Conceptual Issues in Mastery Criteria: Differentiating Uncertainty and Degrees of Knowledge

Mastery learning is a common personalization strategy in adaptive educational systems. A mastery criterion decides whether a learner should continue practice of a current topic or move to a more advanced topic. This decision is typically done based on comparison with a mastery threshold. We argue that the commonly used mastery criteria combine two different aspects of knowledge estimate in the comparison to this threshold: the degree of achieved knowledge and the uncertainty of the estimate. We propose a novel learner model that provides conceptually clear treatment of these two aspects. The model is a generalization of the commonly used Bayesian knowledge tracing and logistic models and thus also provides insight into the relationship of these two types of learner models. We compare the proposed mastery criterion to commonly used criteria and discuss consequences for practical development of educational systems.