How does Bayesian knowledge tracing model emergence of knowledge about a mechanical system

An interactive learning task was designed in a game format to help high school students acquire knowledge about a simple mechanical system involving a car moving on a ramp. This ramp game consisted of five challenges that addressed individual knowledge components with increasing difficulty. In order to investigate patterns of knowledge emergence during the ramp game, we applied the Monte Carlo Bayesian Knowledge Tracing (BKT) algorithm to 447 game segments produced by 64 student groups in two physics teachers' classrooms. Results indicate that, in the ramp game context, (1) the initial knowledge and guessing parameters were significantly highly correlated, (2) the slip parameter was interpretable monotonically, (3) low guessing parameter values were associated with knowledge emergence while high guessing parameter values were associated with knowledge maintenance, and (4) the transition parameter showed the speed of knowledge emergence. By applying the k-means clustering to ramp game segments represented in the three dimensional space defined by guessing, slip, and transition parameters, we identified seven clusters of knowledge emergence. We characterize these clusters and discuss implications for future research as well as for instructional game design.