‘Engaging' problem contexts: undergraduate students’ perspectives

Using ‘engaging' problem contexts is important for teaching mathematics, and the literature contains themes of using contexts that are realistic or enjoyable to motivate students to actually engage in the problem. However, this research often lacks detailed student perspectives on what makes a problem context have one of these characteristics. Our study contributes towards this missing perspective through an initial exploration, specifically at the undergraduate level. We interviewed 11 calculus students and identified themes in what they said regarding the properties of problem contexts that helped them be ‘engaging', by either being in the intersection of realistic + motivating or enjoyable + motivating. For contexts in realistic + motivating, the properties we identified were (a) expansion of awareness, (b) need for mathematics and (c) explicit purpose. For contexts in enjoyable + motivating, the properties we identified were (a) self-projection into context, (b) teacher’s personal story, and (c) absurd story. We also report on a top-level characteristic: variety and novelty. We show the usefulness of these results by critiquing problems in the literature for how engaging they might be to students. As our study is an initial exploration, we also call for additional research to add to, refine, or extend our results.