Tracking student progress in a game-like learning environment with a Monte Carlo Bayesian knowledge tracing model

The Bayesian Knowledge Tracing (BKT) model is a popular model used for tracking student progress in learning systems such as an intelligent tutoring system. However, the model is not free of problems. Well-recognized problems include the identifiability problem and the empirical degeneracy problem. Unfortunately, these problems are still poorly understood and how they should be dealt with in practice is unclear. Here, we analyze the mathematical structure of the BKT model, identify a source of the difficulty, and construct a simple Monte Carlo BKT model to analyze the problem in real data. Using the student activity data obtained from the ramp task module at the Concord Consortium, we find that the Monte Carlo BKT analysis is capable of detecting the identifiability problem and the empirical degeneracy problem, and, more generally, gives an excellent summary of the student learning data. In particular, the student activity monitoring parameter M emerges as the central parameter.