Progmatics Project

Our research study (2017-2022) examines how post-secondary students (mathematics undergraduates) learn to use computer programming for mathematical investigation, simulation, and real-world modeling – in short, ‘progmatics’. The context for our naturalistic case study is a sequence of three mathematics courses offered over three years at Brock University (since 2001) in which students learn to use ‘progmatics’ through weekly labs and 14 ‘progmatics’ project assignments.  For more on this course series, see Integration of Programming in the Undergraduate Mathematics Program at Brock University.

Building on our recent related research, our research questions are:
  • How do post-secondary mathematics students come to adopt ‘progmatics’ as an instrument for their own use?  In other words, how do students learn to use programming for authentic pure or applied mathematical investigations?
  • Is the adoption sustained over time; and if so, how?
  • And how do instructors create a learning environment to support students’ adoption of ‘progmatics’?
Here is a video illustrating the activity of using programming for authentic pure or applied mathematical investigations, including a development process model of the activity:

The theoretical framework grounding our work brings together concepts from:  i) the instrumental approach (Trouche, 2004; Drijvers et al., 2010) to inform our understanding of technology integration in mathematics teaching and learning; ii) the work of Lave and Wenger (1991) on communities of practice (i.e., on ‘legitimate peripheral participation’) to inform our view of learning mathematics; and iii) the work of Weintrop et al. (2016) on computational thinking in mathematics education as well as the constructionism paradigm (Papert and Harel, 1991) to inform our understanding of ‘programming (for) mathematics’ (see Buteau, Muller, Mgombelo, & Sacristan, 2018)

We use a mixed-method, iterative and case study design to document and analyze undergraduates’ learning of ‘progmatics’, their use of ‘progmatics’ beyond course requirements, and the ways instructors support undergraduates’ ‘progmatics’ learning. Our research participants include mathematics majors and future mathematics teachers enrolled in the Mathematics Integrated with Computers and Applications (MICA) I, II, and III courses at Brock University, along with course instructors and teaching assistants.  Data collected yearly from students includes lab session reflections, ‘progmatics’ projects together with reflective journals, interviews, and questionnaires. Data from instructors and teaching assistants consists of interviews, lab session field notes, and course materials.

Our study contributes to the knowledge of how post-secondary students learn to use ‘progmatics’ — a contemporary way of doing and applying mathematics needed in STEM — and to the advancement of post-secondary mathematics/STEM education knowledge. It also provides mathematics departments with a flexible teaching model to implement ‘progmatics’ in post-secondary programs.

For more details, see our publications and results of our ongoing research.

In the video below, we briefly summarize the findings from the first year of our study as presented at the Fields MathEd Forum on Computational Thinking in Mathematics Education (November 2018).  During this year, we followed 6 students in the MICA I course as they engaged in their 4 programming-based project tasks, which accounted for 71% of their final grade.

Buteau, C., Mgombelo, J., & Muller, E. with Anderson, A., Dreise, K., & Gannon, S. (2018). Undergraduate Math Students Appropriating Programming as an Instrument for Math Explorations and Applications: A Longitudinal ResearchFields Mathematics Education Forum (Theme: Computational Thinking in Mathematics Education), Fields Institute for Research in Mathematical Sciences, Toronto (Canada), November 2018.

Gueudet, G., Buteau, C., Muller, E., Mgombelo, J., & Sacristán, A. (2020). Programming as an artefact: What do we learn about university students’ activity? Proceedings of INDRUM 2020 Third Conference of the International Network for Didactic Research in University Mathematics, Bizerte (Tunisia), March 2020.

This research is supported by the Social Sciences and Humanities Research Council of Canada.