Schoenfeld's Anatomy of Mathematical Reasoning by Language Models

arXiv 2512.19995 ↗First posted 23 Dec 2025cs.CL cs.AI cs.LGcited by 8

On the map: LLM reasoning → Mathematical reasoning

Abstract (arXiv)

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.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 42 of its 66 references that are in the map. First posted on arXiv 23 Dec 2025.

Builds on

42 of 66 references.

Closest ancestors · 3

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Other references · 39

2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
2021Training Verifiers to Solve Math Word Problemscited by 10,109
2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
2024GPT-4o System Cardcited by 4,588
2025Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilitiescited by 3,796
2023Let's Verify Step by Stepcited by 3,789
2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameterscited by 1,986
2025s1: Simple test-time scalingcited by 1,341
2023Gemini: A Family of Highly Capable Multimodal Modelscited by 872
2024Phi-4 Technical Reportcited by 711
2023Measuring Faithfulness in Chain-of-Thought Reasoningcited by 703
2024Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMscited by 570

27 more

2025Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoningcited by 559
2025Process Reinforcement through Implicit Rewardscited by 504
2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Modelscited by 464
2025L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learningcited by 384
2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 384
2025Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRscited by 377
2025Training Language Models to Reason Efficientlycited by 247
2025ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learningcited by 192
2025Thought Anchors: Which LLM Reasoning Steps Matter?cited by 129
2025MME-CoT: Benchmarking Chain-of-Thought in Large Multimodal Models for Reasoning Quality, Robustness, and Efficiencycited by 125
2025Thinkless: LLM Learns When to Thinkcited by 113
2025OverThink: Slowdown Attacks on Reasoning LLMscited by 96
2025Efficient Reasoning Models: A Surveycited by 95
2025DeepSeek-R1 Thoughtology: Let's think about LLM Reasoningcited by 92
2025Learn to Reason Efficiently with Adaptive Length-based Reward Shapingcited by 75
2025Understanding Reasoning in Thinking Language Models via Steering Vectorscited by 72
2025Self-rewarding correction for mathematical reasoningcited by 70
2025Missing Premise exacerbates Overthinking: Are Reasoning Models losing Critical Thinking Skill?cited by 58
2025Just Enough Thinking: Efficient Reasoning with Adaptive Length Penalties Reinforcement Learningcited by 52
2025Reasoning Language Models: A Blueprintcited by 42
2025Step Back to Leap Forward: Self-Backtracking for Boosting Reasoning of Language Modelscited by 27
2025Cognitive Foundations for Reasoning and Their Manifestation in LLMscited by 26
2025What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoTcited by 25
2025Does Reasoning Introduce Bias? A Study of Social Bias Evaluation and Mitigation in LLM Reasoningcited by 21
2025What Makes a Good Reasoning Chain? Uncovering Structural Patterns in Long Chain-of-Thought Reasoningcited by 21
2025ASTRO: Teaching Language Models to Reason by Reflecting and Backtracking In-Contextcited by 13
2025What makes Reasoning Models Different? Follow the Reasoning Leader for Efficient Decodingcited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 8.

8 papers.

2026Adaptive Information Control for Search-Augmented LLM Reasoningcited by 11
2026Weak-to-Strong On-Policy Distillationcited by 8
2026Rewarding How Models Think Pedagogically: Integrating Pedagogical Reasoning and Thinking Rewards for LLMs in Educationcited by 3
2026Cognitive Episodes in LLM Reasoning Traces Enable Interpretable Human Item Difficulty Predictioncited by 2
2026ThinkProbe: Beyond Accuracy -- Structural Profiling of Open-Ended LLM Reasoning Traces via Non-Generative Thought Graphscited by 0
2026Cognitive Profiling of LRMs' Reasoning Traces Using Bloom's Taxonomycited by 0
2026SHAPE of Chain-of-Thought in Math Reasoningcited by 0
2026Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVRcited by 0

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