Fuzzy competence-based adaptive recommendations for mastery learning
Gongxun Wang, Jinjin Li, Daxin Zhu, Huilai Zhi · International Journal of General Systems · 2025
Mastery Learning is an educational concept that requires students to fully master previous knowledge before progressing to new content. To support this process, Adaptive Recommendations for Mastery Learning dynamically identify students' weak areas in real-time and provide targeted reinforcement to facilitate mastery. However, traditional mastery learning theory primarily relies on logical narratives and teaching practice summaries, lacking rigorous quantitative analysis and precise characterization of knowledge structures. This limitation hinders its ability to provide accurate and adaptive reinforcement. To address this, we introduce the Fuzzy Competence-based Knowledge Space Theory (FCbKST), which offers rigorous mathematical derivations and a visual representation of knowledge structures, enabling a more precise assessment of students' positions and weak areas in the knowledge structure. Despite its advantages, the inner fringe of a knowledge state may be empty, and the fuzzy competence states and knowledge states in FCbKST do not have a strict one-to-one correspondence, which may lead to the inability to make recommendations in certain situations. To resolve this, we propose a novel reinforcement recommendation method that selects fuzzy skills for students to reinforce based on the inner master fringe of a knowledge state and the representative element of a fuzzy competence state, improving adaptability. Additionally, we introduce a new approach to directly compute these fringes and elements, enhancing computational efficiency. Simulation experiments demonstrate that our algorithm significantly reduces running time and memory usage compared to existing methods, ensuring a more efficient and scalable recommendation process.