| Abstrakt: |
This paper presents evidence that the U.S. curricular introduction to multiplication, and more broadly, "multiplicative relationships," is fundamentally additive and therefore conceptually deficient. Conceptualizing multiplication as the replication of equal-size groups of discrete objects and repeated addition provides insufficient support for understanding the full range of multiplicative relationships, numerically and quantitatively. The additive approach fails to extend sensibly to (a) many multiplicative situations (e.g., Cartesian product, area and volume measure, and scaling) and (b) the multiplication and division of fractions, decimals, and integers. The paper summarizes evidence from three levels of curriculum: The Common Core, elementary mathematics curricula, and mathematics texts for elementary teachers. The analysis points to the need for innovative curriculum development to support multiplicative thinking. [ABSTRACT FROM AUTHOR] |
