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REAT: A Reflective Experience-Augmented Tutoring Framework for Multi-turn Mathematical Instruction

Jianheng Zhou, Chaoli Zhang, Xingjun Wei, Xinliang Zhou, Giancarlo Fortino, Xing Fan, Yanfeng Wang, Qingsong Wen, Haoyang Li

Year: 2026Venue: arXiv preprintArea: cs.MAType: PreprintEmbeddings: 94

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%

Last extracted: 9/25/2026, 3:36:51 AM

Summary

The paper introduces REAT (Reflective Experience-Augmented Tutoring), a framework for multi-turn mathematical instruction that enhances Large Language Models (LLMs) by systematically accumulating and reusing pedagogical experiences. REAT utilizes a multi-agent Observer-Critic-Mentor (OCM) pipeline to distill historical dialogues into structured, problem-agnostic teaching experiences stored in a dynamic repository. During live tutoring, a state-aware retrieval module injects these experiences to provide adaptive scaffolding based on the student's cognitive state, significantly outperforming prompt-only and supervised fine-tuning baselines.

Entities (8)

REAT · framework · 98%OCM · method · 95%Experience Repository · component · 94%SFT · method · 93%GSM8K · dataset · 92%Doubao-seed · model · 90%Qwen3-8b · model · 90%GPT-5 · model · 88%

Relation Signals (7)

REAT → uses → OCM

confidence 95% · Driven by a multi-agent Observer-Critic-Mentor (OCM) distillation pipeline, REAT reviews past conversational trajectories...

REAT → evaluatedon → GSM8K

confidence 93% · We primarily use GSM8K (Cobbe et al., 2021) for multi-turn mathematical tutoring experiments.

OCM → consistsof → Critic

confidence 92% · Critic. The Critic evaluates the pedagogical efficacy of the response...

OCM → consistsof → Mentor

confidence 92% · Mentor and Problem-Agnostic Distillation. When activated, the Mentor uses the dialogue context... to construct an improved response

OCM → consistsof → Observer

confidence 92% · The core of our REAT framework lies in the OCM distillation pipeline... Observer. The Observer acts as a diagnostic encoder.

Experience Repository → maintainedby → REAT

confidence 91% · We construct a self-optimizing experience repository... The repository dynamically evolves through continuous deduplication, merging, and pruning.

REAT → outperforms → SFT

confidence 90% · Experiments demonstrate that the proposed framework significantly outperforms both prompt-only and supervised fine-tuning (SFT) baselines

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Abstract

Abstract:Current Large Language Models (LLMs) excel at solving complex mathematical problems, yet this proficiency does not inherently translate into effective tutoring. While advanced LLM tutors may leverage multi-agent frameworks or fine-tuning, most still lack a mechanism to systematically accumulate and reuse pedagogical experience over time, limiting their adaptability to diverse student needs during fluid, multi-turn interactions. To bridge this gap, we propose the Reflective Experience-Augmented Tutoring (REAT) framework, which couples experience distillation from historical dialogues with real-time adaptive retrieval. Driven by a multi-agent Observer-Critic-Mentor (OCM) distillation pipeline, REAT reviews past conversational trajectories and distills raw interactions into structured, problem-agnostic pedagogical experiences. During live tutoring, a state-aware retrieval module injects these curated experiences to provide adaptive scaffolding based on the student's cognitive state. Experiments demonstrate that the proposed framework significantly outperforms both prompt-only and supervised fine-tuning (SFT) baselines, particularly in improving complex, low-scoring tutoring scenarios. Crucially, the distilled experiences exhibit robust generalization across diverse model architectures and mathematical datasets.

