Concept images of the notion of asymptote: a study with prospective teachers

This study aims to characterize how prospective teachers (PSTs) interpret students’ thinking through a professional task dialogue focused on asymptotes. Drawing on the theory of concept images, we conducted a descriptive and interpretative analysis of the discourse of 38 PSTs. The findings reveal a predominant use of descriptive discourse, evaluations of the teacher's interventions, a focus on task solutions and reliance on their prior experiences as mathematics learners. In terms of concept images, the horizontal asymptote is frequently interpreted as a limit, while the vertical and slant asymptotes are often perceived as linear entities.