Gesture Indicates Productive Struggle in Proof Writing: Case Studies from a Basic Topology Course

Many students struggle with proof writing. However, struggle is not universally bad: researchers have distinguished between productive and unproductive forms of struggle and have identified productive struggle as essential for learning mathematics. Yet, in practice, recognizing when learners are engaged in productive struggle or unproductive struggle can be challenging. In this report, I argue that students' gesture production may indicate engagement in productive struggle. I observed three undergraduate students from an introductory point-set topology course, collaborating in pairs to complete proof tasks. I present evidence from the students' work on two proof tasks that undergraduate students' gesture frequently when they are engaged in productive struggle and that gesture is rare during engagement in unproductive struggle. [For the complete proceedings, see ED630060.]