Tracking Knowledge Structures and Proficiencies of Students With Learning Transfer

In online intelligent education systems, to offer proactive studying services to students (e.g., learning path recommendation), a crucial demand is to track students' knowledge mastery levels over time. However, existing works ignore the impact of learning transfer on knowledge tracing and only track knowledge proficiency. Knowledge proficiency alone cannot fully reflect students' knowledge mastery levels. A student's knowledge structure (the similarities and differences within knowledge concepts) and abstract principle mastery level (common attributes among knowledge concepts, such as learning methods) also need to be tracked. To this end, we propose a novel multilevel Knowledge Tracing model with Learning Transfer (KTLT) to track students' knowledge mastery levels. First, we clarify the relationships among abstract principles, knowledge structure, and knowledge proficiency by utilizing the learning transfer theory in educational psychology. Then, we associate each problem with a knowledge vector in which each element represents an explicit knowledge concept by leveraging educational priors (i.e., a Q-matrix). Correspondingly, each student is represented as a knowledge vector (knowledge proficiency) and an abstract principle vector (abstract principle mastery). Given a student's knowledge and abstract principle vector over time, we use the learning and forgetting curve as priors to capture the student's knowledge proficiency and abstract principle mastery level over time. Furthermore, we embed the knowledge concept by using a student's abstract principle mastery level and obtain a personalized knowledge relevance matrix (a student's knowledge structure) by calculating the cosine similarity among the knowledge embedding results. Finally, we design a probabilistic matrix factorization framework by combining student and problem priors for tracking a student's knowledge mastery. Extensive experiments on two real-world datasets demonstrate both the effectiveness and explanatory ability of the KTLT.