Sternberg R. The Nature of Mathematical Thinking 1996

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Sternberg R. The Nature of Mathematical Thinking 1996

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Textbook in PDF format This volume—the single most comprehensive source of information about the nature of mathematical thinking—is intended for educators and mathematics teachers, psychologists, cognitive scientists, mathematicians, computer scientists, anthropologists, philosophers interested in logical-mathematical thinking, and the interested general public. Essays are written at a level that is accessible to this diversity of audiences. The book is divided into five parts, reflecting psychometric, cognitive/information-processing, cognitive/cultural, cognitive/educational, and mathematical (i.e., mathematicians') approaches to mathematical thinking. The authors of each chapter focus on their own approach but also address a common core of issues, including the nature of mathematical thinking, how mathematical thinking is similar to and different from other kinds of thinking, what makes some people or some groups perform better than others on mathematical thinking tasks, and how mathematical thinking can be taught and assessed. In this way, readers get a balanced introduction to the field, rather than a one-sided presentation or a set of chapters from a biased point of view. All of the contributing authors are distinguished scholars in the domain of mathematical thinking. Preface List of Contributors A Psychometric Approach Mathematical Abilities: Some Results From Factor Analysis (John B. Carroll) Cognitive/Information-Processing Approaches The Process of Understanding Mathematical Problems (Richard E. Mayer & Mary Hegarty) When Erroneous Mathematical Thinking Is Just as "Correct": The Oxymoron of Rational Errors (Talia Ben-Zeev) Cognitive/Cultural Approaches On the Shoulders of Giants: Cultural Tools and Mathematical Development (Kevin F. Miller & David R. Paredes) Culture and Children's Mathematical Thinking (Geoffrey B. Saxe, Venus Dawson, Randy Fall, Sharon Howard) Biology, Culture, and Cross-National Differences in Mathematical Ability (David C. Geary) Cognitive/Educational Approaches Toby's Math (Herbert P. Ginsburg) Fostering Mathematical Thinking in Middle School Students: Lessons From Research (John D. Bransford, Linda Zech, Daniel Schwartz, Brigid Barron, Nancy Vye, & The Cognition and Technology Group at Vanderbilt) Mathematical Approaches On Different Facets of Mathematical Thinking (Tommy Dreyfus & Theodore Eisenberg) Structuralism and Mathematical Thinking (Charles Rickart) Conclusions What is Mathematical Thinking? (Robert J. Sternberg) Author Index Subject Index