Development of Multiplicative Reasoning in the Learning of Mathematics

Guershon Harel is Associate Professor of Mathematics at Purdue University Jere Confrey is Associate Professor of Education at Cornell University.

• IntroductionPart I: Theoretical Approaches1. Children's Multiplying SchemesLeslie Steffe2. Multiplicative Conceptual Field: What and Why?Gerard Vergnaud3. Extending the Meaning of Multiplication and DivisionBrian GreerPart II: The Role of The Unit4. Ratio and Proportion: Cognitive Foundations in Unitizing and NormingSusan Lamon5. Units of Quantity: A Conceptual Basis Common to Additive and Multiplicative StructuresMerlyn Behr, Guershon Harel, Thomas Post, and Richard LeshPart III: Ratio and Rate6. The Development of the Concept of Speed and Its Relationship to Concepts of RatePatrick Thompson7. Missing-Value Proportional Reasoning Problems: Factors Affecting Informal Reasoning PatternsJames Kaput and Mary Maxwell WestPart IV: Multiplicative Worlds8. Splitting, Similarity, and Rate of Change: A New Approach to Multiplication and Exponential FunctionsJere Confrey9. Multiplicative Structures and the Development of Logarithms: What Was Lost by the Invention of Function?Erick Smith and Jere ConfreyPart V: Intuitive Models10. The Impact of the Number Type on the Solution of Multiplication and Division Problems: Further InvestigationsGuershon Harel, Merlyn Behr, Thomas Post, and Richard LeshSummary11. Multiple Views of Multiplicative StructuresThomas KierenIndex

"An excellent state-of-the-art sourcebook." — Anna O. Graeber, University of Maryland, College Park