The Development of Multiplicative Reasoning in the Learning of MathematicsGuershon Harel, Jere Confrey 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. |
Contents
Childrens Multiplying Schemes | 3 |
What | 41 |
Extending the Meaning of Multiplication | 61 |
Cognitive Foundations | 89 |
A Conceptual Basis Common | 121 |
The Development of the Concept of Speed | 179 |
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abstract action analysis approach arithmetic Behr build-up child cognitive composite units conceptual field Confrey construction context Council of Teachers counting create cross-product multiplication decimal dimensional analysis distance divisor example exponential functions Figure Fischbein four fractions geometric geometric series Glasersfeld Greer Harel Hiebert integer intensive quantity intuitive intuitive knowledge involved iterable JJ's Kaput learning Lesh logarithms Mathematical Behavior mathematics education measure spaces mental operations multi multiplica multiplication and division multiplicative comparison multiplicative structures Nesher Nicole Oresme notation Number concepts number line number sequence Okay Piaget product multiplication product units proportional reasoning rabbit ratio and proportion rational numbers real numbers rectangle relationship repeated addition representation result reunitized scheme situations solution solving splitting Steffe strategy symbols Teachers of Mathematics teaching experiment tion tive turtle types understanding unit fractions unit)s-unit uniting operation units of units Vergnaud whole number word problems