SMRC: Aligning Large Language Models with Student Reasoning for Mathematical Error Correction

Large language models (LLMs) often make reasoning errors when solving mathematical problems, and how to automatically detect and correct these errors has become an important research direction. However, existing approaches $\mathit{\text{mainly}}\mathit{\text{focus}}\mathit{\text{on}}\mathit{\text{self-correction}}\mathit{\text{within}}\mathit{\text{the}}\mathit{\text{model}}$, which falls short of the teacher-style correction required in educational settings, $\mathit{\text{i.e.}}$, systematically guiding and revising a student’s problem-solving process. To address this gap, we propose $\mathtt{\text{SMRC}}$ ($\underset{‾}{\mathit{\text{S}}}\mathit{\text{tudent}}\underset{‾}{\mathit{\text{M}}}\mathit{\text{athematical}}\underset{‾}{\mathit{\text{R}}}\mathit{\text{easoning}}\underset{‾}{\mathit{\text{C}}}\mathit{\text{orrection}}$), a novel method that aligns LLMs with student reasoning. Specifically, $\mathtt{\text{SMRC}}$ formulates student reasoning as a multi-step sequential decision problem and introduces Monte Carlo Tree Search (MCTS) to explore optimal correction paths. To reduce the cost of the annotating process-level rewards, we leverage breadth-first search (BFS) guided by LLMs and final-answer evaluation to generate reward signals, which are then distributed across intermediate reasoning steps via a back-propagation mechanism, enabling fine-grained process supervision. Additionally, we construct a benchmark for high school mathematics, MSEB (Multi-Solution Error Benchmark), consisting of 158 instances that include problem statements, student solutions, and correct reasoning steps. We further propose a dual evaluation protocol centered on $\mathbf{\text{solution}}\mathbf{\text{accuracy}}$ and $\mathbf{\text{correct-step}}\mathbf{\text{retention}}$, offering a comprehensive measure of educational applicability. Experiments demonstrate that $\mathtt{\text{SMRC}}$ significantly outperforms existing methods on two public datasets (ProcessBench and MR-GSM8K) and our MSEB in terms of effectiveness and overall performance. The code and data are available at https://github.com/Mind-Lab-ECNU/SMRC.