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 concept knowledge over time, analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc., or the forgetting effect), and estimates the content organization and difficulty of the questions in assessments. These quantities are estimated solely from binary-valued (correct/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. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, analyzing the quality and content organization of learning resources, and estimating the question--concept associations and the question difficulties. 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.