Using Bayesian Networks for Cognitive Assessment of Student Understanding of Buoyancy: A Granular Hierarchy Model

Cognitive diagnostic assessment based on Bayesian networks (BN) is developed in this paper to evaluate student understanding of the physical concept of buoyancy. we propose a three-order granular-hierarchy BN model which accounts for both fine-grained attributes and high-level proficiencies. Conditional independence in the BN structure is tested and utilized to validate the proposed model. The proficiency relationships are verified and the initial Q-matrix is refined. Then, an optimized granular hierarchy model is constructed based on the updated Q-matrix. All variants of the constructed models are evaluated on the basis of the prediction accuracy and the goodness-of-fit test. The experimental results demonstrate that the optimized granular-hierarchy model has the best prediction and model-fitting performance. In general, the BN method not only can provide more flexible modeling approach, but also can help validate or refine the proficiency model and the Q-matrix and this method has its unique advantage in cognitive diagnosis.