Schoenfeld's Anatomy of Mathematical Reasoning by Language Models

• URL: http://arxiv.org/abs/2512.19995v1
• Date: Tue, 23 Dec 2025 02:44:25 GMT
• Title: Schoenfeld's Anatomy of Mathematical Reasoning by Language Models
• Authors: Ming Li, Chenrui Fan, Yize Cheng, Soheil Feizi, Tianyi Zhou,
• Abstract summary: We adopt Schoenfeld's Episode Theory as an inductive, intermediate-scale lens and introduce ThinkARM (Anatomy of Reasoning in Models)<n>ThinkARM explicitly abstracts reasoning traces into functional reasoning steps such as Analysis, Explore, Implement, verify, etc.<n>We show that episode-level representations make reasoning steps explicit, enabling systematic analysis of how reasoning is structured, stabilized, and altered in modern language models.
• Score: 56.656180566692946
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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