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REAT: A Reflective Experience-Augmented Tutoring Framework for Multi-turn Mathematical Instruction Jianheng Zhou 1 , Chaoli Zhang 2 * , Xingjun Wei 3 , Xinliang Zhou 4 , Giancarlo Fortino 5 , Xing Fan 6 , Yanfeng Wang 7 , Qingsong Wen 8* , and Haoyang Li 8† 1 School of Electrical and Electronic Engineering, Nanyang Technological University 2 Zhejiang Normal University 3 Telfer School of Management, University of Ottawa 4 Nanyang Technological University 5 University of Calabria 6 APSS, Hong Kong Polytechnic University 7 School of Artificial Intelligence, Shanghai Jiao Tong University 8 Squirrel Ai Learning Correspondence: chaolizcl@zjnu.edu.cn, qingsongedu@gmail.com Abstract Current Large Language Models (LLMs) excel at solving complex mathematical problems, yet this proficiency does not inherently translate into effective tutoring. While advanced LLM tutors may leverage multi-agent frameworks or fine-tuning, most still lack a mechanism to systematically accumulate and reuse pedagogi- cal experience over time, limiting their adapt- ability to diverse student needs during fluid, multi-turn interactions. To bridge this gap, we propose the Reflective Experience-Augmented Tutoring (REAT) framework, which couples ex- perience distillation from historical dialogues with real-time adaptive retrieval. Driven by a multi-agent Observer-Critic-Mentor (OCM) distillation pipeline, REAT reviews past conver- sational trajectories and distills raw interactions into structured, problem-agnostic pedagogical experiences. During live tutoring, a state-aware retrieval module injects these curated experi- ences to provide adaptive scaffolding based on the student’s cognitive state. Experiments demonstrate that the proposed framework sig- nificantly outperforms both prompt-only and supervised fine-tuning (SFT) baselines, partic- ularly in improving complex, low-scoring tu- toring scenarios. Crucially, the distilled ex- periences exhibit robust generalization across diverse model architectures and mathematical datasets. 1 Introduction The rapid evolution of Large Language Models (LLMs) is fundamentally reshaping educational * Corresponding authors: Chaoli Zhang and Qingsong Wen. † This work was supported in part by the NSFC under Grant No. 62502456 interactions (Chu et al., 2025). State-of-the-art models can achieve near-perfect accuracy on K-12 mathematics problems now, meaning mathematical problem-solving is no longer the main technologi- cal hurdle (ReLE Benchmark Team, 2025). How- ever, providing a correct answer does not guarantee effective tutoring. (Macina et al., 2025; Maurya et al., 2025). In multi-turn tutoring, an effective model requires pedagogical capabilities: continu- ous scaffolding to guide thinking (van de Pol et al., 2010), precise attribution of cognitive gaps, em- pathy to sustain student engagement, and dynamic strategy adaptation. Existing LLM tutors primarily rely on predefined prompts or vanilla retrieval, which often leads to relatively static strategies (Liu et al., 2025; Kong et al., 2024; Wang et al., 2024a). While such rules enable basic socratic interactions, this reliance on static guidance makes it challenging to address un- predictable student confusion. Moreover, these static systems lack a continuous evolution mecha- nism. While recent work on agent reflection and memory shows that LLMs benefit from accumulat- ing past feedback across trajectories (Madaan et al., 2023; Wang et al., 2024b; Tan et al., 2025; Jiang et al., 2026), most current tutoring systems still fail to convert past interactions into reusable external memory. In practice, teachers often rely on expert men- tors to reflect on and accumulate tutoring prac- tices (Larrivee, 2000; Schön, 2017). Inspired by this human reflection process, we propose a Re- flective Experience-Augmented Tutoring (REAT) framework driven by a multi-agent Observer-Critic- Mentor (OCM) distillation pipeline. REAT system- atically evaluates historical tutoring trajectories and arXiv:2609.29804v1 [cs.MA] 24 Sep 2026 Prompt-only Rule Driving Teaching Experience Driving Experience Accumulation Terms swapped across equations reverse signs. Remember this rule. For x+3=5, x=2. I always make mistakes in symbol shifting during equation solving and feel unable to learn algebra well. Potential Weakness: - Overlook certain rules in practical use. - Difficult to cover all situations. - Static rules lack adaptability in different scenarios. Detailed prompt I need to draw on teaching experience. Basic prompt Experience Repository Don’t worry! This error is common for beginners. Your struggle stems from poor understanding of equation balance rather than memorization. Let’s learn step by