Research, Reflection, Practice: Implications of Research on Children's Understanding of Geometry

Abstract

In my mathematics methods course for preservice teachers, I ask my students to assess a group of elementary school students concerning their level of geometric reasoning. To do so, they use tasks that focus on assessing and extending students' geometric understandings. These open-ended tasks, along with a framework developed from research findings involving children's geometric reasoning, are described in this article. An important aspect of these tasks is that they focus on how students communicate their reasoning so that my preservice teachers can make more informed instructional decisions when planning a follow-up geometry lesson. Research on geometric reasoning has shown that a match between students' reasoning level and instructional tasks is crucial if meaningful learning is to occur (Crowley 1987).