Consideration of a Bayesian Hierarchical Model for Assessment and Adaptive Instructions

People appear to practice what they do know rather than what they do not know [1], suggesting a necessity of an improved assessment of multilevel complex skill components. An understanding of the changing knowledge states is also important in that such an assessment can support instructions. The changing knowledge states can be generally visualized through learning curves. These curves would be useful to identify and predict the learner's changing knowledge states in multi-domains, and to understand the features of task/subtask learning. Here, we provide a framework based on a Bayesian hierarchical model that can be used to investigate learning and performance in the learner and domain model context-particularly a framework to estimate learning functions separately in a psychomotor task. We also take an approach of a production rule system (e.g., ACT-R) to analyze the learner's knowledge and skill in tasks and subtasks. We extend the current understanding of cognitive modeling to better support adaptive instructions, which helps to model the learner in multi-domains (i.e., beyond the desktop) and provide a summary of estimating a probability that the learner has learned each of a production rule. We find the framework being useful to model the learner's changing knowledge and skill states by supporting an estimate of probability that the learner has learned from a knowledge component, and by comparing learning curves with varying slopes and intercepts.