Proving and Doing Proofs in High School Geometry Classes: What Is It That Is Going On for Students?

Abstract

In this article we examine students' perspectives on the customary, public work of proving in American high school geometry classes. We analyze transcripts from 29 interviews in which 16 students commented on various problems and the likelihood that their teachers would use those problems to engage students in proving. We use their responses to map the boundaries between activities that (from the students' perspective) constitute normal (vs. marginal) occasions for them to engage in proving. We propose a model of how the public work of proving is shared by teacher and students. This division of labor both creates conditions for students to take responsibility for doing proofs and places boundaries on what sorts of tasks can engage students in proving. Furthermore we show how the activity of proving is a site in which complementarity as well as contradiction can be observed between what makes sense for students to do for particular mathematical tasks and what they think they are supposed to do in instructional situations.