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

Feng Ling; Heng Yu

cs.AIAug 26, 2026

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

Authors: Feng Ling, Heng Yu

Organizations: Beijing Normal University

Abstract

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.

Figures & tables

Figure 1: Comparison between traditional Socratic Teaching and the proposed ToST paradigm. Traditional method (left) employs a 1P1S paradigm with linear reasoning, susceptible to stalling from intermediate errors. In contrast, ToST (right) adopts a 1PMS paradigm via parallel thinking, enabling dynamic redirection when paths fail.

Figure 2: Parallel Reasoning Tree (PRT) structure. The root defines the problem, with branches representing alternative solution paths weighted by complexity, novelty, and depth. Nodes signify correct intermediate steps leading to final answer.

Figure 3: Overview of the Tree-of-Thought Socratic Teaching (ToST) framework. ToST operates on Parallel Reasoning Trees and consists of Parallel Sowing for multi-solution exploration and Multi-Path Adaptive Guidance for personalized Socratic instruction via student–expert tree comparison.

Method	GSM8K					MATH-500
Method	Acc (%)	TreeAcc	$\bar{N}_{\text{Round}}$	TreeAcc-R	$\bar{N}_{\text{Method}}$	Acc (%)	TreeAcc	$\bar{N}_{\text{Round}}$	TreeAcc-R	$\bar{N}_{\text{Method}}$
Raw Students	48.49	37.28	—	—	1.04	61.20	35.82	—	—	1.16
SocraticLM	84.38	57.47	3.33	17.26	1.95	92.60	49.42	2.29	21.58	1.55
EduChat-R1-8b	76.27	51.93	3.94	13.18	1.62	84.40	44.39	2.42	18.34	1.41
EduChat-R1-32b	79.45	54.37	3.51	15.49	1.78	86.80	47.18	2.33	20.25	1.58
TutorRL-7B	89.61	60.17	2.86	21.04	1.91	91.80	48.99	2.26	21.68	1.52

Table 1: Performance comparison. Original student performance (before guidance) is reported as "Raw Students". Acc denotes final problem-solving accuracy, while TreeAcc ,

\bar{N}_{\text{Round}}

, and TreeAcc-R are defined in Section 5.2 .

\bar{N}_{\text{Method}}

denotes the average number of solution strategies attempted. ToST w/o PS and ToST w/o MPAG denote ablations removing Parallel Sowing, and Multi-Path Adaptive Guidance, respectively.

Figure 4: Comparison of guidance methods with five diagnostic protocol metrics on GSM8k, MATH-500, AIME24, and AIME25.

System	Helpfulness $\uparrow$	Clarity $\uparrow$	Understanding $\uparrow$	Willingness $\uparrow$	Burden $\uparrow$	$\kappa$
SocraticLM	3.39 $\pm$ 0.019	3.43 $\pm$ 0.222	3.56 $\pm$ 0.090	3.25 $\pm$ 0.196	4.33 $\pm$ 0.088	0.82
EduChat-R1-32b	3.21 $\pm$ 0.078	3.02 $\pm$ 0.062	3.65 $\pm$ 0.065	3.14 $\pm$ 0.097	4.19 $\pm$ 0.078	0.75
TutorRL-7B	3.75 $\pm$ 0.002	4.02 $\pm$ 0.211	4.86 $\pm$ 0.011	3.73 $\pm$ 0.216	4.37 $\pm$ 0.066	0.80
DeepSeek V3.2	4.42 $\pm$ 0.117	4.13 $\pm$ 0.119	4.92 $\pm$ 0.225	4.69 $\pm$ 0.070	4.68 $\pm$ 0.170	0.68
ToST (Ours)	4.66 $\pm$ 0.128	4.68 $\pm$ 0.071	4.89 $\pm$ 0.191	4.93 $\pm$ 0.209	4.95 $\pm$ 0.220	0.74

Table 2: Student study results (Track A, learner self-report). Participants rated their tutoring session on five dimensions using a 5-point Likert scale (mean

\pm

std).

\kappa

: Fleiss’ inter-rater agreement. Teacher/expert and LLM judge results are in Appendix F . Bold : best per column.

Figure 5: Stage promotion results with SocraticLM and ToST. Diagonal entries indicate no cognitive progression; upper-right entries correspond to upward stage transitions. ToST induces substantially more upward transitions (e.g., 73.3% S3 $\rightarrow$ S4); some downward entries (e.g., 17.8% S3 $\rightarrow$ S2) reflect adaptive consolidation under increased task difficulty.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

LoRA Fine-Tuning		ToST
Parameter	Value	Parameter	Value
lora rank	8	$\gamma$	0.6
lora alpha	16	$\sigma$	0.5
lora target	q,k	$\delta$	0.1
lora dropout	0.1	$\alpha$	0.52
learning rate	5e-5	$\beta$	0.39

Appendix

Table 3: Parameters for LoRA Finetuning (left) and ToST (right).

