Dynamic Student Knowledge Modelling via Bayesian Deep Networks in Adaptive Learning Environments

Adaptive learning systems require student models that remain accurate, calibrated, and robust under sparse interaction histories, noisy outcomes, and shifting content distributions. This paper introduces a Bayesian deep knowledge modelling framework that represents learner mastery as a dynamic latent state while quantifying epistemic uncertainty through variational Bayesian inference. Experiments on temporally blocked evaluation demonstrate consistent gains over deterministic counterparts. The Bayesian Transformer achieved an AUC of 0.892 and NLL of 0.401, improving upon the best deterministic baseline (AUC 0.861, NLL 0.451), alongside reductions in Brier score (0.151 vs. 0.176) and Expected Calibration Error (0.021 vs. 0.046). Early-trajectory performance improved materially, with AUC increasing from 0.824 to 0.868 and NLL decreasing from 0.503 to 0.431, indicating stronger reliability when evidence is limited. Under robustness stressors, the Bayesian model degraded less under content shift (AUC 0.871, NLL 0.435) and cold-start (AUC 0.862, NLL 0.447) than deterministic modelling (AUC 0.821 and 0.803; NLL 0.507 and 0.528), while reducing high-confidence overconfidence rates (0.087 vs. 0.214). When integrated into an uncertainty-aware sequencing policy, Bayesian routing increased normalized learning gain (0.324 vs. 0.291 deterministic and 0.268 static) and reduced attempts-to-mastery (14.8 vs. 16.9 deterministic and 18.6 static). Policy behavior metrics indicate improved instructional stability, with lower difficulty jump rate (0.108 vs. 0.231) and higher instructor agreement (0.652 vs. 0.574), supporting deployment feasibility and auditability.