Autograding Mathematical Induction Proofs with Natural Language Processing

Writing mathematical proofs has been identified as an important [1-3] and yet challenging topic [4] in computing education and mathematics education. A large body of research has shown that timely feedback is crucial to student learning [5, 6]. However, students are largely unable to receive timely feedback on written proofs due to the need to have proofs collected and hand-graded by instructors or teaching assistants. The ability to grade student proofs fully automatically with natural language processing (NLP) alleviates this need by allowing us to give students instant feedback on their proofs to let students iteratively enhance the quality of their proofs. In this paper, we propose a novel set of training methods and models capable of autograding freeform mathematical proofs, a problem at the intersection of mathematical proof education and Automatic Short Answer Grading (ASAG), by using existing NLP models and other machine learning techniques. Our proof autograder enables the development of grading systems that provide instant feedback to students without needing attention from instructors. It can also be deployed in large-scale educational platforms, allowing for more access for students. The main contributions of this paper are: Introducing the first pipeline of machine learning models capable of autograding mathematical proofs with similar accuracy to human graders Quantifying the amount of training data needed to achieve a satisfactory performance from the grading models Publishing an anonymized and labeled mathematical proof dataset that can be used in future model developments [7] Creating a set of autograded problems using the grading pipeline, and performing a user study that answers the following research questions: - Are students able to write better proofs by interacting with the autograder and the feedback it generates?