Mathematical modeling as a component of understanding ratio-as-measure: A study of prospective elementary teachers

Abstract

The authors employed a whole-class teaching experiment in a mathematics class for prospective elementary teachers to study the development of the ability to identify a ratio as the appropriate measure of a given attribute (“ratio-as-measure”). Prior studies as well as pretest data for this study demonstrated that students often invoke additive comparisons when multiplicative comparisons are appropriate. Analysis of the difficulties which students encountered in considering a ratio as an appropriate measure of an attribute of a physical situation led to the hypothesis that an understanding of ratio-as-measure requires, in addition to an understanding of aspects of multiplicative relationships, an understanding of mathematical modeling.