What we can learn from analyzing the teacher’s role in collective argumentation

In this paper, I use analyses of collective argumentation in a variety of classroom settings, from elementary school to a university-level differential equations class to illustrate various roles the teacher plays. These include initiating the negotiation of classroom norms that foster argumentation as the core of students’ mathematical activity, providing support for students as they interact with each other to develop arguments, and supplying argumentative supports (data, warrants, and backing) that are either omitted or left implicit. We gain two important insights from these analyses. First, an emphasis on argumentation can be used productively to provide openings in mathematical discussions for new mathematical concepts and tools to emerge. Second, the analyses demonstrate that teachers need to have both an in-depth understanding of students’ mathematical conceptual development and a sophisticated understanding of the mathematical concepts that underlie the instructional activities being used.