Orchestrating Mathematical Classroom Discourse About Various Solution Methods: Case Study of a Teacher's Development

Developing and orchestrating classroom discourse about students' different solution methods is an essential yet complex task for mathematics teachers. This study reports on the first stages of classroom discourse development of one Dutch higher secondary school mathematics teacher who had no prior experience in including classroom discourse in her teaching practice. Four lessons in analytic geometry were developed iteratively, in collaboration with the teacher. The lessons consisted of students working on a mathematical problem plus classroom discourse concerning students' different solution methods. Classroom discourse video recordings were collected and analyzed in order to develop a framework to characterize the teacher's actions, and to describe the change in the teacher's role in classroom discourse. The results reveal three main changes in the teacher's role: First, the way the teacher reacted to correct or incorrect solution methods shifted from confirming or setting aside suggestions, toward making the solution methods the subject of discussion; second, the distribution of turns changed such that more students were involved in the discourse and in reacting to each other's solution methods; third, the teacher's actions shifted from convergent, teacher-led actions toward divergent, student-led actions. These results show that within four lessons, an important step has been taken toward establishing a discourse community.