Nature of Mathematical Thinking

Robert J. Sternberg, Talia Ben-Zeev

• Contents: Preface. Part I: A Psychometric Approach.J.B. Carroll, Mathematical Abilities: Some Results from Factor Analysis. Part II: Cognitive/Information-Processing Approaches.R.E. Mayer, M. Hegarty, The Process of Understanding Mathematical Problems. T. Ben-Zeev, When Erroneous Mathematical Thinking is Just as "Correct": The Oxymoron of Rational Errors. Part III: Cognitive/Cultural Approaches.K.F. Miller, D.R. Paredes, On the Shoulders of Giants: Cultural Tools and Mathematical Development. G.B. Saxe, V. Dawson, R. Fall, S. Howard, Culture and Children's Mathematical Thinking. D.C. Geary, Biology, Culture and Cross-National Differences in Mathematical Ability. Part IV: Cognitive/Educational Approaches.H.P. Ginsburg, Toby's Math. J. Bransford, L. Zech, D. Schwartz, B. Barron, N. Vye, The Cognition and Technology Group at Vanderbilt, Fostering Mathematical Thinking in Middle School Students: Lessons from Research. Part V: Mathematical Approaches.T. Dreyfus, T. Eisenberg, On Different Facets of Mathematical Thinking. C. Rickart, Structuralism and Mathematical Thinking. Part VI: Conclusions.R.J. Sternberg, What is Mathematical Thinking?

"Scholars and researcher [psychologists of every hue, psychometricians, sociologists, philosophers, educators, teachers, mathematicians, and policy makers] are likely to find something of interest in The Nature of Mathematical Thinking....I will return to several of the book's chapters because they are like binoculars magnifying particular details that I would like to follow up in the future."—Journal for Research in Mathematics Education"...as a whole [the chapters] offer a wealth of hypotheses and insights."—The American Mathematical Monthly"The book successfully offers a fresh perspective for researchers and theorists and at the same time makes some of the more technical aspects of the research accessible to nonspecialists."—Mathematics Teacher"...this book is valuable and makes a contribution to the cause of multidiciplinary investigations. This book will benefit the preparation of future scholars and teachers, too."—Teaching Children Mathematics"The success of this volume lies in the collection of clearly written chapters by authors who could aptly be said to represent prominent examples of distinct traditions in research on mathematical thinking."—Contemporary Psychology"...this volume represents a very useful bringing together of a broad range of approaches and will certainly be of great interest to all students and researchers concerned with mathematical thinking."—British Journal of Mathematical & Statistical Psychology"With such an ambitious project, one expects a very rich book, addressed to a very wide audience. A very difficult task. The reader is rewarded. It does not mean she/he will find the answers to so well posed and straightforward questions, but will surely learn about the progress made by scholars, of different areas, to deal with these questions. The difficult task of preparing a book with such a large scope depends largely on a good organization and a well chosen team of experts. The editors succeeded in this double strategy."—Zentralblatt MATH"The volume is intended for educators and mathematics teachers, psychologists, cognitive scientists, mathematicians, computer scientists, anthropologist, 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."—Zentralblatt fr Didaktik der Mathematik