Erin Ottmar

Siddhartha Pradhan, Yanping Pei, Morgan Lee et al.

Bayesian Knowledge Tracing (BKT) is a widely used and interpretable student modeling approach in intelligent tutoring systems and educational data mining. However, most implementations rely on expectation-maximization or related optimization methods that yield only point estimates, limiting uncertainty quantification and principled comparisons across learners and conditions. We introduce StanBKT, an open-source Python package for estimating BKT models using Bayesian inference in Stan. StanBKT provides a unified framework supporting Hamiltonian Monte Carlo, variational inference, Pathfinder, and optimization-based estimation while preserving the hidden Markov structure and interpretability of classical BKT. It supports standard, grouped, and hierarchical BKT models, flexible prior specification, posterior predictive inference, and utilities for visualization and diagnostics. We evaluate StanBKT on large-scale observational and controlled educational datasets. On the ASSISTments 2020 dataset, we show that supported inference methods achieve comparable predictive performance while differing in computational efficiency and posterior fidelity. We further demonstrate how posterior inference enables principled comparison of condition-specific parameters in an educational intervention involving perceptual cue manipulations. Results illustrate how uncertainty quantification facilitates more reliable interpretation of differences in learning, forgetting, guessing, and slipping parameters across experimental conditions. Overall, StanBKT extends BKT beyond point estimation by providing a flexible framework for probabilistic student modeling, uncertainty quantification, and hierarchical inference in educational data mining.

Siddhartha Pradhan, Ethan Prihar, Erin Ottmar

Pretrained encoders for mathematical texts have achieved significant improvements on various tasks such as formula classification and information retrieval. Yet they remain limited in representing and capturing student strategies for entire solution pathways. Previously, this has been accomplished either through labor-intensive manual labeling, which does not scale, or by learning representations tied to platform-specific actions, which limits generalizability. In this work, we present a novel approach for learning problem-invariant representations of entire algebraic solution pathways. We first construct transition embeddings by computing vector differences between consecutive algebraic states encoded by high-capacity pretrained models, emphasizing transformations rather than problem-specific features. Sequence-level embeddings are then learned via SimCSE, using contrastive objectives to position semantically similar solution pathways close in embedding space while separating dissimilar strategies. We evaluate these embeddings through multiple tasks, including multi-label action classification, solution efficiency prediction, and sequence reconstruction, and demonstrate their capacity to encode meaningful strategy information. Furthermore, we derive embedding-based measures of strategy uniqueness, diversity, and conformity that correlate with both short-term and distal learning outcomes, providing scalable proxies for mathematical creativity and divergent thinking. This approach facilitates platform-agnostic and cross-problem analyses of student problem-solving behaviors, demonstrating the effectiveness of transition-based sequence embeddings for educational data mining and automated assessment.

Anand Ramakrishnan, Brian Zylich, Erin Ottmar et al.

In this work we present a multi-modal machine learning-based system, which we call ACORN, to analyze videos of school classrooms for the Positive Climate (PC) and Negative Climate (NC) dimensions of the CLASS observation protocol that is widely used in educational research. ACORN uses convolutional neural networks to analyze spectral audio features, the faces of teachers and students, and the pixels of each image frame, and then integrates this information over time using Temporal Convolutional Networks. The audiovisual ACORN's PC and NC predictions have Pearson correlations of $0.55$ and $0.63$ with ground-truth scores provided by expert CLASS coders on the UVA Toddler dataset (cross-validation on $n=300$ 15-min video segments), and a purely auditory ACORN predicts PC and NC with correlations of $0.36$ and $0.41$ on the MET dataset (test set of $n=2000$ videos segments). These numbers are similar to inter-coder reliability of human coders. Finally, using Graph Convolutional Networks we make early strides (AUC=$0.70$) toward predicting the specific moments (45-90sec clips) when the PC is particularly weak/strong. Our findings inform the design of automatic classroom observation and also more general video activity recognition and summary recognition systems.