How humans learn to think mathematically : exploring the three worlds of mathematics
(Book)

Book Cover
Published:
Cambridge : Cambridge University Press, 2013.
Format:
Book
Physical Desc:
xxi, 457 pages : illustrations ; 24 cm.
Status:
ASU Main (3rd floor)
QA8.4 .T33 2013
Copies
Location
Call Number
Status
ASU Main (3rd floor)
QA8.4 .T33 2013
On Shelf
Citations
APA Citation (style guide)

Tall, D. O. (2013). How humans learn to think mathematically: exploring the three worlds of mathematics. Cambridge: Cambridge University Press.

Chicago / Turabian - Author Date Citation (style guide)

Tall, David Orme. 2013. How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics. Cambridge: Cambridge University Press.

Chicago / Turabian - Humanities Citation (style guide)

Tall, David Orme, How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics. Cambridge: Cambridge University Press, 2013.

MLA Citation (style guide)

Tall, David Orme. How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics. Cambridge: Cambridge University Press, 2013. Print.

Note! Citation formats are based on standards as of July 2010. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
Description
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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Language:
English
ISBN:
9781107035706, 1107035708, 9781107668546, 1107668549

Notes

Bibliography
Includes bibliographical references (pages 433-445) and index.
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5050 |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.
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