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 \textit{mainly focus on self-correction within the model}, which falls short of the ``teacher-style`` correction required in educational settings, \textit{i.e.}, systematically guiding and revising a student's problem-solving process. To address this gap, we propose \texttt{SMRC} (\textit{\underline{S}tudent \underline{M}athematical \underline{R}easoning \underline{C}orrection}), a novel method that aligns LLMs with student reasoning. Specifically, \texttt{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 \textbf{solution accuracy} and \textbf{correct-step retention}, offering a comprehensive measure of educational applicability. Experiments demonstrate that \texttt{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.

DOP: Diagnostic-Oriented Prompting for Large Language Models in Mathematical Correction

Math world problems correction(MWPC) is a novel task dedicated to rectifying reasoning errors in the process of solving mathematical problems. In this paper, leveraging the advancements in large language models (LLMs), we address two key objectives:(1) Distinguishing between mathematical reasoning and error correction; (2) Exploring strategies to enhance the error correction capabilities of LLMs in mathematics to solve MWPC task. We noticed that, in real-time education,assisting students in recognizing their mistakes is more crucial than simply providing correct answers. However, current research tends to prioritize obtaining accurate solutions to math problems rather than correcting potentially incorrect ones. Therefore, we modify the research paradigm, demonstrating that improving mathematical reasoning abilities does not equate to mastery in error correction. Meanwhile, we propose a novel method called diagnostic-oriented promping(DOP) aimed at facilitating LLMs to excel in error correction. In experiments, DOP has shown outstanding performance, highlighting its significant impact. We argue that in mathematical education, the demand for outstanding correctors surpasses that for proficient reasoners. Codes and data are available on https://github.com/ChenhaoEcnuCS/Reason-Correct.