Dataset / Split	# Problems	Avg. Input Tokens	Avg. Output Tokens
GSM8k (Train)	7,473	25,761	5,432
MATH (Train)	7,498	29,447	6,210
GSM8k (Test)	1,319	25,658	5,411
MATH-500	500	32,369	6,826
AIME24	360	30,292	6,388
AIME25	480	36,786	7,757

Appendix

Table 4: PRT construction cost analysis.

Figure 6: Overview of the Parallel Reasoning Tree (PRT) construction pipeline.

Source Dataset	# Problems	Avg. # Paths	Avg. # Nodes
GSM8k (Train)	7,473	5.64	22.57
MATH (Train)	7,498	4.95	25.80
GSM8k (Test)	1,319	5.48	22.48
MATH-500	500	4.90	28.36
AIME24	360	4.76	26.54
AIME25	480	4.17	32.23

Appendix

Table 5: Statistics of the Enhanced Multi-Path Problem-Solving Collection in the MPSG-Bench dataset. Problems are grouped by their source datasets. For each subset, we report the number of problems, the average number of reasoning paths per PRT, and the average number of nodes per PRT.

Subset	# Problems	# Dialogues
Question-Scope-Oriented Single-Round Dialogue Corpus	11.5k	11.5k
Student-Diversity-Oriented Multi-Round Dialogue Corpus	3.5k	16.5k
Teaching Evaluation Set	1.8k	3.2k
Total	16.8k	31.2k

Appendix

Table 6: Statistics of the Multi-Path Teaching Dialogue Dataset in the MPSG-Bench dataset. We report the number of underlying problems and the total number of dialogue instances for each subset.

Pairwise Comparison	PDC (%)	NMR (%)
DeepSeek V3.2 vs. GPT-5	99.48	98.78
DeepSeek V3.2 vs. Gemini-2.5-pro	99.68	96.92
GPT-5 vs. Gemini-2.5-pro	98.52	97.36
Average	99.23	97.69

Appendix

Table 7: Consistency of solution tree parsing across APIs. Agreement results on sampled MPSG-Bench student responses demonstrate reliability of PRT parsing.

Dimension	Rating anchors (1 $\rightarrow$ 5)
Diagnostic accuracy	Incorrect diagnosis or misses the student’s actual issue $\rightarrow$ precisely identifies the student’s misconception or latent valid path.
Guidance naturalness	Awkward, abrupt, or overly scripted tutoring language $\rightarrow$ smooth, conversational, and pedagogically natural tutoring language.
Preservation of correct progress	Discards or ignores correct partial reasoning $\rightarrow$ explicitly preserves and builds on what the student already got right.
Switch naturalness	Path transition is abrupt or confusing $\rightarrow$ transition is well-motivated and smoothly bridged through reusable intermediate steps.
Overall helpfulness	Guidance is unlikely to help the student progress $\rightarrow$ guidance is highly useful for moving the student forward.
Cognitive load appropriateness	Overwhelming or under-informative relative to student state $\rightarrow$ well-calibrated support with appropriate challenge and pacing.

Appendix

Table 8: Teacher/expert rubric for blinded dialogue review. All dimensions use a 5-point Likert scale.

Dimension	Rating anchors (1 $\rightarrow$ 5)
Perceived helpfulness	The tutor was not helpful for solving the problem $\rightarrow$ the tutor was very helpful.
Clarity	The tutor’s guidance was hard to understand $\rightarrow$ the tutor’s guidance was very clear.
Understanding support	The interaction did not improve my understanding $\rightarrow$ the interaction substantially improved my understanding.
Willingness to continue exploring	I would not want to continue with this tutoring style in the future $\rightarrow$ I would like to continue exploring with this tutor.
Perceived burden	The interaction felt overly stressful or cognitively heavy $\rightarrow$ the interaction felt well-paced and manageable.

Appendix

Table 9: Student post-interaction questionnaire. All dimensions use a 5-point Likert scale.

System	Diag. Acc. $\uparrow$	Guidance Nat. $\uparrow$	Pres. Correct $\uparrow$	Switch Nat. $\uparrow$	Overall Help. $\uparrow$	Cog. Load $\uparrow$	$\kappa$
SocraticLM	4.08 $\pm$ 0.049	3.26 $\pm$ 0.153	2.85 $\pm$ 0.024	2.52 $\pm$ 0.103	2.23 $\pm$ 0.029	3.81 $\pm$ 0.107	0.73
EduChat-R1-32b	4.35 $\pm$ 0.148	3.51 $\pm$ 0.174	3.69 $\pm$ 0.022	3.37 $\pm$ 0.216	2.34 $\pm$ 0.010	3.37 $\pm$ 0.244	0.76
TutorRL-7B	4.80 $\pm$ 0.071	3.17 $\pm$ 0.001	3.96 $\pm$ 0.238	4.15 $\pm$ 0.228	3.35 $\pm$ 0.231	3.66 $\pm$ 0.046	0.74
DeepSeek V3.2	4.96 $\pm$ 0.149	4.09 $\pm$ 0.045	4.57 $\pm$ 0.026	4.61 $\pm$ 0.074	3.89 $\pm$ 0.190	4.78 $\pm$ 0.211	0.70
ToST (Ours)	4.94 $\pm$ 0.090	4.19 $\pm$ 0.219	4.77 $\pm$ 0.203	4.80 $\pm$ 0.008	4.42 $\pm$ 0.218	4.66 $\pm$ 0.181	0.75

