Teachers’ perceptions of students’ mathematical work while making conjectures: an examination of teacher discussions of an animated geometry classroom scenario

Abstract

Background: This paper reports on a study examining teachers’ perceptions of students they observed in an animated episode and who were engaged in the work of making conjectures in a geometry classroom. We examined eight conversations among subsets of 29 experienced geometry teachers with respect to how they described students and the mathematical work they perceived students to be engaged in. Results: Across the study group conversations, participants described students in terms of the tasks’ mathematical resources which students could understand or misunderstand and the tasks’ material and social resources which they could use or misuse, but participants paid little attention to the operations that students might employ in the task or the goals that students were working toward in the task. Conclusions: This study suggests that, when supporting students’ work on conjecturing tasks, teachers focus on the tasks’ resources which students use. This conjecture suggests in turn that in exchanging students’ work on conjecturing tasks for claims that students have learned a bit of the geometry curriculum, teachers might deem that particular work valuable on account of the resources used.