The role of framing in productive classroom discussions: A case for teacher learning

• A microanalysis of an algebra lesson for elementary teachers training to become elementary mathematics specialists.
• Uses ethnography of argumentation and Toulmin's theory of argument to conduct this microanalysis.
• Contrasts two arguments to illustrate the role that argumentative supports and framings play in opportunities for learning.
• Mathematical discussions are more productive when they are framed by teachers’ understandings of fundamental ideas.

In this paper, we contrast two mathematical arguments that occurred during an algebra lesson to illustrate the importance of relevant framings in the ensuing arguments. The lesson is taken from a graduate course for elementary teachers who are enrolled in a mathematics specialist program. We use constructs associated with enthnography of argumentation to characterize the framings for warrants and backings that supported the ensuing arguments. Our findings suggest that teachers fully participated in argumentations that were framed by problem situations that were familiar to them, ones that were couched in elementary, fundamental mathematical ideas, and that these types of argumentations were arguably more productive in terms of opportunities for learning.