Appendix

Table 10: Teacher/expert blinded evaluation results (Track A). Expert raters evaluated anonymized tutoring dialogues from five systems on six pedagogical dimensions using a 5-point Likert scale (mean

\pm

std).

\kappa

: Fleiss’ inter-rater agreement (substantial

>

0.6). Student self-report results are in Table 2 . Bold : best per column.

System	Helpfulness $\uparrow$	Clarity $\uparrow$	Diag. Correct $\uparrow$	Switch Nat. $\uparrow$	Win Rate $\uparrow$	$\rho_{T}$ $\uparrow$	$\rho_{S}$ $\uparrow$
SocraticLM	3.45 $\pm$ 0.307	3.78 $\pm$ 0.232	3.11 $\pm$ 0.136	2.80 $\pm$ 0.827	0.34 $\pm$ 0.031	0.82	0.82
EduChat-R1-32b	3.19 $\pm$ 0.296	3.60 $\pm$ 0.167	3.57 $\pm$ 0.015	2.96 $\pm$ 0.693	0.24 $\pm$ 0.084	0.71	0.78
TutorRL-7B	4.39 $\pm$ 0.260	4.17 $\pm$ 0.304	3.64 $\pm$ 0.188	3.00 $\pm$ 0.855	0.65 $\pm$ 0.096	0.84	0.81
DeepSeek V3.2	4.62 $\pm$ 0.008	4.51 $\pm$ 0.160	4.64 $\pm$ 0.186	3.91 $\pm$ 0.803	0.77 $\pm$ 0.021	0.80	0.86
ToST (Ours)	4.70 $\pm$ 0.107	4.69 $\pm$ 0.260	4.90 $\pm$ 0.119	4.17 $\pm$ 0.940	0.86 $\pm$ 0.066	0.74	0.87

Appendix

Table 11: Independent LLM judge results (Track B) and human–LLM agreement. An independent general-purpose LLM rated anonymized dialogues on four dimensions (mean

\pm

std). Win Rate: fraction of samples in which the system is preferred over all others.

\rho_{T}

\rho_{S}

: Spearman rank correlation with teacher / student scores. Bold : best per column.

Figure 7: Expert-review interface. The blinded rating interface presents anonymized tutoring dialogues side-by-side and collects six-dimension Likert scores with optional free-text rationale.

Figure 8: Student-study interface. The learner-facing page displays the tutoring dialogue in a chat format and collects five-dimension post-session Likert ratings with optional free-text reflection.

Figure 9: Prompt template for Parallel Reasoning Tree parsing. $\{\text{problem\_statement}\}$ , $\{\text{expert\_tree}\}$ , $\{\text{current\_path\_context}\}$ , and $\{\text{response}\}$ denote placeholders for the target mathematical problem, the reference solution tree provided by the MPSG-Bench dataset (shown in the standard Solution Tree format), the student’s current problem-solving trajectory, and the raw student response, respectively.

Figure 10: Prompt template for instructional guidance under dual pedagogical modes. $\{\text{problem\_statement}\}$ , $\{\text{analysis}\}$ , and $\{\text{advice}\}$ denote placeholders for the target problem, the path-level analysis report and the recommended instructional guidance provided by the Automatic Path Analyzer, respectively.

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Large Language Models (LLMs) show strong potential as educational tutors. Existing approaches typically train them to solve problems and provide correct answers, but this problem-solving-centered paradigm overlooks key requirements of effective tutoring: progressive guidance and the coordination of multiple pedagogical objectives across multi-turn interactions. Developing such tutors remains challenging because student behavior varies substantially with individual knowledge states, pedagogical effectiveness depends on multiple factors beyond final-answer correctness, and coordinating these objectives over tutor-student interactions is inherently difficult. To address these challenges, we propose PEARL, a PEdagogically Aligned Reinforcement Learning framework for training Socratic tutoring agents. First, we introduce a controllable student simulator that disentangles latent cognitive states from response generation, enabling simulation of diverse abilities and misconceptions. Second, we develop a pedagogically aligned reward model that jointly assesses pedagogical quality and objective correctness. Finally, we propose a stable multi-objective reinforcement learning approach that balances competing pedagogical objectives during tutor training. Experiments across multiple benchmarks show that PEARL performs competitively against tutoring-specific open-source systems and leading proprietary LLMs.

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