When learning stumbles upon identity and affect: a loaded student–student collaboration in linear algebra

Abstract

In undergraduate mathematics education, students’ collaborations have gained a reputation as a ‘good’ learning practice. A more complex image emerges once collaborations are construed as an arena where cognitive, social, and affective matters intertwine in ways that can fuel and impede learning. In this study, I take a close look at a twenty-minute-long interaction between two first-year students who engaged in a sequence of routine problems about dot products presented in a computer-based learning-support system. The commognitive analysis of the interaction revealed an asymmetrical structure: one student led the mathematizing, while his partner followed and invested considerable efforts to avoid making a mathematical contribution. The leader’s attempts to switch positions and inquiry into the follower’s recurrent refusals to mathematize entailed loaded exchanges that took a toll on both students in terms of identity and affect. I compare these findings to previous studies with school students to discuss possible sources of ineffective communication in situations where students are expected to learn through collaborations.