Abstract

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for educational applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA) that jointly traces learner con-cept knowledge over time, analyzes learner concept knowl-edge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc., or the forgetting effect), and estimates the content organiza-tion and difficulty of the questions in assessments. These quantities are estimated solely from binary-valued (cor-rect/incorrect) graded learner response data and the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instant. Exper-imental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner’s con-cept knowledge evolution over time, analyzing the quality and content organization of learning resources, and estimat-ing the question–concept associations and the question dif-ficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses compared to existing collaborative filtering and knowledge tracing methods.