Schoenfeld's Anatomy of Mathematical Reasoning by Language Models
This work provides a systematic method for analyzing reasoning in language models, which is incremental as it builds on existing theories to offer new insights into model behavior.
The authors tackled the problem of analyzing the underlying cognitive structure of reasoning in large language models by introducing ThinkARM, a framework that abstracts reasoning traces into functional steps like Analysis and Explore, revealing reproducible thinking dynamics and structural differences in mathematical problem solving.
Large language models increasingly expose reasoning traces, yet their underlying cognitive structure and steps remain difficult to identify and analyze beyond surface-level statistics. We adopt Schoenfeld's Episode Theory as an inductive, intermediate-scale lens and introduce ThinkARM (Anatomy of Reasoning in Models), a scalable framework that explicitly abstracts reasoning traces into functional reasoning steps such as Analysis, Explore, Implement, Verify, etc. When applied to mathematical problem solving by diverse models, this abstraction reveals reproducible thinking dynamics and structural differences between reasoning and non-reasoning models, which are not apparent from token-level views. We further present two diagnostic case studies showing that exploration functions as a critical branching step associated with correctness, and that efficiency-oriented methods selectively suppress evaluative feedback steps rather than uniformly shortening responses. Together, our results demonstrate that episode-level representations make reasoning steps explicit, enabling systematic analysis of how reasoning is structured, stabilized, and altered in modern language models.