The development of students' mathematical reasoning in Calculus courses

The aim is to understand how the students' involvement in solving and discussing exploratory tasks, combined with the teacher's actions, can contribute to the development of their mathematical reasoning (MR) in a Differential and Integral Calculus course. The study was qualitative, with an interpretive approach, and the participants were undergraduate engineering students. The data consists of (a) protocols containing written records of students' discussions; (b) audio recordings of these discussions; and (c) video of the plenary discussion facilitated by the teacher. We discuss the MR processes that students mobilize, in particular conjecturing, generalizing, and justifying. We point out which of the teacher's actions can contribute to the development of MR, in a continuous and growing movement, essentially related to the deepening of discussions based on elements presented by the students themselves, and the opportunities that are created in this process.