Productive Failures: From Class Requirement to Fostering a Support Group

Mistakes occur frequently in mathematics. Reframing mistakes into positive moments can be psychologically important in a student's educational journey. We investigated two tertiary math classes that explicitly valued mistakes through a pedagogical requirement called "productive failure". For a percentage of their grade, students demonstrated how they made mistakes in their problem solving and, most importantly, how they overcame those mistakes. Through interviews, video-stimulated recalls, and evaluations of the course all from students, we initially looked for affectual responses to the pedagogical allowance and student-led demonstration. Many of the responses, both benefits and drawbacks of the productive failure, were interpreted by the research group to resemble the psychology literature on peer-led support groups. Descriptions of both productive failure and support groups, as well as quotes from the students, aim to shed light on psychological benefits of valuing mistakes. Finally, we believe that productive failures benefitted many students because it made the human aspect of mathematics more explicit.