Planning for the unexpected in the mathematics classroom: an account of teacher and student change

This article focuses on 'the unexpected' in relation to teacher change. We take an enactivist approach to charting the parallel development of one teacher (Hannah) as she learnt to value and plan for unexpected events in her mathematics classroom, and one of her students as he learnt to notice and trust mathematical patterns. Shifts are juxtaposed not to suggest causality but to give a sense of the interplay over time of the teacher's increasing focus on creative, co-produced, mathematical processes and all the unexpectedness that entails, and the student's increasing sense of control over the subject. We analyse changes in Hannah's teaching in relation to Gattegno's notion of the subordination of teaching to learning and suggest that what changes for her was not centrally about new subject knowledge, but rather a new relationship to the unexpected (including, but not limited to, mathematics).