11: Using Video Cases to Unpack the Mathematics in Students’ Thinking¹

This chapter reports an investigation of ways that a video-case based curriculum, in concert with skilled facilitation, can promote shifts in the ways teachers use video cases to consider issues of students’ algebraic understanding. Eight teachers participated in a 12-session professional development seminar for middle- and high-school teachers that used the Learning to Teach Linear Functions: Video Cases for Mathematics Professional Development materials. The first and eighth sessions of the seminar involve analysis of the same video clip. Analysis of the group discussions from these two sessions indicate that the later viewing yielded a more extensive, complex, and elaborated discussion than the one that took place five months earlier. Teachers’ mathematical analyses of the students’ thinking were more detailed and robust, and focused on students’ potential for further learning rather than a narrow evaluation of what the students did or did not know. Although the written seminar materials were designed and structured to provide opportunities for teachers to develop deeper understanding of students’ algebraic thinking, we believe that the facilitator also played a central role in helping teachers to focus on the key ideas emphasized in the curriculum.