Between expert and student perspectives: on the intersection of affect and heuristic-didactic discourse in the undergraduate classroom

This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative emotional reactions, while the other positive emotional reactions–a phenomenon we aimed at explaining. The main data comprise the filmed lessons and subsequent stimulated-recall interviews with nine students. The analysis draws on conceptual tools from three perspectives: mathematical discourse, variation theory, and a recently developed construct of key memorable events (KMEs) that offers an affective-cognitive lens for investigating the interrelation between teaching and learning. The findings indicate that the positively-perceived lesson contained instances of what we call heuristic-didactic discourse: a meta-level discourse that presents heuristics monitored from an expert’s perspective, yet derived from a student’s perspective. Implications for research and practice are drawn.