Overcoming impasses in proving processes: Novice provers’ productive actions when encountering stuck points

Abstract

Research has shown that many undergraduate students struggle to learn to prove, including those who major in mathematics (Moore, 1994; Selden, 2012). While studies have explored how expert mathematicians construct proofs to inform teaching practices, expert strategies might not be equally beneficial to novice provers with limited abilities in proving. Novice provers often face difficulties and impasses when engaged in problem-solving or proving tasks. Looking through the lenses of impasses, this study provides a more fine-grained account by characterizing novice provers’ navigating actions when they encounter impasses to better support them in their proving processes. This research draws on task-based interviews conducted with undergraduates enrolled in a transition-to-proof course. A framework was developed to identify productive actions students took when navigating stuck points in the proving process. The result of this study shows that productive actions around stuck points can develop important proof skills in students, even if the student did not ultimately complete the proof successfully. Therefore, instructors are encouraged to recognize and support these productive actions, prioritizing them over mere proof completion when guiding students in their proving processes.