Development of Multiplicative Reasoning in the Learning of Mathematics

Inbunden, Engelska, 1994

1 159 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating.This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.

Produktinformation

Utgivningsdatum1994-06-28
Mått152 x 229 x 25 mm
Vikt744 g
FormatInbunden
SpråkEngelska
SerieSUNY series, Reform in Mathematics Education
Antal sidor407
FörlagState University of New York Press
ISBN9780791417638

Tillhör följande kategorier

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