E-Book Overview
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.
E-Book Content
Cambridge University Press 978-1-107-03570-6 - How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics David Tall Frontmatter More information How Humans Learn to Think Mathematically 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. David Tall is Emeritus Professor of Mathematical Thinking at the University of Warwick and Visiting Professor at the Mathematics Education Centre, Loughborough University. He is internationally known for his research into long-term mathematical development at all levels, from preschool to the frontiers of research, including in-depth studies explaining mathematical success and failure. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-03570-6 - How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics David Tall Frontmatter More information © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-03570-6 - How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics David Tall Frontmatter More information LEARNING IN DOING: SOCIAL, COGNITIVE AND COMPUTATIONAL PERSPECTIVES SERIES EDITOR EMERITUS John Seely Brown, Xerox Palo Alto Research Center GENERAL EDITORS Roy Pea, Professor of Education and the Learning Sciences and Director, Stanford Center for Innovations in Learning, Stanford University Christian Heath, The Management Centre, King’s College, London Lucy A. Suchman, Centre for Science Studies and Department of Sociology, Lancaster University, UK BOOKS IN THE SERIES The Construction Zone: Working for Cognitive Change in School Denis Newman, Peg Griffin, and Michael Cole Situated Learning: Legitimate Peripheral Participation Jean Lave and Etienne Wenger Street Mathematics and School Mathematics Terezinha Nunes, David William Carraher, and Analucia Dias Schliemann Understanding Practice: Perspectives on Activity and Context Seth Chaiklin and Jean Lave, Editors Distributed Cognitions: Psychological and Educational Considerations Gavriel Salomon, Editor The