Using Item-type Performance Covariance to Improve the Skill Model of an Existing Tutor

Using data from an existing pre-algebra computer-based tutor, we analyzed the covariance of item-types with the goal of describing a more effective way to assign skill labels to item-types. Analyzing covariance is important because it allows us to place the skills in a related network in which we can identify the role each skill plays in learning the overall domain. This placement allows more effective and automatic assignment of skills to item- types. To analyze covariance we used POKS (partial order knowledge structures) to analyze item-type outcome relationships and Pearson correlation to capture item-type duration relationships. Hierarchical agglomerative clustering of these item-types was also performed using both outcome and duration covariance patterns. These analyses allowed us to propose improved skill labeling that removes irrelevant item-types, clusters related types, and clarifies the optimal temporal ordering of these clusters during practice.