Preservice Middle School Mathematics Teachers' Strategy Repertoire in Proportional Problem Solving

Abstract

This study examined 91 preservice mathematics teachers' strategy repertoire that they referred to when solving one direct and one inverse proportion missing-value word problems. When encouraged to provide multiple solutions, the preservice teachers exhibited the ability to solve the two problems using more than one strategy. However, they used a significantly greater number of strategies for solving the direct than for the inverse proportion problem. The most frequently used strategies for the two problems were the cross-multiplication and across-multiplication, respectively, and many of the preservice teachers also used these two strategies as their first strategy. On the other hand, the number of strategies applied by the preservice teachers did not differ significantly according to their first choice of strategies. A key finding of this study was that the preservice teachers possessing less common strategies in their repertoire had a significantly larger strategy repertoire than those who had more common strategies.