Autograding Mathematical Induction Proofs with Natural Language Processing

Abstract

In mathematical proof education, there remains a need for interventions that help students learn to write mathematical proofs. Research has shown that timely feedback can be very helpful to students learning new skills. While for many years natural language processing models have struggled to perform well on tasks related to mathematical texts, recent developments in natural language processing have created the opportunity to complete the task of giving students instant feedback on their mathematical proofs. In this paper, we present a set of training methods and models capable of autograding freeform mathematical proofs by leveraging existing large language models and other machine learning techniques. The models are trained using proof data collected from four different proof by induction problems. We use four different robust large language models to compare their performances, and all achieve satisfactory performances to various degrees. Additionally, we recruit human graders to grade the same proofs as the training data, and find that the best grading model is also more accurate than most human graders. With the development of these grading models, we create and deploy an autograder for proof by induction problems and perform a user study with students. Results from the study shows that students are able to make significant improvements to their proofs using the feedback from the autograder, but students still do not trust the AI autograders as much as they trust human graders. Future work can improve on the autograder feedback and figure out ways to help students trust AI autograders.