Can designed student responses support teachers to interact with students in a productive way?

This paper introduces the use of pre-designed student responses to unstructured mathematics problems as a possible resource for teachers to develop their capacity of acting contingently in the mathematics classroom in a productive way, whilst teaching. We frame our argument around the notion that contingent moments can be regarded as problem-situations that are, at times, too demanding for the teacher to effectively solve. We provide an unstructured mathematics problem and accompanying designed student responses to illustrate and explain our thinking, considering how this approach has the potential to help teachers flexibly and productively engage with students’ reasoning in-the-moment of instruction. We end the paper with a call for empirical studies to explore these ideas further.