Mathematics Learning by Programming in a Game Engine: Development of Knowledge and Student Motivation

This paper emerges from our research focusing on mathematics education in trans-disciplinary engineering programs and presents a case study in such an engineering discipline, namely the Media Technology program at Aalborg University Copenhagen, Denmark. In this case study, we substituted traditional mathematics assignments with a programming project in a game engine (Unity) when teaching the reflection and refraction vector calculation. The main concept of this approach was that students get simple projects in Unity, where mathematics is used for game mechanics, and they have to modify or further develop these projects. We conducted interviews with nine students who participated in this case study, and we analysed their mathematical work in Unity. For analysing students’ mathematical practice, we employed the anthropological theory in didactics and the instrumental approach. The analysis of student responses and projects provided insights on how students apply knowledge from a mathematical model to implement a physical model. This study shed light on students’ misconceptions and difficulties but also on opportunities for them to challenge their understanding. Moreover, it revealed that students do not always internalize the mathematical knowledge they acquire, and they may get correct results without understanding their mathematical meaning. We conclude that this type of activities is more beneficial for these students compared to mathematical exercises, because they challenge their understanding and confront them with their misconceptions.