Schoenfeld's Anatomy of Mathematical Reasoning by Language Models

This paper introduces ThinkARM, a framework based on Schoenfeld's Episode Theory, to analyze the reasoning processes of large language models (LLMs) in mathematical problem-solving. It moves beyond surface-level analysis by abstracting reasoning traces into functional steps like Analysis, Explore, Implement, and Verify. The study reveals distinct thinking dynamics between reasoning and non-reasoning models, highlighting the importance of exploration as a branching step towards correctness. Furthermore, it shows that efficiency-oriented methods in LLMs can selectively suppress evaluative feedback, impacting the quality of reasoning. This episode-level representation offers a systematic way to understand and improve the reasoning capabilities of LLMs.