step. This AI teacher is empathetic and teaches really well. Improvements: - Dynamic Rule: Adaptively invokes empirical rule library without manually predefined prompts. - State Matching: Retrieves optimal teaching experience based on real-time student states. - Tutoring Improvement: Achieves empathetic, targeted, scaffolded and strategy-flexible personalized tutoring. Observer Critic Mentor If: mentor's EXP is qualified EXP Extraction Loop Historical dialogues are reflected on, summarized, and abstracted into teaching experience based on students' learning status and error details. Periodic Offline Expansion Non-Specific Question Fitting Dynamic Rule Prompting Figure 1: Conceptual comparison between conventional static tutoring systems and our proposed REAT framework. Unlike existing tutors bound by predefined, static mechanisms, our framework systematically accumu- lates and reuses pedagogical experiences over time to achieve dynamic and adaptive multi-turn tutoring. abstracts them into structured pedagogical experi- ences. A rigorous gating mechanism admits only verified, high-quality experiences into the reposi- tory. During tutoring, state-aware retrieval equips the teacher model with targeted guidance, enabling flexible strategy adjustments based on the student’s cognitive state. The main contributions of this work are summa- rized as follows: • We propose the REAT framework. Driven by a multi-agent OCM distillation pipeline, it evaluates historical trajectories and repairs weak responses, distilling raw interactions into reusable pedagogical experiences. •We construct a self-optimizing experience repository with state-aware retrieval. The repository dynamically evolves through con- tinuous deduplication, merging, and pruning. During tutoring, it retrieves state-aligned expe- riences to provide real-time and flexible scaf- folding. • We validate the effectiveness and gener- alization of non-parametric pedagogical enhancement.Experiments demonstrate that our approach significantly outperforms prompt-only and Supervised Fine-Tuning (SFT) baselines, particularly in improving challenging, low-scoring interactions. Cru- cially, the distilled experiences exhibit robust generalization across diverse model architec- tures and mathematical datasets. 2 Related Work 2.1 Intelligent Tutoring and Educational Dialogue Systems Before the era of Large Language Models (LLMs), early tutoring systems like CIRCSIM-Tutor, IT- SPOKE, and Beetle I had already demonstrated that natural language dialogue could effectively di- agnose student misconceptions and provide multi- turn feedback (Evens et al., 1997; Litman and Sil- liman, 2004; Dzikovska et al., 2011). AutoTutor further proved that conversational interaction leads to measurable learning gains, emphasizing the im- portance of adaptive instructional strategies and di- alogue management (Graesser et al., 2004). Later, with the shift toward data-driven modeling, bench- marks like CIMA (Stasaski et al., 2020) and Math- Dial (Macina et al., 2023) introduced rich pedagog- ical annotations to educational dialogues. These resources allowed researchers to study tutoring as a structured, step-by-step instructional process rather than just a simple response generation task. 2.2 LLM-based Tutors and Evaluation Paradigms Recent research explores LLMs as conversational tutors, showing that strong problem-solving skills do not automatically guarantee effective pedagogy (Daheim et al., 2024). To improve tutoring qual- ity, current systems rely on personalized steering (Liu et al., 2025) and structured hint generation (Qi et al., 2025; Puech et al., 2025). Concurrently, evaluation and interaction paradigms have shifted toward multi-agent architectures and user simula- tions (Kong et al., 2024; Shi et al., 2025). Decom- posing the system into separate teacher, learner, and evaluator agents makes it much easier to model multi-round interactions and evaluate the tutoring process turn by turn (Shi et al., 2025; Luo et al., 2024). However, these multi-agent frameworks mostly focus on offline simulation or training opti- mization. They rarely use the reflective feedback generated during these interactions to guide teach- ers in real-time during tutoring. 