Teaching and learning mathematics in the collective

• Analyses teaching and learning in highly interactive, inquiry-oriented classrooms.
• Draws on enactivism to explicate group processes.
• Focuses on role of the teacher in establishing and sustaining the collective.
• Reveals teaching practices that value, capitalize upon, and promote group cognition.
• Positions such work as teaching a way of being with mathematics.

In this paper we analyse and explore teaching and learning in the context of a high school mathematics classroom that was deliberately structured as highly interactive and inquiry-oriented. We frame our discussion within enactivism—a theory of cognition that has helped us to understand classroom processes, particularly at the level of the group. We attempt to show how this classroom of mathematics learners operated as a collective and focus in particular on the role of the teacher in establishing, sustaining, and becoming part of such a collective. Our analysis reveals teaching practices that value, capitalize upon, and promote group cognition, our discussion positions such work as teaching a way of being with mathematics, and we close by offering implications for teaching, educational policy, and further research.