**ERIC Number:**ED379161

**Record Type:**RIE

**Publication Date:**1994

**Pages:**407

**Abstractor:**N/A

**ISBN:**ISBN-0-7914-1764-6

**ISSN:**N/A

**EISSN:**N/A

The Development of Multiplicative Reasoning in the Learning of Mathematics.

Harel, Guershon, Ed.; Confrey, Jere, Ed.

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the Unit: "Ratio and Proportion: Cognitive Foundations in Unitizing and Norming" (S. Lamon), "Units of Quantity: A Conceptual Basis Common to Additive and Multiplicative Structures" (M. Behr, G. Harel, T. Post, and R. Lesh); (3) Ratio and Rate: "The Development of the Concept of Speed and Its Relationship to Concepts of Rate" (P. Thompson), "Missing-Value Proportional Reasoning Problems: Factors Affecting Informal Reasoning Patterns" (J. Kaput and M. West); (4) Multiplicative Worlds: "Splitting, Similarity, and Rate of Change: A New Approach to Multiplication and Exponential Functions" (J. Confrey), "Multiplicative Structures and the Development of Logarithms: What Was Lost by the Invention of Functions" (E. Smith & J. Confrey); (5) Intuitive Models; "The Impact of the Number Type on the Solution of Multiplication and Division Problems: Further Investigations" (G. Harel, M. Behr, T. Post, and R. Lesh); and (6) Summary: "Multiple Views of Multiplicative Structures" (T. Kieren). Author and subject indexes are included. (MKR)

Descriptors: Addition, Arithmetic, Cognitive Development, Division, Elementary Secondary Education, Learning Theories, Mathematical Concepts, Mathematics Instruction, Multiplication, Number Concepts, Ratios (Mathematics)

State University of New York Press, State University Plaza, Albany, NY 12246 (cloth: ISBN-0-7914-1763-8, $73.50; paperback: ISBN-0-7914-1764-6, $24.95).

**Publication Type:**Books; Collected Works - General; Information Analyses

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A