FAR-BKT: Fuzzy Adaptive Revision of Static Educational Content Using Bayesian Knowledge Tracing

Abstract

Predefined educational content provides curricular control and consistent quality but remains non-personalized when all learners receive the same sequence and amount of practice. This study proposes Fuzzy Adaptive Revision with Bayesian Knowledge Tracing (FAR-BKT), a framework based on the assumption that educational items assessing the same or closely related knowledge can share learner evidence while retaining separate question-level mastery estimates and revision decisions. FAR-BKT extends fixed-parameter BKT through three adaptive mechanisms: a dynamic learning-transition probability p(T), a context-sensitive slip probability p(S), and an adaptive fuzzy mastery threshold θ. The transition probability is adjusted based on group-level response accuracy, p(S) from option confusability and learner error history, and the threshold determines whether individual questions remain active for further revision. Six matched policies were evaluated using 1000 heterogeneous synthetic learners, 24 questions, and eight knowledge groups. Dynamic p(T) produced the greatest standalone improvement. FAR-BKT achieved the highest mastery coverage (0.462), lowest final estimation MAE (0.167), and highest removal precision (0.453), but required 11.1% more attempts than fixed BKT. The findings demonstrate an interpretable effectiveness–effort trade-off and provide computational, rather than classroom, evidence.