Integrating latent-factor and knowledge-tracing models to predict individual differences in learning

An effective tutor—human or digital—must determine what a student does and does not know. Inferring a student’s knowledge state is challenging because behavioral observations (e.g., correct vs. incorrect problem solution) provide only weak evidence. Two classes of models have been proposed to address the challenge. Latent-factor models employ a collaborative filtering approach in which data from a population of students solving a population of problems is used to predict the performance of an individual student on a specific problem. Knowledge-tracing models exploit a student’s sequence of problem-solving attempts to determine the point at which a skill is mastered. Although these two approaches are complementary, only preliminary, informal steps have been taken to integrate them. We propose a principled synthesis of the two approaches in a hierarchical Bayesian model that predicts student performance by integrating a theory of the temporal dynamics of learning with a theory of individual differences among students and problems. We present results from three data sets from the DataShop repository indicating that the integrated architecture outperforms either alone. We find significant predictive value in considering the difficulty of specific problems (within a skill), a source of information that has rarely been exploited.