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

• 作者： Tall, David Orme, author.
• 其他題名：
  • Learning in doing: social, cognitive and computational perspectives.
• 出版： Cambridge : Cambridge University Press
• 叢書名： Learning in doing: social, cognitive and computational perspectives
• 主題： Mathematics--Philosophy. , Mathematics--Psychological aspects. , Mathematics--Study and teaching. , Thought and thinking. , Knowledge, Theory of. , Cognition. , Cognition in children.
• ISBN： 9781139565202 (electronic bk.) 、 9781107035706 (hardback) 、 9781107668546 (paperback)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
• More
• 摘要註: 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.
• 讀者標籤：

  需登入
• 引用連結：

  Copy Link
• 目前引用數
• Share: