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ToST: A Tree-of-Thought Socratic Teaching Framework for Multi-Path Guidance and Parallel Thinking

Feng Ling, Heng Yu

arXiv:2608.25775v1cs.AI

TL;DR

Existing Socratic teaching largely follows a single linear solution path, leaving multi-path guidance and its evaluation underdeveloped. ToST combines a parallel reasoning tree, Parallel Sowing, and adaptive path guidance, while MPSG-Bench provides a 31K-dialogue SOLO-based benchmark. Experiments report an 11% average improvement in guidance success rate over educational LLM baselines and richer solution-path exploration.

  • Problem

    Existing approaches typically use one-problem–one-solution guidance, limiting instructional flexibility and parallel thinking, while multi-path instruction poses concurrent path-tracking and trajectory-switching challenges.

  • Method

    ToST instantiates one-problem–multiple-solutions teaching with a parallel reasoning tree, Parallel Sowing, and Multi-Path Adaptive Guidance, complemented by MPSG-Bench and SOLO-based evaluation.

  • Results

    11% average improvement in guidance success rate over educational LLM baselines was reported, with more efficient exploration of multi-solution reasoning trees.

  • Takeaways & Limitations

    ToST supports flexible multi-path Socratic guidance and richer exploration of alternative solution paths within the evaluated mathematical problem-solving setting.

  • Takeaways & Limitations

    The experiments and benchmark focus on mathematical problem-solving, ToST depends on reliable target-domain reasoning trees, and ethical effects on learner autonomy remain unexamined.

Abstract

from arXiv · show

Large Language Models (LLMs) exhibit strong problem-solving abilities, positioning them as promising agents for Socratic teaching to guide students through step-by-step heuristic questioning. However, existing approaches typically adopt a one-problem-one-solution paradigm, restricting the teaching guidance to a single linear reasoning path. This design limits instructional flexibility, weakens error recovery, and restricts students' ability to engage in parallel thinking to explore multiple valid solutions. To overcome these, we propose ToST, a Tree-of-Thought Socratic Teaching framework that explicitly supports multi-path guidance under a one-problem-multiple-solutions paradigm. ToST employs Parallel Sowing, a parallel-thinking-oriented questioning strategy to encourage students to approach problems from diverse perspectives, and a Multi-Path Adaptive Guidance mechanism to provide more robust and non-linear instructions across alternative solution trajectories. Concurrently, to fill the void in systematically evaluating such non-linear instructional capabilities, we advance the task of multi-path Socratic guidance by establishing MPSG-Bench, a comprehensive benchmark that includes a dataset of 31K multi-path teaching dialogues and a five-dimensional evaluation framework grounded in the SOLO (Structure of Observed Learning Outcomes) theory to assess parallel-thinking guidance. Experimental results demonstrate that ToST significantly enhances guidance success rates while empowering students to navigate and explore multiple solution paths more effectively under both automatic and human metrics.

1 Introduction

Existing Socratic teaching typically follows one linear solution path, limiting flexibility and parallel thinking. ToST addresses this gap with multi-path guidance and MPSG-Bench evaluation.

  • Most existing approaches use a one-problem–one-solution paradigm, restricting guidance to a single path and making recovery from ineffective guidance difficult.
  • Multi-path instruction creates System 2 planning challenges because LLMs must track progress across concurrent paths and decide when to switch trajectories.
  • ToST formalizes Socratic teaching as a parallel reasoning tree that tracks student progress across concurrent solution paths and models inter-path pedagogical relationships.
  • Parallel Sowing elicits multiple perspectives, while multi-path adaptive guidance switches trajectories when misconceptions arise and reuses validated steps as transition scaffolding.
  • MPSG-Bench contains 31k teaching dialogues and a five-dimensional SOLO-based framework for assessing multi-path guidance and parallel thinking.
  • 11% average improvement in guidance success rate over educational LLM baselines was reported, alongside more efficient exploration on multi-solution reasoning trees.

2 Related Work

Related work establishes personalized LLM tutoring and Socratic scaffolding, while highlighting the underdeveloped 1PMS perspective. Parallel thinking and SOLO provide conceptual foundations for multi-path instruction.

