Abstract
Proof Blocks (proofblocks.org) is a software tool that allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. 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 benchmark a novel algorithm for finding the edit distance from an arbitrary student submission to some correct solution of a Proof Blocks problem on thousands of student submissions, showing that our novel algorithm can perform over 100 times better than the naïve algorithm on real data. Our new algorithm has further applications in grading Parson’s Problems, task planning problems, and any other kind of homework or exam problem where the solution space may be modeled as a directed acyclic graph.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Darrah, M., Fuller, E., Miller, D.: A comparative study of partial credit assessment and computer-based testing for mathematics. J. Comput. Math. Sci. Teach. 29(4), 373–398 (2010)
Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring network structure, dynamics, and function using networkx. In: Varoquaux, G., Vaught, T., Millman, J. (eds.) Proceedings of the 7th Python in Science Conference, pp. 11–15. Pasadena, CA USA (2008)
Poulsen, S., Kulkarni, S., Herman, G., West, M.: Efficient partial credit grading of proof blocks problems. arXiv preprint arXiv:2204.04196 (2022)
Poulsen, S., Viswanathan, M., Herman, G.L., West, M.: Evaluating proof blocks problems as exam questions. In: Proceedings of the 17th ACM Conference on International Computing Education Research, pp. 157–168 (2021)
Poulsen, S., Viswanathan, M., Herman, G.L., West, M.: Proof blocks: autogradable scaffolding activities for learning to write proofs. In: Proceedings of the 27th ACM Conference on Innovation and Technology in Computer Science Education V. 1. Association for Computing Machinery, New York, NY, USA (2022). https://doi.org/10.1145/3502718.3524774
Weber, K.: Student difficulty in constructing proofs: the need for strategic knowledge. Educ. Stud. Math. 48(1), 101–119 (2001). https://doi.org/10.1023/A:1015535614355
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Poulsen, S., Kulkarni, S., Herman, G., West, M. (2022). Benchmarking Partial Credit Grading Algorithms for Proof Blocks Problems. In: Rodrigo, M.M., Matsuda, N., Cristea, A.I., Dimitrova, V. (eds) Artificial Intelligence in Education. Posters and Late Breaking Results, Workshops and Tutorials, Industry and Innovation Tracks, Practitioners’ and Doctoral Consortium. AIED 2022. Lecture Notes in Computer Science, vol 13356. Springer, Cham. https://doi.org/10.1007/978-3-031-11647-6_34
Download citation
DOI: https://doi.org/10.1007/978-3-031-11647-6_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-11646-9
Online ISBN: 978-3-031-11647-6
eBook Packages: Computer ScienceComputer Science (R0)