013 PROSE Award for Psychology

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