Towards Interpretable and Consistent Multi-Step Mathematical Reasoning in Large Language Models

作者：Xinyue Huang, Zeyu Wang, Xin Liu, Yueqi Tian, Qian Leng · 年份：2025 · DOI：10.1109/aiim67611.2025.11232978 · 被引用次数：3 · 研究领域：Intelligent Tutoring Systems and Adaptive Learning、Cognitive and developmental aspects of mathematical skills、Mathematics Education and Teaching Techniques

Mathematical reasoning, particularly within the K-12 education context, demands models that provide not only correct answers but also transparent, interpretable solution paths. Existing large language models (LLMs) often struggle with multi-step math problems due to their limited capacity for symbolic manipulation and structured reasoning. To address these challenges, we propose MetaMath-LLaMA, a novel metacognitive modular framework designed to enhance the reasoning abilities of LLMs through dynamic task orchestration. This framework integrates three core components: a Transformer-based metacognitive scheduler that learns to allocate reasoning subtasks adaptively; a symbolic parser with semantic grounding that fuses syntactic structure with contextual embeddings; and a hybrid symbolic-neural computation unit that seamlessly transitions between deterministic symbolic logic and neural approximation. The entire model is optimized through a multi-task training scheme coupled with curriculum learning and multi-tiered selfvalidation to mitigate reasoning errors and improve interpretability. We expect MetaMath-LLaMA to improve classroom usability by producing clearer step-by-step solution paths, aiding educators in assessment and supporting student conceptual understanding. Our approach offers a more modular, explainable, and effective solution for handling diverse mathematical tasks in K-12 education, and it outperforms traditional monolithic reasoning systems in logical fidelity ...