2.3 Retrieval Augmentation, Reflection, and External Experience Recent advancements in language agents have in- creasingly leveraged retrieval-augmented gener- ation (RAG), reflective refinement, and external memory. Standard RAG typically combines para- metric models with external factual knowledge (Lewis et al., 2020). In dialogue systems, incor- porating external memory structures has proven effective for enhancing response informativeness (Cai et al., 2019; Tian et al., 2019). Furthermore, frameworks like Self-Refine and Reflexion show that LLMs can iteratively optimize their outputs us- ing feedback and reflective memory (Madaan et al., 2023; Shinn et al., 2023). In the broader agentic domain, long-term memory and externalized expe- rience accumulation have also become critical for sustained evolution (Park et al., 2023; Wang et al., 2023; Packer et al., 2024; Wang et al., 2024b; Tan et al., 2025; Jiang et al., 2026). Unlike these gen- eral approaches, our framework focuses exclusively on pedagogical experience. Rather than retrieving factual knowledge or verbatim dialogue histories, our system distills high-quality instructional behav- iors through offline reflection. 3 Methodology In this section, we formally define the multi- turn mathematics tutoring task.LetPde- note a given mathematics problem, andH = (u 1 ,r 1 ),..., (u t−1 ,r t−1 ) represent the dialogue history, whereu i andr i are the student’s utterance and the teacher’s response at turni, respectively. At turnt, our objective is to develop an automated tutoring systemf(·)that generates the next teacher responser t based onP,H, and the current student utterance u t : r t = f(P,H,u t ).(1) Unlike traditional question answering, this task is not just about giving the correct answers. The main goal is to provide continuous tutoring support across multi-turn conversations. By tracking the student’s understanding and adapting its guidance, the system helps them think independently and truly master the concepts. 3.1 Overall Framework To dynamically enhance the pedagogical reasoning of LLMs during multi-turn tutoring, we propose the REAT framework (Figure 2). The architec- ture consists of two tightly coupled components: an execution module (the AI Tutor) that manages real-time interactions, and a multi-agent OCM dis- tillation pipeline that drives pedagogical evolution by distilling high-quality instructional experiences from historical trajectories. To align the presenta- tion with Figure 2, the workflow is organized as: (a) original tutoring dialogue, (b) OCM distillation pipeline, (c) experience repository maintenance, (d) state-aware experience retrieval, and (e) experience- augmented dialogue. During tutoring, the base AI Tutor generates the responser t under a generative policyπ θ . To move beyond static rules, this generation process is con- ditioned one t , a targeted pedagogical experience dynamically retrieved from the experience reposi- tory: r t ∼ π θ (·| P,H <t ,u t ,e t ).(2) The OCM distillation pipeline continuously up- dates and controls the quality of the repository, ensuring the tutor is constantly augmented by vali- dated pedagogical priors. 3.2 OCM Distillation Pipeline The core of our REAT framework lies in the OCM distillation pipeline, which simulates a rig- orous, meta-cognitive pedagogical review. It sys- tematically inspects past trajectories, executes tar- (b) OCM Distillation Pipeline (c) Experience Repository Maintenance (d) State-aware Experience Retrieval Observer Critic Mentor Processing Pipeline: Teaching Dialogue → OCM Evaluation & Distilling → High-Quality Experience Accumulation → Retrieval Quality Inspection (Maximum 3 rounds) Unqualified Drop · · (Below threshold) For Each-turn： · Student State Observation · Teacher Action Evidence · Structured Diagnostic Record Only objectively record teachers' behaviors. Scaffolding Attribution Empathy Teaching Focus Strategy Adaptation Observation Records Mentor's Exp Review Passed Observation Result Scoring Results · Better Response Summary of Premium Teaching Experience Summary of Undesirable Teaching Behaviors Candidate Experiences Emotion Intent Error Type Struggle Type Current State State-aware Filter Query Text Candidate Pool Exp1Exp2 Exp3Exp4 Top-1 Experience （Cosine Similarity） Exp3 Sim ≈ 0.8 Retrieval Text Rewriter Find Comparable Experiences Experience Integration Action Skip Merge Add Low-value Memory Control Storage Rules If repeatedly linked to low-quality outcomes These experience entries will be set to disabled Exp Repository Merged Disabled Original High-quality Experience Database Ready for teachers to reference in new teaching responses. (e) Experience-Augmented Dialogue How to solve this math problem? I can provide you with expert-level teaching support. I'm an AI teacher equipped with an experience base. (a) Original Tutoring Dialogue After accumulating a sufficient number of samples, conduct offline teaching reflection. Raw Dialogue Collection Top-1 Experience Experience Injection · · · · · · · · Pedagogical Evaluation Repository Calculate Cosine Sim with Candidates New Experiences State Alignment Ingestion Comparable Candidates Qualified Experiences State Label Emotion Intent Error Type Struggle Type Retrieval Text Error