Subspace Clustering of Skill Mastery: Identifying Skills that Separate Students

In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. We adopt a faster, simpler approach: cluster a capability matrix estimating each student’s individual skill knowledge to generate skill set profile clusters of students. We complement this approach with the introduction of an automatic subspace clustering method that first identifies skills on which students are well-separated prior to clustering smaller subspaces. This method also allows teachers to dictate the size and separation of the clusters, if need be, for practical reasons. We demonstrate the feasibility and scalability of our method on several simulated datasets and illustrate the difficulties inherent in real data using a subset of online mathematics tutor data.