An intersubjective view of creative collaborative proving in undergraduate mathematics

다국어 초록 (Multilingual Abstract)

Working creatively and producing mathematical ideas collaboratively is a cornerstone of the professional work of mathematicians, thus it is critical to engage undergraduate students in these practices for them to grow from novice to expert in the mathematical community.
Very little, however, is known about how undergraduate students perceive themselves and their classmates as creative through collaborative activities. In this study, I use a lens of participatory intersubjectivity to explore a single case of three undergraduate students from the United States engaged in in-class collaborative mathematical proving. Written individual narrative data and group stimulated-recall interview data were used to investigate how students experienced creativity at both the individual and collective levels during their collaboration. Results indicate that the collaborative team engaged in a proving process characterized by the emergence of two distinct initial ideas for approaching the proving task, a decision to pursue one of these ideas, and an eventual divergence by one group member from her peer’s idea to revisit her initial intuition for the proof. Moreover, the individual reflections of each group member indicate that different moments of the collaborative proving process facilitated the students’ creative contributions to the proof. I describe potential instructional implications as well as directions for future research on instruction to foster collaborative creativity and more robustly understand collaborative mathematical creativity as a construct.