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 observa-tions (e.g., correct vs. incorrect problem solution) provide only weak evidence. Two classes of models have been pro-posed to address the challenge. Latent-factor models em-ploy 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 deter-mine the point at which a skill is mastered. Although these two approaches are complementary, only preliminary, infor-mal steps have been taken to integrate them. We propose a principled synthesis of the two approaches in a hierarchi-cal 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 archi-tecture outperforms either alone. We find significant predic-tive value in considering the difficulty of specific problems (within a skill), a source of information that has rarely been exploited