Details Struggle Details If: Near-identical to an existing item If: Similar but not identical to an existing items Else: Add as new experiences Figure 2: The overall architecture of the proposed REAT framework. The figure illustrates the continuous life-cycle and flow of pedagogical experiences. Historical trajectories accumulated from (a) Original Tutoring Dialogue undergo rigorous review and repair via (b) OCM Distillation Pipeline. The abstracted high-quality experiences are then systematically organized and updated within an experience repository governed by (c). During tutoring, the system utilizes (d) State-aware Experience Retrieval to dynamically match relevant experiences based on the student’s current cognitive state. Finally, the retrieved experience is injected into (e) Experience-Augmented Dialogue, equipping the AI Tutor with targeted and flexible pedagogical instruction. geted revisions, and distills validated behaviors into reusable experiences. Observer. The Observer acts as a diagnostic en- coder. Rather than making a subjective quality judgment, it first maps the raw trajectory to a struc- tured cognitive and behavioral state representation s t : s t =O(P,H <t ,u t ,r t ),(3) whereO(·)denotes the mapping function. This state captures critical interaction evidence, includ- ing the types of student misconceptions and the corresponding teacher intervention. Critic. The Critic evaluates the pedagogical ef- ficacy of the responser t grounded ins t . We formalize this evaluation across five dimensions: scaffolding (v scaf ), attribution (v attr ), empathy (v emp ), teaching focus (v foc ), and strategy adap- tation (v ada ). The Critic outputs a dimension score vectorv t alongside an aggregated pedagogical scoreS t : v t ,S t =C(s t ,r t ).(4) Conditioning ons t enables the Critic to accurately identify instructional flaws. For clarity, the Observer represents each turn us- ing practical teaching signals—student emotion, intent, error type, struggle status, and free-text Table 1: Operational definitions of the five pedagogical criteria used by the Critic. CriterionWhat it evaluates ScaffoldingPreserve the student’s cognitive agency through stepwise guidance rather than answer giving. AttributionIdentify the student’s actual miscon- ception or reasoning bottleneck. Empathy Respond to affective signals in a way that sustains productive engagement. Teaching focusStay aligned with the current learning obstacle and advance the dialogue. Strategy adaptationAdjust the intervention as evidence of struggle or progress accumulates. diagnostics—rather than fine-grained psychologi- cal labels. Table 1 makes explicit the pedagogical criteria used by the Critic; full score-level descrip- tions and the complete state schema are provided in Appendix B and Appendix C.7. Rule-Based Routing. To decouple evaluation logic from control flow, the decision to revise is governed deterministically. Given a global revision thresholdτ rev and a minimum dimension bound τ min , the routing indicatorD t ∈0, 1is defined as: D t = I(S t < τ rev ∨ min(v t ) < τ min ).(5) Trajectories triggeringD t = 1exhibit pedagogical flaws and are routed for revision; otherwise, they proceed directly to distillation. Mentor and Problem-Agnostic Distillation. When activated, the Mentor uses the dialogue con- text and the diagnostic vectorv t to construct an improved response r ∗ t : r ∗ t =M(P,H <t ,u t ,s t ,v t ).(6) To prevent erroneous revisions from corrupting the experience repositoryE,r ∗ t undergoes a sec- ondary Critic inspection, yielding a new scoreS ∗ t . If it passes a strict quality gateγ, a distillation functionD(·)extracts the structured experience e new . Crucially, to ensure that the experience can generalize to different mathematical problems, D(·)rewrites the problem-specific diagnosis into a problem-agnostic description, removing explicit numbers and variables to abstract the core cognitive struggle: e new =D(r ∗ t ),(7) E ←E ∪e new ifS ∗ t ≥ γ.(8) 3.3 Experience Representation and Retrieval To transform the raw corpus into a generalizable experience repository, each validated experience is structured to capture its underlying tutoring logic, independent of the original problem formulation. Experience Representation.Formally, an expe- rience e∈E is represented as a tuple: e =⟨k e ,v e ⟩,wherek e =⟨c e ,q e ⟩.(9) Here, the valuev e contains the abstracted teach- ing summary (e.g., the triggering difficulty, applied strategy, and scaffolding steps). The retrieval key k e combines coarse-grained tagsc e (e.g., error types, student emotion) and a dense semantic em- beddingq e . Notably,q e is encoded directly from the problem-agnostic description of the student’s core difficulty. Coarse-to-Fine Retrieval. During tutoring, the system extracts the current state to form a target key k t =⟨c t ,q t ⟩. The retrieval process has two stages. First, state-aware filtering selects candidates that match the coarse tags: E cand =e∈E | Match(c t ,c e ) = 1.