Learning programming for mathematical investigations: an instrumental and community of practice approach

In this article, we seek to understand how university students learn to use programming for mathematical investigations; our precise focus is on how the analysis of social elements in operational knowledge elucidates this learning. We propose a framework coordinating the instrumental approach and communities of practice (CoP) theory. We apply it in the context of project-based university courses (MICA courses), where the CoP of mathematicians using programming for their research is a reference. We investigate the schemes associated with the programming language and its environment developed by students along trajectories of legitimate peripheral participation. We focus on the scheme developed for the goal "validating the programmed mathematics." Our results indicate that for the same goal, common rules-of-action are developed by students, but differences can appear concerning theorems-in-action. This study also suggests theoretical developments linked with the coordination of the instrumental approach and CoP theory.