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 mainly focus on self-correction within the model, which falls short of the “teacher-style” correction required in educational settings, i.e., systematically guiding and revising a student’s problem-solving process. To address this gap, we propose SMRC (Student Mathematical Reasoning Correction), a novel method that aligns LLMs with student reasoning. Specifically, 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 solution accuracy and correct-step retention, offering a comprehensive measure of educational applicability. Experiments demonstrate that SMRC significantly outperforms existing methods on two public datasets (ProcessBench and MR-GSM8K) and our MSEB in terms of effectiveness and overall performance.

Reusable skills are becoming a common interface for extending large language model agents, packaging procedural guidance with access to files, tools, memory, and execution environments. However, this modularity introduces attack surfaces that are largely missed by existing safety evaluations: even when the user request is benign, unsafe influence may reside in skill guidance, local artifacts, or execution-environment files that steer the agent toward unsafe actions. We present **SkillSafetyBench**, a runnable benchmark for evaluating such skill-mediated safety failures. SkillSafetyBench includes 155 adversarial cases across 47 tasks, 6 risk domains, and 30 safety categories, each evaluated with a case-specific rule-based verifier. Experiments with multiple CLI agents and model backends show that non-user attacks can consistently induce unsafe behavior, with distinct failure patterns across domains, attack methods, and scaffold–model pairings. Our findings suggest that agent safety depends not only on model-level alignment, but also on how agents interpret skills, trust workflow context, and act through executable environments. We release the data and code in an anonymous repository to support reproducibility. The complete benchmark is available at https://github.com/AI45Lab/skill-safety-bench.