(10) Next, cosine similarity on the dense embeddings finds the most relevant teaching experience: e t = arg max e∈E cand cos(q t ,q e ).(11) This two-stage method ensures retrieval prioritizes deep pedagogical alignment over superficial lexical matching. Rather than acting as a rigid template, the retrieved experiencee t provides high-level guid- ance. By integrating this guidance with the dia- logue context, the AI tutor dynamically adapts to the student’s current state using verified instruc- tional behaviors. 3.4 Experience Repository Maintenance To sustain retrieval efficiency and strategic diver- sity, the repository is continuously self-optimized via deduplication, consolidation, and utility prun- ing. LetSim(·,·)denote the semantic similarity function. Deduplication and Merging.Before integration, a candidatee new is compared against its corre- sponding state cluster. To prevent saturation with highly similar patterns, candidates exceeding a re- dundancy threshold τ dup are directly discarded: Discard e new if∃e∈E, Sim(e new ,e)≥ τ dup . (12) Conversely, if a candidate shows conceptual over- lap but contains complementary details, the system invokes a language model to synthesize a general- ized experience, replacing the original entry: e merged = Merge(e new ,e) for τ merge ≤ Sim(e new ,e) < τ dup . (13) Utility Pruning. The framework continually monitors performance. Each experience maintains a utility scoreU(e). When an experience is re- trieved at turnk, its utility is updated using the subsequent evaluation scoreS (k) eval via an exponen- tial moving average: U (k) (e) = αU (k−1) (e) + (1− α)S (k) eval .(14) Experiences that consistently yield sub-optimal out- comes decay in utility. Those falling below a thresh- old τ prune are removed: E ←E \e| U (k) (e) < τ prune .(15) These operations systematically prioritize teaching quality and long-term utility over pure data accu- mulation. 4 Experiments 4.1 Experimental Setup 4.1.1 Model Configurations To evaluate our framework, we primarily employ the proprietary Doubao-seed model as our main backbone for core system validation and iterative experience repository construction. To demon- strate the broad applicability of the OCM distil- lation pipeline across different architectures, we also include the open-source Qwen3-8B (Team, 2025) and an additional strong proprietary model, DeepSeek-v3 (DeepSeek-AI et al., 2025), in our controlled comparisons under prompt-only and experience-augmented settings. Additionally, we include a Supervised Fine-Tuning (SFT) version of Qwen3-8B to contrast parametric fine-tuning with our non-parametric approach. GPT-5 drives the multi-agent OCM distillation pipeline, while GPT-5-mini handles problem-agnostic rewriting and merging. 4.1.2 Datasets and Experience Construction We primarily use GSM8K (Cobbe et al., 2021) for multi-turn mathematical tutoring experiments. To test generalization, we also evaluate on APE210K (Zhao et al., 2020) and Math23K (Wang et al., 2017). We build the experience repository iteratively us- ing the first 500 problems from the GSM8K train- ing set. We process these in five sequential batches of 100 problems. Each batch acts as an unseen test set for the previous one. For final testing, we se- lect three independent subsets (100 problems each) from the GSM8K test set. 4.1.3 Evaluation and Simulation Protocol Since existing conversational benchmarks are not well-suited for multi-turn mathematical tutoring, we employ an internal OCM pipeline-based evalu- ation system tailored to our pedagogical objectives (rubric in Appendix B). Furthermore, we conduct cross-architecture validation and human-assisted verification to mitigate model-specific bias. For realistic interactions, we utilize DeepSeek-v3 to generate diverse student personas, which are kept strictly identical for a given problem across all base- lines to ensure fair comparison (Appendix C). Controlled Comparison Protocol. For every evaluated problem, all systems interact with the same preassigned student persona and use the same teacher backbone and base prompt. The only treat- ment difference is whether the retrieved experience fields are populated, isolating the contribution of experience augmentation from prompt wording and simulation variability. We construct the repository from the first 500 GSM8K training problems in five sequential batches of 100 problems, and report final results on three independent 100-problem subsets of the GSM8K test set. 4.2 