An investigation of prospective elementary teachers' use of mathematical representation as exhibited in their lesson plans

Abstract

The purpose of this study was to investigate how the notion of representation occurs within the context of prospective teachers' thinking about planning for instruction in mathematics. This study was designed to seek out patterns within the types of mathematical representations that preservice teachers use in designing lesson plans. Major goals of this study were to uncover aspects of how prospective teachers' knowledge develops in the area of mathematics instruction, with respect to representation. Specifically, this study sought to (1) determine the types and frequency of mathematical representations used by prospective teachers when designing lesson plans regarding various topics in K--8 mathematics and (2) ascertain any changes that occurred over the course of a semester with respect to the uses of representations as revealed in prospective teachers' lesson plans. The study involved thirty-two elementary education majors enrolled in a 15-week field-based mathematics methods course at a large southwestern university. The findings were reported by representation type, namely, concrete , linguistic, symbolic, semi-concrete, and contextual. From the initial to the final interval, the overall percentages of the: (a) concrete manipulative representation increased; (b) linguistic representation increased; (c) symbolic representation decreased; (d) semi-concrete pictorial and the contextual representations both remained more or less the same. Overall, the linguistic representation was the most used representation; specifically, the informational and/or procedural subcategory of the linguistic representation was used the most, and in contrast, the discourse subcategory of the linguistic representation was used the least. Five cases were developed to illustrate the preservice teachers' thinking individually and as a group with respect to the uses of mathematical representations on given topics in individual lesson plans and group lesson plans. The process of moving from individual planning to group planning indicated some degree of malleability with respect to the uses of mathematical representations. Ten individual cases were analyzed with respect to the initial and final intervals. Seven of the 10 cases showed results in which the preservice teachers' preconceptions regarding the use of mathematical representations evolved. These findings are discussed relative to their implications for research, practice, and teacher education.