Preservice elementary teachers' conceptions of algebra and algebraic equivalence.

摘要

This study examined conceptions of algebra and algebraic equivalence held by 30 preservice elementary teachers prior to discussion of these topics in a methods course in order to assess their initial preparedness to engage students in algebraic reasoning. In addition to exploring participants' general “definitions” of algebra, this study examined their recognition of opportunities present in particular tasks to promote an understanding of equivalence and engage students in relational thinking as well as their knowledge of student thinking around these issues.;Findings from this study suggest that preservice elementary teachers' conceptions of algebra as a subject matter are rather narrow. Most preservice teachers equated algebra with the manipulation of symbols. Fewer than half identified other forms of reasoning—in particular, relational thinking—with the algebra label. On the other hand, preservice teachers did collectively demonstrate an awareness of relational thinking both in identifying opportunities to engage students in this thinking and in identifying this thinking in samples of student work. Few participants, however, demonstrated an understanding that many elementary school students hold misconceptions about the meaning of the equal sign in proposing difficulties students might have with selected tasks.;Implications for mathematics teacher education resulting from this study include a need to expand preservice elementary teachers' conceptions of algebra as a subject matter in a way that highlights the importance of engaging elementary students in discussions around the meaning of the equal sign and relational thinking. Although the finding that many participants had an understanding of relational thinking was encouraging, participants did not demonstrate the belief that this particular kind of thinking deserved special emphasis in the classroom. It is suggested that this lack of emphasis on relational thinking is related to participants' narrow conceptions of algebra and that what is needed—beyond exposing preservice teachers to relational thinking tasks and discussing the mathematics behind them—is attention to why a teacher might want to pose such tasks to her students.