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 andpresents a case study in such an engineering discipline, namely the Media Technology program at Aalborg UniversityCopenhagen, Denmark. In this case study, we substituted traditional mathematics assignments with a programmingproject in a game engine (Unity) when teaching the reflection and refraction vector calculation. The main concept of thisapproach was that students get simple projects in Unity, where mathematics is used for game mechanics, and they have tomodify 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 theanthropological theory in didactics and the instrumental approach. The analysis of student responses and projectsprovided insights on how students apply knowledge from a mathematical model to implement a physical model. This studyshed 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 getcorrect results without understanding their mathematical meaning. We conclude that this type of activities is morebeneficial for these students compared to mathematical exercises, because they challenge their understanding and confrontthem with their misconceptions.