Comparing student strategies in a game-based and pen-and-paper task for linear algebra

This study examines the mathematical activity involved in engaging with two tasks designed for introductory linear algebra: the Vector Unknown digital game and the pen-and-paper Magic Carpet Ride task. Five undergraduate students worked on both tasks, and we qualitatively analyzed their strategies using a modified version of a framework from prior literature. In the findings, we report on the seven distinct strategies seen in our data set. We found that while our participants did use some of the same strategies on both tasks, there were also certain strategies which were more characteristic of work on one task or the other. In our discussion, we consider how the design differences in the tasks may influence the strategy differences, and how our findings can be leveraged by instructors of linear algebra in selecting tasks. Finally, we conclude by discussing broader implications for mathematics education research in comparing game-based and nongame-based tasks.