Automatic short answer grading at scale using Large Language Models

Providing evaluations to student work is a critical component of effective student learning, and automating its process can significantly reduce the workload on human graders. 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. We first present a set of training methods and models capable of autograding freeform mathematical proofs by leveraging existing Large Language Models (LLMs) 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 in terms of grading accuracy. 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. We then present an Automatic Short Answer Grading (ASAG) pipeline leveraging state-of-the-art generative LLMs. Our new LLM-based ASAG pipeline achieves better performances than existing custom-built models on the same datasets. We also compare the grading performance of three OpenAI models: GPT-4, GPT-4o, and o1-preview. Our results demonstrate that GPT-4o achieves the best balance between accuracy and cost-effectiveness. On the other hand, o1-preview, despite higher accuracy, exhibits a larger variance in error that makes it less practical for classroom use. We investigate the effects of incorporating instructor-graded examples into prompts using no examples, random selection, and Retrieval-Augmented Generation (RAG)-based selection strategies. Our findings indicate that providing graded examples enhances grading accuracy, with RAG-based selection outperforming random selection. Additionally, integrating grading rubrics improves accuracy by offering a structured standard for evaluation.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Zhao, Chenyan

Contributors dc:contributor

• Silva, Mariana

• Automatic Short Answer Grading

Statement dc:rights

• Copyright 2025 Chenyan Zhao

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129919

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129919