Understanding the Thinking Process of Reasoning Models: A Perspective from Schoenfeld's Episode Theory

• Existing analyses of LRM thinking often rely on observation rather than solid theoretical grounding, leaving their problem-solving organization insufficiently understood.The paper also asks whether human cognitive theories can analyze LRM behavior.Source: §1 · p. 1
• The authors apply Schoenfeld’s Episode Theory as a cognitive framework for analyzing LRM reasoning traces.They describe the framework as a fine-grained lens for examining expert and novice problem-solving strategies.Source: §1 · p. 1
• All seven episode categories—Read, Analyze, Plan, Implement, Explore, Verify, and Monitor—appear in LRM traces and align with similar problem-solving processes.Representative examples for each category are shown in Table 1.Source: §1 · p. 1, Table 1 · p. 2
• The study applies the framework to DeepSeek-R1 responses on 1,385 SAT Mathematics items and annotates traces at paragraph and sentence levels.The manually annotated set contains 38 math problems, 915 paragraphs, and 3,087 sentences.Source: §1 · pp. 1–2
• The authors release an open annotation protocol and annotated corpus with thousands of annotations, making LRM reasoning analysis a well-defined task.They also evaluate LLM- and SLM-based labeling for efficiency and consistency with human labeling.Source: §1 · p. 2

2.1 Large Reasoning Models

• LRMs allocate training and inference compute to explicit chain-of-thought, producing longer, more flexible reasoning traces than earlier instruction-following models.The passage describes reinforcement learning and test-time reasoning as examples of this approach.Source: §2.1 · p. 2

2.2 Schoenfeld’s Episode Theory

• Schoenfeld’s Episode Theory models problem solving as temporally ordered episodes, separating a solver’s knowledge from its strategic deployment.Its original six categories are Read, Analyze, Plan, Implement, Explore, and Verify.Source: §2.2 · pp. 2–3

2.3 Why Episode Theory Fits LRM Traces

• LRM traces typically move from Read and Analyze to Plan and Implement, sometimes using Explore and Verify when problems are difficult.The paper relates Explore and Verify to test-time scaling and the “aha moment.”Source: §2.3 · p. 3
• Because LRM episode transitions are externalized in natural language, traces can be segmented and annotated at fine-grained levels to expose metacognitive regulation.The paper presents this as a useful fit for analyzing LRM reasoning behavior.Source: §2.3 · p. 3

3.1 Data Source

• The source set contains 1,385 SAT Mathematics items, with 38 DeepSeek-R1 responses annotated across 19 skill categories.The annotated responses comprise 915 paragraphs and 3,087 sentences.Source: §3.1 · p. 3

3.2 Data Annotation

• The hierarchical strategy labels paragraphs for broad behaviors and sentences for finer strategies, helping resolve subtle boundaries such as planning within verification.The approach uses paragraph context to clarify sentence-level labels.Source: §3.2 · pp. 3–4
• Paragraphs receive General, Explore, or Verify labels, while sentences receive one of seven episode labels, including Monitor for transitions such as self-monitoring or hesitation.Annotators label paragraphs first, then extracted sentences.Source: §3.2 · p. 4
• A pilot annotation informed revisions to the guidebook before three trained annotators completed the remaining responses.The full guidebooks and an annotated example are provided in the appendices.Source: §3.2 · p. 4
• Figure 1 visualizes sentence-level ground-truth state transitions, with darker cells indicating higher transfer probabilities between states.Source: Figure 1 · p. 4

4 Experiments and Analysis

• The experiment section evaluates automated annotation methods for the task.The reported analyses include the ground-truth transition matrix, zero-shot prompting methods, and training-based methods.Source: §4 · p. 4

4.1 Transition Matrix

• The darkest off-diagonal transitions are Read–Analyze, Plan–Implement, and Explore–Analyze, indicating these episode categories are more likely to occur consecutively.Plan–Implement specifically indicates that Implement is more likely to follow Plan.Source: §4.1 · p. 4

4.2 LLM-based Zero-shot Methods

• Guidebook prompting substantially improves automatic annotation; GPT-4.1 performs best most often, while Gemini-2.0 leads in in-context-learning scenarios.The comparison covers paragraph- and sentence-level accuracy across Base, Guidebook, Example, and Ex+Guide prompting.Source: §4.2 · pp. 4–5, Table 2 · p. 5

4.3 Training-based methods

• GPT-4.1 achieves the highest reported accuracy (0.805) and κ (0.764); among training-based methods, BERT performs best, while Verify-related label confusions remain difficult.The largest off-diagonal confusions are Analyze–Verify, Implement–Verify, and Verify–Implement.Source: §4.3 · p. 5, Table 4 · p. 5

5 Conclusion

• The authors present the corpus and reusable annotation protocol as a foundation for studying structured, episodic reasoning in LRMs.They make both publicly available and describe the analysis as offering initial insights into current models’ thinking patterns.Source: §5 · p. 5

Limitations

• The study covers only SAT math, whose difficulty is described as relatively moderate, and automatic annotation accuracy is not very high.The authors identify adding other sources, including more challenging math Olympiad items, and improving annotation accuracy as future work.Source: Limitations · p. 6

