Many students tend to inappropriately apply natural-number-biased reasoning in fraction and decimal tasks, including believing multiplication always makes bigger and division makes smaller. In this study, we examined individual differences in the game play of NanoRoboMath, a digital game designed to improve students' rational number knowledge. Examining the game performance of 90 seventh grade students allowed us to find four player profiles that were connected to learning the effects of multiplicative operations. Students in the High profile used multiplication and division by numbers less than one more frequently and had stronger learning gains with operation knowledge results compared to Long play low gain profile. This suggests that the player profiles reflect some features of students' game play and performance that may be relevant for conceptual change processes of understanding the effects of multiplicative operations.
Educational relevance and implications statement: The present study provides novel insights into individual differences in students' performance while playing a game aimed at promoting conceptual knowledge of rational numbers. It manifests a relation between player profiles and learning gains. The study contributes to the design of game-based learning environments by suggesting that providing students with repeated opportunities to confront their prior misconceptions in game-based learning environments may be beneficial for supporting conceptual development. The study also indicates that there may be multiple ways to productively engage with educational games. This is valuable for educators in understanding how to employ game-based learning environments in their classrooms.