Emergent storylines that influence positions and mathematical status in collaborative small-group proof activity

Abstract In this paper, we used positioning theory to examine storylines that emerged in students’ discourse as they collaborated on a proof construction task. We purposefully selected a case of group work from an inquiry-oriented introduction to proof course as prior analyses showed it was highly collaborative (Alzaga Elizondo, 2022), yet power dynamics seemed unbalanced. We hypothesized that positioning theory could provide a useful lens to interrogate such power dynamics. Through this analysis, we identified several implicit storylines that influenced the interaction related to the nature of proofs, the nature of mathematics, writing proofs, the role of an external authority, and university culture. In our findings, we illustrate how these storylines impacted students’ relative mathematical status via rights and duties, connecting the right to validate the group’s work to an expert position. In light of our findings, we argue for a broadened view of what counts as “doing mathematics” that acknowledges creativity, intuition, and collaboration alongside precision, logic, and authority.