Will Teachers Create Opportunities for Discussion when Teaching Proof in a Geometry Classroom?

Abstract

This study presents an analysis of whether geometry teachers create opportunities for student discussion when engaging students in proving as revealed through the use of a multimedia survey instrument. We presented 42 secondary mathematics teachers with 8 multimedia narratives set in the situation of doing proofs in high school geometry and asked them to choose what they would do next, presenting options that included a normative instructional action which closed off discussion and less typical actions that encouraged student discussion. Our analysis provides insight into the professional obligations that teachers use to justify their departure from the norm in order to encourage student talk as well as the background variables that are associated with such decisions. We found that while secondary mathematics teachers frequently chose to promote discussion in their classrooms, the rationale that they chose for this decision and the reasons they might choose not to immediately encourage discussion differed according to the amount of experience they had teaching geometry. We use these differences to illustrate how the professional obligations can be used to better understand how teacher decisions are rationalized at the level of the instructional situation.