Preservice Middle Grades Mathematics Teachers’ Strategies for Solving Geometric Similarity Problems

Abstract

Proportional relationships and geometric similarity are two of the critical topics in school mathematics. Students and even teachers often struggle with recognizing the proportional relationships in geometric similarity problems. The purpose of this study was to investigate preservice middle-grades mathematics teachers’ (PSTs) strategies when solving geometric similarity problems. Furthermore, we also examined the influence of the problem characteristics on the PSTs’ solution strategies. The data for the present study came from 32 PSTs’ responses to a geometric similarity test consisting of five problems and individual semi-structured interviews with three of these PSTs. The results revealed that the PSTs used a limited number of strategies when solving the similarity problems and usually relied on the cross-multiplication strategy in their solutions. Only a few PSTs were able to explain proportional relationships between corresponding sides of the geometric figures in the given problems. The PSTs’ overreliance on the cross-multiplication strategy appeared to constrain their identification of proportional relationships. Based on the results of the present study, we propose the use of dilating perspective, a dynamic dilation-oriented method that promotes side-by-side comparison of similar figures in teaching geometric similarity.