The Development of Multiplicative Reasoning in the Learning of Mathematics: Luce Irigaray and the Greeks

Couverture
Guershon Harel, Jere Confrey
SUNY Press, 1 janv. 1994 - 407 pages
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.
 

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Table des matières

Childrens Multiplying Schemes
3
Multiplicative Conceptual Field What and Why?
41
Extending the Meaning of Multiplication and Division
61
THE ROLE OF THE UNIT
87
Ratio and Proportion Cognitive Foundations in Unitizing and Norming
89
Units of Quantity A Conceptual Basis Common to Additive and Multiplicative Structures
121
RATIO AND RATE
177
The Development of the Concept of Speed and Its Relationship to Concepts of Rate
179
MULTIPLICATIVE WORLDS
289
Splitting Similarity and Rate of Change A New Approach to Multiplication and Exponential Functions
291
Multiplicative Structures and the Development of Logarithms What Was Lost by the Invention of Function?
331
INTUITIVE MODELS
361
The Impact of the Number Type on the Solution of Multiplication and Division Problems Further Investigations
363
SUMMARY
385
Multiple Views of Multiplicative Structure
387
Index
399

MissingValue Proportional Reasoning Problems Factors Affecting Informal Reasoning Patterns
235

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À propos de l'auteur (1994)

Guershon Harel is Associate Professor of Mathematics at Purdue University

Jere Confrey is Associate Professor of Education at Cornell University.

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