How humans learn to think mathematically : exploring the three worlds of mathematics
David Orme Tall
Bok Engelsk 2013
| Annen tittel | |
|---|---|
| Utgitt | Cambridge : Cambridge University Press , 2013
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| Omfang | 1 online resource (xix, 457 pages) : : digital, PDF file(s).
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| Opplysninger | Bibliographic Level Mode of Issuance: Monograph. - 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.. - 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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| Emner | Cognition
Cognition in children Knowledge, Theory of Thought and thinking Vis mer... Kognisjon
Matematikk Mathematical Theory Mathematics Pedagogisk psykologi Physical Sciences & Mathematics Psykologi Tenkning matematikk filosofi matematikkundervisning kunnskapsteori |
| Dewey | |
| ISBN | 9781107035706. - 9781107668546
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How humans learn to think mathematically : exploring the three worlds of mathematics
by David Tall
Daisy lydbok · Engelsk · 2017
Tilhører NLB
Vis hos NLB
by David Tall
Daisy lydbok · Engelsk · 2017
Tilhører NLB
Vis hos NLB
