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arXiv · 2511.01182

MiRAGE: Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion

Cuong Van Duc·Thai Tran Quoc·Minh Nguyen Dinh Tuan·Tam Vu Duc·Son Nguyen Van·Hanh Nguyen Thi
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Abstract

Detecting student misconceptions in open-ended responses is a longstanding challenge, demanding semantic precision and logical reasoning. We propose MiRAGE - Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion, a novel framework for automated misconception detection in mathematics. MiRAGE operates in three stages: (1) a Retrieval module narrows a large candidate pool to a semantically relevant subset; (2) a Reasoning module employs chain-of-thought generation to expose logical inconsistencies in student solutions; and (3) a Reranking module refines predictions by aligning them with the reasoning. These components are unified through an ensemble-fusion strategy that enhances robustness and interpretability. On mathematics datasets, MiRAGE achieves Mean Average Precision scores of 0.82/0.92/0.93 at levels 1/3/5, consistently outperforming individual modules. By coupling retrieval guidance with multi-stage reasoning, MiRAGE reduces dependence on large-scale language models while delivering a scalable and effective solution for educational assessment.

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Cuong Van Duc, Thai Tran Quoc, Minh Nguyen Dinh Tuan, Tam Vu Duc, Son Nguyen Van, Hanh Nguyen Thi. 2025-11-03. MiRAGE: Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion. https://arxiv.org/abs/2511.01182

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