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

ABSTRACT

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.

KEYWORDS:

• Communities of practice
• instrumental approach
• programming for mathematical investigation

Acknowledgements

This work is funded by the Social Sciences and Humanities Research Council of Canada (#435-2017-0367). It has received ethics clearance from the Research Ethics Board at Brock University (REB #17-088). We also thank all of the research assistants involved in our project for their valuable work toward our research, in particular Kirstin Dreise and Jessica Sardella for their assistance with the analysis.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 There are two third-year MICA courses, one for mathematics and science majors (denoted MICA III), and one for future mathematics teachers (denoted MICA III*).

2 See Appendix D for an example of programming and mathematics project sequence illustrating this increasing complexity.

3 We used Kassie and Mark’s interviews while they were MICA II students in Bill’s class, but the questionnaire with the two scheme questions was conducted starting the following year.

Additional information

Funding

This work was supported by Social Sciences and Humanities Research Council of Canada: [Grant Number 435-2017-0367].