عنوان

How humans learn to think mathematically :

(Number (ISBN

1107035708

(Number (ISBN

1107668549

(Number (ISBN

9781107035706

(Number (ISBN

9781107668546

Title Proper

How humans learn to think mathematically :

General Material Designation

[Book]

Other Title Information

exploring the three worlds of mathematics /

First Statement of Responsibility

David Tall, emeritus professor in mathematical thinking, University of Warwick, visiting professor, Mathematics Education Centre, Loughborough University.

Place of Publication, Distribution, etc.

Cambridge :

Name of Publisher, Distributor, etc.

Cambridge University Press,

Date of Publication, Distribution, etc.

2013.

Specific Material Designation and Extent of Item

xix, 457 pages :

Other Physical Details

illustrations ;

Dimensions

24 cm.

Series Title

Learning in doing : social, cognitive and computational perspectives

Text of Note

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

Text of Note

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.

0

Text of Note

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.

Source for Acquisition/Subscription Address

Cambridge Univ Pr, 100 Brook Hill Dr, West Nyack, NY, USA, 10994-2133, (845)3537500

Cognition in children.

Cognition.

Knowledge, Theory of.

Mathematics-- Philosophy.

Mathematics-- Psychological aspects.

Mathematics-- Study and teaching.

Thought and thinking.

Cognition in children.

Cognition.

Denken

Formalismus.

Knowledge, Theory of.

Kognition

Kognition.

Matematik-- psykologiska aspekter.

Matematik-- teori, filosofi.

Mathematics-- Philosophy.

Mathematics-- Psychological aspects.

Mathematics-- Study and teaching.

Mathematik.

Mathematikunterricht

Metamatematik.

Symbolische Form

Tänkande.

Thought and thinking.

Number

Edition

Class number

Book number

Tall, David Orme.

Date of Transaction

20200822150555.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y