TITLE:
FQ-Ada-γ Knowledge Tracing Model for Adaptive Intelligent Tutoring Systems in Secondary Mathematics Education
AUTHORS:
Marcellin Aska Gnambe, Pacôme Brou, Klanan Bertrand Bamba, Hyacinthe Kouassi Konan, Adama Konate
KEYWORDS:
FQ-Ada-γ Intelligent Tutoring, Bayesian Knowledge Tracing, Mathematical Learning Modeling, Personalized Learning, Educational Data Mining
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.5,
May
15,
2026
ABSTRACT: The teaching of mathematics at the secondary level is a key lever for the development of students’ analytical and reasoning skills. However, classrooms generally show a high level of heterogeneity in student abilities, which limits teachers’ capacity to effectively adapt instructional content to individual learners’ needs. In this context, Intelligent Tutoring Systems (ITS) offer a promising solution for personalizing learning by using artificial intelligence and educational data analytics. Nevertheless, the effectiveness of these systems strongly depends on the accuracy and adaptability of the mathematical model used to be and track learners’ knowledge evolution. In this paper, we propose an adaptive probabilistic mathematical model for knowledge tracing, called FQ-Ada-γ Intelligent Tutoring, based on an extension of Bayesian Knowledge Tracing. The model introduces a continuous representation of the probability of concept mastery, along with an adaptive mechanism regulated by a parameter γ that dynamically modulates the learning progression. It incorporates a Bayesian updating process that accounts for the probability of learning, the probability of error despite mastery (slip), and the probability of correctly answering by chance (guess), while improving the granularity of modeling compared to classical approaches. Numerical simulations conducted on a dataset forming 1000 learners, 10 mathematical concepts, and 50,000 student-exercise interactions show a significant improvement in the average probability of concept mastery, increasing from 0.21 to 0.79 after 50 interactions. At the same time, the average correct response rate rises from 42% to 84%, reflecting a substantial improvement in student performance. The model also effectively finds unmastered concepts with a detection accuracy of 86%. In terms of overall performance, the model achieves an average accuracy of 0.83 and an estimated AUC of 0.85, positioning it above classical probabilistic models and at a level comparable to advanced neural approaches, while keeping strong interpretability. These results prove that the FQ-Ada-γ Intelligent Tutoring model provides a robust and efficient foundation for the development of adaptive intelligent tutoring systems, capable of promoting personalized mathematics learning at the secondary level while balancing predictive performance, explainability, and computational efficiency.