# Personalized Auto-Grading and Feedback System for Constructive Geometry Tasks Using Large Language Models on an Online Math Platform

arXiv: https://arxiv.org/abs/2509.25529 · HTML: https://mlsanity.com/paper/2509.25529/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 40 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 6 of 6)

- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Evaluating Mathematical Reasoning Beyond Accuracy](https://mlsanity.com/paper/2404.05692/) (2024)
- [Beyond Final Answers: Evaluating Large Language Models for Math Tutoring](https://mlsanity.com/paper/2503.16460/) (2025)
- [UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2501.13766/) (2025)
- [Mathematical Computation and Reasoning Errors by Large Language Models](https://mlsanity.com/paper/2508.09932/) (2025)

## Built on by (most cited first, 2 of 2)

- [LLM-Driven Rubric-Based Assessment of Algebraic Competence in Multi-Stage Block Coding Tasks with Design and Field Evaluation](https://mlsanity.com/paper/2510.06253/) (2025)
- [LLMs as Teaching Assistants for Mathematics Exam Grading: Reliability, and Practical Usability](https://mlsanity.com/paper/2607.01247/) (2026)

## Abstract (arXiv)

As personalized learning gains increasing attention in mathematics education, there is a growing demand for intelligent systems that can assess complex student responses and provide individualized feedback in real time. In this study, we present a personalized auto-grading and feedback system for constructive geometry tasks, developed using large language models (LLMs) and deployed on the Algeomath platform, a Korean online tool designed for interactive geometric constructions. The proposed system evaluates student-submitted geometric constructions by analyzing their procedural accuracy and conceptual understanding. It employs a prompt-based grading mechanism using GPT-4, where student answers and model solutions are compared through a few-shot learning approach. Feedback is generated based on teacher-authored examples built from anticipated student responses, and it dynamically adapts to the student's problem-solving history, allowing up to four iterative attempts per question. The system was piloted with 79 middle-school students, where LLM-generated grades and feedback were benchmarked against teacher judgments. Grading closely aligned with teachers, and feedback helped many students revise errors and complete multi-step geometry tasks. While short-term corrections were frequent, longer-term transfer effects were less clear. Overall, the study highlights the potential of LLMs to support scalable, teacher-aligned formative assessment in mathematics, while pointing to improvements needed in terminology handling and feedback design.