Ethan Prihar

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.

Jia Tracy Shen, Michiharu Yamashita, Ethan Prihar et al.

Since the introduction of the original BERT (i.e., BASE BERT), researchers have developed various customized BERT models with improved performance for specific domains and tasks by exploiting the benefits of transfer learning. Due to the nature of mathematical texts, which often use domain specific vocabulary along with equations and math symbols, we posit that the development of a new BERT model for mathematics would be useful for many mathematical downstream tasks. In this resource paper, we introduce our multi-institutional effort (i.e., two learning platforms and three academic institutions in the US) toward this need: MathBERT, a model created by pre-training the BASE BERT model on a large mathematical corpus ranging from pre-kindergarten (pre-k), to high-school, to college graduate level mathematical content. In addition, we select three general NLP tasks that are often used in mathematics education: prediction of knowledge component, auto-grading open-ended Q&A, and knowledge tracing, to demonstrate the superiority of MathBERT over BASE BERT. Our experiments show that MathBERT outperforms prior best methods by 1.2-22% and BASE BERT by 2-8% on these tasks. In addition, we build a mathematics specific vocabulary 'mathVocab' to train with MathBERT. We discover that MathBERT pre-trained with 'mathVocab' outperforms MathBERT trained with the BASE BERT vocabulary (i.e., 'origVocab'). MathBERT is currently being adopted at the participated leaning platforms: Stride, Inc, a commercial educational resource provider, and ASSISTments.org, a free online educational platform. We release MathBERT for public usage at: https://github.com/tbs17/MathBERT.

Jia Tracy Shen, Michiharu Yamashita, Ethan Prihar et al.

Educational content labeled with proper knowledge components (KCs) are particularly useful to teachers or content organizers. However, manually labeling educational content is labor intensive and error-prone. To address this challenge, prior research proposed machine learning based solutions to auto-label educational content with limited success. In this work, we significantly improve prior research by (1) expanding the input types to include KC descriptions, instructional video titles, and problem descriptions (i.e., three types of prediction task), (2) doubling the granularity of the prediction from 198 to 385 KC labels (i.e., more practical setting but much harder multinomial classification problem), (3) improving the prediction accuracies by 0.5-2.3% using Task-adaptive Pre-trained BERT, outperforming six baselines, and (4) proposing a simple evaluation measure by which we can recover 56-73% of mispredicted KC labels. All codes and data sets in the experiments are available at:https://github.com/tbs17/TAPT-BERT