Tracking Knowledge Proficiency of Students with Educational Priors

Diagnosing students' knowledge proficiency, i.e., the mastery degrees of a particular knowledge point in exercises, is a crucial issue for numerous educational applications, e.g., targeted knowledge training and exercise recommendation. Educational theories have converged that students learn and forget knowledge from time to time. Thus, it is necessary to track their mastery of knowledge over time. However, traditional methods in this area either ignored the explanatory power of the diagnosis results on knowledge points or relied on a static assumption. To this end, in this paper, we devise an explanatory probabilistic approach to track the knowledge proficiency of students over time by leveraging educational priors. Specifically, we first associate each exercise with a knowledge vector in which each element represents an explicit knowledge point by leveraging educational priors (i.e., Q-matrix). Correspondingly, each student is represented as a knowledge vector at each time in a same knowledge space. Second, given the student knowledge vector over time, we borrow two classical educational theories (i.e., Learning curve and Forgetting curve) as priors to capture the change of each student's proficiency over time. After that, we design a probabilistic matrix factorization framework by combining student and exercise priors for tracking student knowledge proficiency. Extensive experiments on three real-world datasets demonstrate both the effectiveness and explanatory power of our proposed model.