The Development of Multiplicative Reasoning in the Learning of Mathematics: Luce Irigaray and the GreeksGuershon 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. |
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 |
399 | |
MissingValue Proportional Reasoning Problems Factors Affecting Informal Reasoning Patterns | 235 |
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Expressions et termes fréquents
abstract action analysis approach arithmetic Behr build-up child cogeneration cognitive composite units Confrey construction context counting create cross-product multiplication curriculum decimal dimensional analysis distance divisor example exponential functions Figure Fischbein four fractions geometric geometric series Greer Harel Hiebert integer intensive quantity intuitive intuitive knowledge involved iterable JJ's Kaput learning Lesh logarithmic mathematics education mathematics of quantity measure spaces mental operations miles per hour multi multiplica multiplication and division multiplicative comparison multiplicative structures Nesher Nicole Oresme notation Number concepts number line number sequence Okay Piaget placemat product multiplication product units proportional reasoning quantitative operation rabbit ratio and proportion rational numbers real numbers rectangle relationship repeated addition representation result reunitized scheme situations solution solving splitting Steffe strategy symbols teaching experiment tion tive turtle types understanding unit fractions unit)s-unit uniting operation units of units Vergnaud whole number word problems