The inclusion degrees of skill maps and knowledge structures

Knowledge and learning assessment is a popular topic. In existing models for constructing the knowledge structure of an individual, it is often considered whether an individual has mastered the skills to solve the corresponding item. However, the relationship between the number of skills an individual has mastered and the item is ignored. It is not reasonable to explain the phenomenon that individuals solve the same item but have different knowledge structures behind it. This paper introduces the concept of skill inclusion degree and constructs the variable precision alpha-models to delineate knowledge structures. The skill inclusion degree takes into account an individual's mastery of the number of skills assigned to each item. Firstly, the concept of the skill inclusion degree is given, and some of its properties are discussed. Then, the variable precision alpha-model is constructed. Moreover, the relationship between knowledge structures delineated via the variable precision alpha-models by a skill map is studied, and the algorithm of knowledge structures delineated via these models by a skill map is designed. Finally, the experimental results on a real dataset demonstrate the feasibility and effectiveness of the proposed algorithm.