Optimizing Personalized Learning Paths through Bayesian Knowledge Tracing and Gradient Boosting

Adaptive learning systems increasingly rely on data-driven approaches to tailor instruction to individual learners, yet many existing methods fail to fully capture the latent mastery dynamics underlying observable performance. This study proposes a hybrid framework that integrates Bayesian Knowledge Tracing (BKT) with Gradient Boosting to optimize personalized learning paths using fine-grained interaction data. The model was trained on sequential learner logs, generating mastery probabilities that were subsequently embedded into Gradient Boosting feature sets. Experimental results show that incorporating BKT features significantly enhanced predictive performance: Accuracy improved from 0.76 to 0.84, F1-score from 0.73 to 0.82, and AUC from 0.81 to 0.90. Error stability also increased, with RMSE decreasing from 0.31 to 0.24 and MAE from 0.25 to 0.18. In evaluating path efficiency, the optimized learning path reduced time-to-mastery by approximately 28% compared to fixed sequencing, requiring only 13 steps instead of 18. Attempts-per-skill also decreased from 5.2 to 3.7, while mastery gain rate improved from 0.045 to 0.072, demonstrating more effective practice allocation. Visual trajectory analysis highlighted smoother and more consistent mastery growth for optimized paths, with difficulty levels progressing in alignment with learner readiness rather than rigid curriculum order.  The study contributes a scalable and interpretable framework for personalized learning, offering actionable insights for intelligent tutoring systems seeking to balance cognitive modeling and machine learning for improved instructional outcomes.