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" How humans learn to think mathematically : "
David Tall, emeritus professor in mathematical thinking, University of Warwick, visiting professor, Mathematics Education Centre, Loughborough University.
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BL
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| Record Number
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839306
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| Main Entry
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Tall, David Orme.
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| Title & Author
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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.
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| Publication Statement
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Cambridge :: Cambridge University Press,, 2013.
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| Series Statement
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Learning in doing : social, cognitive and computational perspectives
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| Page. NO
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xix, 457 pages :: illustrations ;; 24 cm.
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| ISBN
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1107035708
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: 1107668549
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: 9781107035706
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: 9781107668546
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| Bibliographies/Indexes
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Includes bibliographical references (pages 433-445) and index.
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| Contents
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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.
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| Abstract
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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.--Publisher website.
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Cognition in children.
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Cognition.
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Knowledge, Theory of.
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Mathematics-- Philosophy.
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Mathematics-- Psychological aspects.
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Mathematics-- Study and teaching.
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Thought and thinking.
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Cognition in children.
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Cognition.
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Denken
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Formalismus.
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Knowledge, Theory of.
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Kognition
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Kognition.
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Matematik-- psykologiska aspekter.
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Matematik-- teori, filosofi.
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Mathematics-- Philosophy.
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Mathematics-- Psychological aspects.
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Mathematics-- Study and teaching.
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Mathematik.
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Mathematikunterricht
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Metamatematik.
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Symbolische Form
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Tänkande.
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Thought and thinking.
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| Dewey Classification
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510.1
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| LC Classification
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QA8.4.T33 2013
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