An Integrated Machine Learning and Hierarchical Variance Decomposition Pipeline for Student Performance Prediction and Metacognitive Calibration on Multi-Signal Telemetry

We introduce the Unified Neural Variational Measurement of Proficiency (UNVaMP) architecture, a knowledge tracing method that integrates observed student-item interactions with internal memory to produce evolving latent representations of student knowledge. These representations support accurate predictions of future responses while enabling explicit control over the smoothness of estimated learning trajectories. UNVaMP can be configured as either a purely neural model or a hybrid model that predicts responses through an interpretable measurement function over the latent space. We show that a pure neural configuration (UNVaMP-MLP) achieves the strongest predictive performance among compared models on three out of four datasets. Meanwhile, a hybrid configuration (UNVaMP-MIRT, using a 1PL MIRT measurement function) lags only slightly behind UNVaMP-MLP, indicating that the predictive cost of interpretability is modest. Beyond predictive accuracy, UNVaMP provides the following: a principled mechanism for controlling volatility when estimating student latent variables, quantification of uncertainty over student knowledge state estimates, and flexible input specification that supports heterogeneous student-item interaction features. In addition, the hybrid UNVaMP-MIRT configuration generates interpretable moment-in-time student knowledge state estimates. Using an experimental dataset, we show that auxiliary inputs induce structured changes in the predictive behavior of UNVaMP-MIRT, consistent with sensitivity to underlying structure beyond response correctness. Furthermore, through a simulation study, we show that UNVaMP yields well-behaved knowledge state estimates under controlled measurement conditions. In total, these results indicate that UNVaMP is both useful for real-world education systems and capable of recovering underlying structure from student-item interactions.

Sustained effort is essential for realizing the benefits of intelligent tutoring systems (ITS), yet many learners disengage or underuse available practice time. We introduce engagement forecasting as a supervised prediction task based on ITS logs, targeting two outcomes central to effort and learning progress: minutes practiced per week and new skills mastered per week. Using interaction log data from 425 middle-school students over a school year, we benchmark fifteen predictors including regressions, decision trees, and neural networks. We show that these feature-based models reduce mean absolute error (MAE) by 22-33% relative to heuristic baselines, including fixed-percentile rules adapted from prior work in other behavioral domains. We find that percentile heuristics systematically overpredict, whereas feature-based models better track student practice trajectories across weeks. To support explainability, we analyze feature importance and ablations, revealing target-specific patterns: effort forecasting is driven mainly by recent activity features, while progress forecasting depends more on learner-state and content difficulty signals. Finally, in a semi-structured user interview case study with eight college tutors, we examine how tutors reasoned about system-generated predictive features when setting goals with students. We find that tutors reasoned differently about effort versus progress goals in ways that mirror our pattern analysis. Together, these results establish a reproducible benchmark for forecasting weekly effort and learning progress in ITS. By making patterns of sustained effort and progress visible at a weekly timescale, engagement forecasting offers a foundation for supporting tutor-learner goal setting and timely instructional decisions.

Knowledge Tracing (KT) models students' knowledge states based on learning interactions to predict performance. While deep learning-based KT models have boosted predictive accuracy, most models rely on deterministic vector embeddings and opaque latent state transitions, limiting interpretability regarding how specific past behaviors influence predictions. To address this limitation, we propose Probabilistic Logical Knowledge Tracing (PLKT), an interpretable KT framework that formulates prediction as a goal-conditioned evidence reasoning process over historical learning behaviors. Instead of representing knowledge states as deterministic vector embeddings, PLKT employs robust Beta-distributed probabilistic embeddings to represent student knowledge states. This probabilistic foundation allows us to model the uncertainty of historical behaviors and perform explicit logical operations (e.g., conjunction), constructing transparent reasoning paths that reveal how specific past interactions contribute to the prediction. Extensive experiments show that PLKT outperforms state-of-the-art KT methods while achieving superior interpretability. Our code is available at https://anonymous.4open.science/r/PLKT-D3CE/.