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

Abstract

Proportional relationships and geometric similarity are two of thecritical topics in school mathematics. Students and even teachers oftenstruggle with recognizing the proportional relationships in geometricsimilarity problems. The purpose of this study was to investigate preservicemiddle-grades mathematics teachers’ (PSTs) strategies when solving geometricsimilarity problems. Furthermore, we also examined the influence of the problemcharacteristics on the PSTs’ solution strategies. The data for the presentstudy came from 32 PSTs’ responses to a geometric similarity test consisting offive problems and individual semi-structured interviews with three of thesePSTs. The results revealed that the PSTs used a limited number of strategieswhen solving the similarity problems and usually relied on thecross-multiplication strategy in their solutions. Only a few PSTs were able toexplain proportional relationships between corresponding sides of the geometricfigures in the given problems. The PSTs’ overreliance on thecross-multiplication strategy appeared to constrain their identification ofproportional relationships. Based on the results of the present study, wepropose the use of dilating perspective, a dynamic dilation-oriented methodthat promotes side-by-side comparison of similar figures in teaching geometricsimilarity.