  • LLM tutoring research covers adaptive instruction, student simulation, learning-path planning, and pedagogical alignment through rules, pretraining, or reinforcement learning.
  • The 1P1S paradigm limits cultivation of one-problem–multiple-solutions reasoning.
  • The 1PMS paradigm explores diverse valid solution paths, aligning with parallel thinking’s simultaneous consideration of multiple reasoning strategies.
  • The SOLO taxonomy supplies a principled basis for assessing learning progression in structure-aware, multi-path instructional settings.

3 Background and Notation

The Parallel Reasoning Tree represents multiple valid solution trajectories for one problem as a rooted directed acyclic graph. The formulation tracks path properties and student progress for guidance selection.

  • A Parallel Reasoning Tree represents alternative valid solution strategies within one hierarchical structure, with each root-to-leaf path forming a complete reasoning trajectory.
  • Each path is annotated by depth, complexity, and innovativeness to characterize its reasoning trajectory.
  • The formal tree T = (V, P, D, C, I) contains a problem root, intermediate reasoning nodes, solution leaves, root-to-leaf paths, and path attributes.
  • Expert paths and student-generated paths are distinguished, while student intermediate nodes are classified as correctly solved, unsolved, or reusable.
  • Guidance selection jointly optimizes student–expert path alignment with reasoning depth and cognitive load under the 1PMS setting.

4 Tree-of-Thought Socratic Teaching

ToST represents Socratic teaching with parallel reasoning trees, combining multi-path exploration with adaptive, tree-based guidance selection. Its components diagnose student progress across paths and support switching when alternatives offer better instructional value.

  • Framework overview: ToST uses expert and incrementally parsed student reasoning trees to diagnose progress across concurrent solution paths.The framework compares student and expert trees to support personalized Socratic instruction.
  • Parallel Sowing: Parallel Sowing initializes student-tree branches through teacher-guided exploration of multiple perspectives and partial solution ideas.It does not require novice learners to independently enumerate complete solutions.
  • Multi-Path Adaptive Guidance: Multi-Path Adaptive Guidance combines a Tree-based Student Cognitive Manager with an Automatic Path Analyzer for progress estimation, error localization, and path selection.The manager performs path and node matching as dialogue proceeds.
  • Path evaluation: The guidance value H(P_t) integrates student progress, remaining difficulty, instructional investment, novelty relative to complexity, and cognitive load.These factors favor reliable progress, manageable difficulty, useful novelty, sufficient investment, and bounded load.
  • Path switching: MPAG switches from the current path only when an alternative exceeds it by the threshold θ_switch, reducing oscillation through an interpretable inertia margin.The next guidance path is selected from candidate expert paths using a greedy switching rule.
  • Instructional effect: Joint tree updates and path selection enable adaptive one-problem–multiple-solutions instruction intended to promote students’ parallel thinking.The framework supports non-linear instructional actions across alternative trajectories.

5 Benchmark: MPSG-Bench

MPSG-Bench evaluates multi-path Socratic guidance through structured problem-solving trajectories, teaching dialogues, and five SOLO-grounded metrics. Its measures cover both parallel-thinking development and stage-specific instructional effectiveness.

  • Benchmark construction: MPSG-Bench contains 31k PRT-grounded teaching dialogues for evaluating multi-path problem-solving and Socratic guidance.The benchmark addresses the limitations of datasets that assume a single canonical solution.
  • Benchmark construction: Its problem collection expands GSM8K and MATH problems into annotated parallel reasoning trees with approximately five distinct solution paths per problem.Student, Teacher, and Expert agents generate dialogues under six student archetypes.
  • Benchmark purpose: The benchmark supports standardized evaluation of error recovery and path consistency, capabilities traditional single-path datasets cannot measure.It also facilitates fine-tuning on structured, non-linear instructional turns.
  • Evaluation framework: The five-dimensional SOLO-grounded framework measures structure-aware reasoning, path-sensitive diagnosis, and guidance efficiency.It is designed as an interpretable alternative to final-answer accuracy or heuristic judgments alone.
  • Evaluation metrics: SAS measures SOLO-level cognitive change, while DP, PG, and SG assess diagnosis, persistence along current paths, and gains after path switching.PG and SG correspond to progression from prestructural toward unistructural, multistructural, and relational cognition.
  • Evaluation metrics: TreeAcc jointly evaluates node-level reasoning quality, path-level methodological alignment, and final-answer correctness within the parallel reasoning tree.Its formulation combines node, path, and final-answer components with weighted coefficients.
  • Evaluation metrics: TreeAcc-R captures the accuracy–efficiency trade-off by relating TreeAcc to the average number of dialogue rounds.Efficiency depends on both reasoning correctness and how quickly guidance facilitates convergence.
  • Evaluation framework: Together, SAS, TreeAcc-R, and DP quantify parallel-thinking development, while PG and SG quantify stage-specific instructional effectiveness.Figure 4 compares guidance methods on these five diagnostic metrics across GSM8K, MATH-500, AIME24, and AIME25.

