MathBERT: A Pre-trained Language Model for General NLP Tasks in Mathematics Education

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 {\em 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.