WHAT NONVERBAL INTERACTIONS WITH DIAGRAMS TEACHERS PERCEIVE AS MEANINGFUL ELEMENTS OF STUDENTS ’ MATHEMATICAL WORK

The work of teaching includes processing input from many students and in many modalities: their speech, but also their facial expressions, gestures, and actions. We investigate the rationality invested by teachers in perceiving important nonverbal interactions of students with diagrams. Through examining how geometry teachers re-enacted and then discussed a conversation between two students about a proof we show examples of the kind of nonverbal interactions that are meaningful for teachers. This examination helps extend our knowledge of the work of teaching and guide the work of developing media for representing classroom episodes. STUDYING THE RATIONALITY OF TEACHING The research reported here is inscribed in an effort to understand the rationality of teachers of high school geometry. Building on Bourdieu’s (1998) work on practical reason and on Goodwin’s (1994) notion of “professional vision, ” we hypothesize that teachers have (often tacit) professional resources (or dispositions) that enable them to perceive and appreciate events and things in their practice. The need for those professional resources is justified on a theoretical perspective on the complex work o