6 Experiments and Results

Across benchmark, ablation, and human-evaluation settings, ToST improves multi-path guidance and supports upward cognitive-stage transitions. Learner, expert, and independent LLM judgments provide convergent evidence for its effectiveness.

  • 6.2 Main Results and Ablation Study: 11% average guidance-success improvement over single-chain tutoring methods was achieved by ToST across the evaluated datasets.ToST also remained competitive with larger general-purpose LLMs despite using a 7B teacher model.
  • 6.2 Main Results and Ablation Study: Up to 20% TreeAcc-R gains over SocraticLM were observed on GSM8K, while ToST exceeded the strongest general-purpose LLM baseline by approximately 8% on AIME25.The reported gains were consistent across problem difficulties.
  • 6.2 Main Results and Ablation Study: Removing Parallel Sowing reduced explored strategies from 2.12 to 1.53 on MATH-500, while removing Multi-Path Adaptive Guidance degraded solution quality.Parallel Sowing alone improved raw students by 3.71% but was insufficient by itself.
  • 6.3 Human Pilot Evaluation: ToST received the strongest learner ratings for helpfulness, clarity, willingness to continue exploring, and perceived burden/manageability.The expert review and independent LLM judge showed the same broad pattern, with ToST ranking first or near first on multi-path tutoring-control dimensions.
  • 6.4 Pedagogical Advantages of the ToST Framework: 73.3% of S3→S4 transitions under ToST indicated upward cognitive-stage movement, while 17.8% of S3→S2 transitions reflected adaptive consolidation under increased task difficulty.Figure 5 compares stage transitions with SocraticLM using SOLO-based cognitive stages.

7 Conclusion

The paper presents ToST for flexible multi-path Socratic guidance and MPSG-Bench for systematic evaluation of multi-path teaching. Experiments show improved guidance effectiveness and richer exploration of solution paths.

  • 7 Conclusion: ToST enables flexible multi-path guidance under the one-problem–multiple-solutions paradigm.Its design integrates Parallel Sowing with Multi-Path Adaptive Guidance.
  • 7 Conclusion: MPSG-Bench contains 31K dialogues and a SOLO-based evaluation framework for assessing multi-path teaching.The benchmark is intended to systematically assess parallel-thinking guidance.
  • 7 Conclusion: Experiments show that ToST significantly improves guidance effectiveness and supports richer exploration of solution paths.This is the paper’s concluding experimental claim.

Limitations

The current evidence is bounded by mathematical problem-solving, reliance on sufficiently reliable domain-specific PRTs, and unresolved ethical questions about learner autonomy and AI dependence. Future work targets broader domains, larger cohorts, and ethical safeguards.

  • Limitations: The current experiments and MPSG-Bench remain focused on mathematical problem-solving, including arithmetic and algebra.This limits the demonstrated domain scope of the framework and benchmark.
  • Limitations: ToST depends on sufficiently reliable PRTs for the target problem domain, creating upfront construction requirements.Adaptive expansion of tree structure during tutoring is identified as a direction for reducing those requirements.
  • Limitations: Potential over-reliance on AI-generated guidance and effects on learners’ autonomy and critical thinking have not been systematically examined.The paper also warns that overly prescriptive deployment may encourage passive learning or narrow problem-solving patterns.
  • Limitations: Future research will expand evaluation to larger cohorts, extend MPSG-Bench to other domains, and prioritize bias mitigation and ethical safeguards.These directions address the stated evaluation, scope, and ethics boundaries.

