Mathematical Reasoning: Analogies, Metaphors, and Images

ISBN-13: 9780805819793 / Angielski / Miękka / 1997 / 392 str.

English; Lyn D. English; Lyn English

Opis

Presents the latest research on how reasoning with analogies, metaphors, metonymies, and images can facilitate mathematical understanding. For math education, educational psychology, and cognitive science scholars.

Recenzje

"The topic addressed by this book is an important one both practically and theoretically....This book provides a relatively easy introduction to the relativist view that mathematical systems are culturally constructed rather than objectively real."
—The British Journal of Educational Psychology

"I found this book to be an excellent catalyst for furthering my own understanding as well as my graduate students' understanding of mathematical reasoning. A collection of thoughtful articles challenged us to reconsider the nature of mathematics and mathematical thought."
—Mathematics Teaching in the Middle School

"Together, the contributed articles form a rich and provocative collection, challenging some widely held ideas. They deserve careful reading by psychologists, mathematics educators, and philosophers of mathematics. Lyn English has done an outstanding job organizing varied viewpoints into a volume that is readable and well structured."
—Contemporary Psychology

Spis treści

Contents: Preface. Part I: Introduction. L.D. English, Analogies, Metaphors, and Images: Vehicles for Mathematical Reasoning. Part II: Cognitive Foundations for a Mind-Based Mathematics. G. Lakoff, R.E. Núñez, The Metaphorical Structure of Mathematics: Sketching Out Cognitive Foundations for a Mind-Based Mathematics. Part III: Mathematical Reasoning: Analogies. R.B. Davis, C.A. Maher, How Students Think: The Role of Representations. P.A. Alexander, C.S. White, M. Daugherty, Analogical Reasoning and Early Mathematics Learning. B. Gholson, D. Smither, A. Buhrman, M.K. Duncan, K.A. Pierce, Children's Development of Analogical Problem-Solving Skill. L.D. English, Children's Reasoning Processes in Classifying and Solving Computational Word Problems. M. Bassok, Two Types of Reliance on Correlations Between Content and Structure in Reasoning About Word Problems. M.J. Rattermann, Commentary: Mathematical Reasoning and Analogy. Part IV: Mathematical Reasoning: Metaphors, Metonymies, and Images. N.C. Presmeg, Reasoning With Metaphors and Metonymies in Mathematics Learning. G.H. Wheatley, Reasoning With Images in Mathematical Activity. N.C. Presmeg, Generalization Using Imagery in Mathematics. D.H. Clements, J. Sarama, Children's Mathematical Reasoning With the Turtle Programming Metaphor. A. Sfard, Commentary: On Metaphorical Roots of Conceptual Growth.

O autorze

Lyn D. English