Efficient Partial Credit Grading of Proof Blocks Problems

Proof Blocks is a software tool which allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. In this paper, we address the problem of assigning partial credit to students completing Proof Blocks problems. Because of the large solution space, it is computationally expensive to calculate the difference between an incorrect student solution and some correct solution, restricting the ability to automatically assign students partial credit. We propose a novel algorithm for finding the edit distance from an arbitrary student submission to some correct solution of a Proof Blocks problem. We benchmark our algorithm on thousands of student submissions from Fall 2020, showing that our novel algorithm can perform over 100 times better than the naive algorithm on real data. Our new algorithm has further applications in grading Parson's Problems, as well as any other kind of homework or exam problem where the solution space may be modeled as a directed acyclic graph.