Ethical Considerations

LLM-based tutoring offers educational potential but raises risks involving bias, data privacy, and loss of human oversight. The paper addresses these concerns through a custom model emphasizing granular data control and evaluates ToST against educational and general LLM baselines.

  • LLM tutoring introduces risks involving bias, data privacy, and loss of human oversight.
  • The paper emphasizes continuous, rigorous evaluation of learning outcomes to support pedagogical effectiveness and prevent unintended negative consequences.
  • The custom model prioritizes granular data control to keep learner information out of large-scale systems where re-identification risks exist.
  • The benchmark construction combines multi-path problem-solving collections with teaching dialogue data annotated or structured for adaptive instruction.

B.2 PRT Construction Cost Analysis

PRT construction is an offline preprocessing expense, while MPSG-Bench combines structured multi-path problems with diverse teaching dialogues for adaptive guidance. The resulting framework supports multiple reasoning paths, student behaviors, and transferable tutoring scenarios.

  • B.2 PRT Construction Cost Analysis: PRT construction is a bounded offline preprocessing cost rather than a per-turn tutoring cost.Each problem requires 27,901 input tokens and 5,884 output tokens on average.
  • B.2 PRT Construction Cost Analysis: AIME25 has the highest construction token cost because its PRTs are deeper, whereas GSM8k requires fewer tokens because its solution chains are shorter.
  • Dataset Construction: MPSG-Bench contains explicit Parallel Reasoning Trees and a Multi-Path Teaching Dialogue Dataset built from them.
  • Dataset Construction: The two dialogue corpora vary problem scope, interaction length, and student archetypes to provide complementary supervision signals for adaptive instruction.
  • Student Modeling: Six student archetypes represent distinct problem-solving preferences, including algebraic, logical, combinatorial, trial-and-error, equation-oriented, and non-specialized strategies.
  • Transferability: PRT-based tutoring can transfer beyond mathematics when tasks have explicit multi-step reasoning, multiple valid strategies, checkable intermediate states, and a shared target.Examples span physics, coding, and evidence-based scientific reasoning.

F.5 Detailed Evaluation Results

Across complementary human and independent LLM evaluations, ToST receives the highest or near-highest overall ratings, while DeepSeek V3.2 is marginally stronger on some dimensions. ToST’s strongest ratings concern multi-path tutoring control, despite added reasoning demands.

  • ToST consistently achieves the highest or near-highest ratings across human participants and the independent LLM judge.
  • DeepSeek V3.2 is marginally higher than ToST on diagnostic accuracy and cognitive load appropriateness in expert ratings.
  • ToST’s multi-path state maintenance and path transitions introduce more instructional structure and active reasoning demands, making it somewhat less lightweight to some evaluators.
  • ToST receives the strongest ratings for guidance naturalness, preservation of correct intermediate reasoning, switch naturalness, and overall helpfulness.

G Parser Agreement Analysis of Parallel Reasoning Tree Parsing

The study evaluates PRT parsing consistency across multiple LLM backends and provides interfaces and prompt templates for expert review, student studies, tree parsing, and instructional guidance.

  • Parser Agreement Analysis: PRT parsing agreement is evaluated on 332 sampled student responses using identical prompts across DeepSeek V3.2, GPT-5, and Gemini-2.5-pro.
  • Parser Agreement Analysis: Average Path Diversity Consistency reaches 99.23%, while Node Match Rate reaches 97.69% across three LLM backends.
  • Evaluation Interfaces: The expert-review interface presents anonymized tutoring dialogues side-by-side and collects six-dimension Likert scores with optional rationale.
  • Evaluation Interfaces: The student-study interface displays tutoring dialogues in chat format and collects five-dimension post-session Likert ratings with optional reflection.
  • Prompt Templates: The PRT parsing prompt uses the problem statement, expert tree, current path context, and raw student response to produce a parsed response.
  • Prompt Templates: The instructional guidance prompt uses the problem statement, path-level analysis report, and recommended guidance from the Automatic Path Analyzer.
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