Mining Mathematical Misconceptions Using Deep Learning and Large Language Models

Abstract

Mathematical misconceptions represent one of the most persistent and consequential barriers to STEM education, systematically blocking student progression from elementary arithmetic to advanced calculus. Automated detection of these errors remains difficult because traditional classification approaches struggle with the extreme class imbalance inherent in misconception detection, where thousands of possible errors must be distinguished from limited training examples. This paper presents a retrieval-based system that combines dense neural search with Large Language Model (LLM) reasoning to match student errors to known misconceptions. A finetuned MathBERT bi-encoder retrieves the top- 25 semantically relevant misconceptions from 2,587 candidates, achieving 93% recall. Two LLM-based reranking strategies refine these results: ReAct-style reasoning with chain-of-thought prompting, and pairwise comparison with majority voting. The ReAct agent using DeepSeek-R1 improves mean average precision at rank 5 from 0.70 to 0.80. Unlike classification models that output opaque probability distributions, this approach retrieves humanreadable misconception descriptions, providing teachers with interpretable, verifiable explanations of student errors. Results demonstrate that retrieval-based architectures offer superior scalability for educational diagnosis tasks.