A Theories of Mathematical Problem Solving

• Bloom’s Taxonomy organizes educational learning objectives but does not capture the nuanced and iterative strategies of mathematical problem-solving.The paper therefore regards it as inconsistent with the study’s annotation purpose.Source: A Theories of Mathematical Problem… · p. 10
• Pólya’s four phases describe a high-level ideal solving process, but do not distinguish the varied cognitive actions within each phase.The passage characterizes the framework as a prescriptive guide and reflective tool rather than a fine-grained analytical scheme.Source: A Theories of Mathematical Problem… · p. 10
• Mason’s and Yeo and Yeap’s phase models support reflective instruction, but their subtasks were not fully operationalized or validated for empirical annotation.The passage says their use in systematic behavior annotation and empirical cognitive analysis has been limited.Source: A Theories of Mathematical Problem… · p. 10
• Greenes’ framework foregrounds monitoring and evaluation, but its sequential stages can constrain coding of nonlinear, iterative problem-solving.Its five stages range from problem representation and strategy design through implementation, evaluation, and reflection.Source: A Theories of Mathematical Problem… · p. 10
• Schoenfeld’s empirically validated episodes capture cognitive and metacognitive behavior, including strategic transitions and monitoring, making the framework suited to detailed analysis of human and AI reasoning.The paper contrasts this fine-grained coding approach with instructional models and argues that it supports annotation of AI-generated mathematical reasoning.Source: A Theories of Mathematical Problem… · pp. 10–11

B SAT Data Source

• SAT Math covers Algebra, Advanced Math, Problem Solving and Data Analysis, and Geometry and Trigonometry across 19 distinct skills.The listed skills include linear equations, functions, ratios, data inferences, geometry, and trigonometry.Source: B SAT Data Source · p. 12
• Items are multiple-choice or student-produced response and include question text, domain, skill, difficulty, and a step-by-step human rationale.The collected records also include fields such as answer choices, tables, and figures when applicable.Source: B SAT Data Source · p. 12
• The source data are stored as JSON, and the mathematical language was converted to LaTeX for machine processing.The passage lists fields including Question ID, Assessment, Test, Correct Answer Rationale, Table, and Figure.Source: B SAT Data Source · p. 12

D Paragraph-level Annotation Guidebook

• Paragraph labels distinguish General solution progress, Explore detours driven by uncertainty, and Verify checks of a candidate result.General covers the main solution path, while Explore investigates alternatives and Verify retrospectively evaluates correctness; paragraph labels depend on the paragraph’s overall purpose and context.Source: D Paragraph-level Annotation Guidebook · p. 15, §1 · p. 15, §2 · p. 16

1. Read •

• Read captures restating the problem’s information, conditions, or goal without analyzing or choosing a strategy.It usually appears at the start, but can recur mid-reasoning to ensure the problem was understood correctly.Source: §1 · p. 18

2. Analyze •

• Analyze captures certain explanations and inferences about relevant concepts, symbols, or relationships, before concrete calculations.It excludes substitutions and calculations, which belong to Implement.Source: §2 · pp. 18–19

3. Plan •

• Plan marks a committed statement of the next step or overall strategy before execution begins.It differs from Analyze’s explanation and Explore’s tentative possibilities.Source: §3 · p. 19

4. Implement •

• Implement captures execution of a strategy through concrete operations, calculations, diagrams, or intermediate results.A conclusion immediately following mathematical execution can also be labeled Implement.Source: §4 · p. 19

5. Explore •

• Sentence-level Explore marks tentative ideas, guesses, or trial approaches without commitment to a solution path.Within an Explore paragraph, sentences that analyze, calculate, or verify retain those sentence-level labels rather than Explore.Source: §5 · p. 20

6. Verify •

• Sentence-level Verify evaluates whether a result or method is correct, effective, or reasonable.It focuses on checking or confirming rather than generating the result, often by comparing it with conditions or using another method.Source: §6 · p. 20

7. Monitor •

• Monitor identifies brief interjections or meta-comments signaling self-monitoring, hesitation, reflection, or transitions between episodes.These short pauses generally lack substantial problem-solving content.Source: §7 · pp. 20–21
• Monitor sentences such as “Hmm...” and “Let me think” are brief indicators of internal processing flow that bridge more substantive stages.They lack the substantive content characteristic of other categories.Source: §7 · p. 21

Important Considerations for Annotators

• Sentence labels should follow each sentence’s primary function and context, with keywords treated as clues rather than decisive evidence.The guide also recommends using its examples and additional examples as annotation references.Source: Important Considerations for Annotators · p. 21

The Relation between Paragraph-level and Sentence-level Annotation

• Paragraph-level General, Explore, and Verify phases can span sentences with different functions, so hierarchical labels capture both the phase and each sentence’s behavior.For example, a sentence can be labeled Plan at the sentence level within a paragraph labeled Verify, avoiding a forced choice between the two.Source: The Relation between Paragraph-level… · p. 21

Some points that are easily misunderstood:

• Examples distinguish Monitor from planning or exploration, tentative proposals from concluded analysis, and explicit correctness checks from exploratory uncertainty.A request to parse information is Monitor; a tentative question can be Explore; and “let me check again” signals Verify.Source: Some points that are easily… · pp. 21–22
• Calculation and data-preparation examples are Analyze rather than Implement, Verify, or Read when they perform analytic work or set up further calculations.The guide distinguishes an arithmetic micro-check within ongoing work from a separate verification stage.Source: Some points that are easily… · p. 22