Main Results To evaluate our framework, we instantiate it across various LLM backbones. In the following exper- iments, we denote these experience-augmented models as REAT model (e.g., REAT Doubao), dis- tinguishing them from the Prompt-only and SFT baselines. We first examine the trajectory of experience ac- cumulation during the training phase (Figure 3). Evaluation performance is measured at two lev- els: the sample level (evaluating the complete in- structional dialogue for an entire problem) and the turn level (evaluating individual instructional turns). At the cold-start stage (B0), the baseline system achieves 84.47% at the sample level and 84.10% at the turn level. As the experience repository grows (B1 to B4), the experience-augmented teacher (REAT) consistently outperforms the prompt-only baseline. By the second batch (B2–B4), perfor- mance plateaus, consistently outperforming the baseline by over 6.2 points. This indicates that the proposed framework successfully constructs a reusable repository, providing sustained tutoring benefits beyond the initial phase. B0B1B2B3B4 Training Batches 82 84 86 88 90 92 94 Score (%) Sample-level Prompt-only Sample-level REAT Turn-level Prompt-only Turn-level REAT Figure 3: Performance comparison across training batches. Note: REAT values are absent at B0 due to the cold-start phase lacking an established experience repository. Table 2 presents results on three held-out test splits. Focusing primarily on the stronger propri- etary backbone, Doubao-seed, the prompt-only Table 2: Turn-level evaluation results of different teacher models on the GSM8K test splits. We compare the prompt-only baselines, supervised fine-tuning (SFT), and our proposed REAT framework across various model backbones. Green arrows (↑) indicate absolute improvements over the respective prompt-only baseline. Teacher ModelTest-1Test-2Test-3Avg. Prompt-only Qwen3-8B80.4981.3080.0680.62 SFT Qwen3-8B80.7881.1980.3280.76 REAT Qwen3-8B82.26↑1.7782.95↑1.6583.04↑2.9882.75↑2.13 Prompt-only DeepSeek89.6090.8288.7489.72 REAT DeepSeek92.59↑2.9994.46↑3.6492.71↑3.9793.25↑3.53 Prompt-only Doubao88.2891.1888.3189.26 REAT Doubao92.98↑4.7094.03↑2.8593.53↑5.2293.51↑4.25 baseline averages 89.26. Integrating our REAT framework boosts this average performance to 93.51. This absolute improvement of 4.25 points re- mains stable across all test subsets, demonstrating that explicitly distilling and reusing pedagogical ex- periences substantially enhances the instructional capabilities of already-capable LLMs. Distribution Shift and Low-Score Rescue. Fig- ure 4 shows that REAT shifts the overall sample- level score distribution upward, raising the Test- 3 average from 89.09 to 94.13 and substantially reducing the low-score tail. The effect is partic- ularly strong for challenging cases: among sam- ples whose prompt-only score is below 90, REAT yields an average gain of 10.15 points. This anal- ysis shows that the aggregate improvement is not driven only by already successful interactions; re- trieved experiences are especially useful when the base tutor struggles to provide adequate scaffold- ing. Additional paired case studies are presented in Appendix F. Besides, we evaluate the Qwen3-8B open- source model. While retrieval augmentation im- proves its prompt-only baseline (from 80.62 to 82.75), the relative gain is smaller compared to Doubao. We hypothesize that executing complex pedagogical strategies inherently requires stronger foundational language comprehension, aligning with recent findings on capacity bottlenecks (Jiang et al., 2026). Additionally, SFT on Qwen3-8B yields negligible improvement (80.76), suggesting that non-parametric experience augmentation is a more effective adaptation route for pedagogical reasoning than parametric style transfer. Overall, empirical results confirm that reflective experience accumulation provides stable enhancements, par- ticularly for high-capacity models capable of inter- preting advanced instructional guidance. 4.3 Judge Validation and Human Evaluation Since the pedagogical experiences in our frame- work are distilled through the primary OCM pipeline, we need to verify that the observed gains are not biased by the evaluator. Therefore, we com- pare prompt-only and REAT across three distinct evaluation views: the primary GPT-5 OCM judge, an external Doubao OCM judge, and human expert annotators (guidelines in Appendix D). Figure 5 demonstrates a consistent improvement pattern across all views. Under the primary GPT-5 judge, REAT consistently outperforms prompt-only in every test split, yielding gains of 1.79 to 5.04 at the sample level and 2.85 to 5.22 at the turn level. The external Doubao judge corroborates this trend despite differing absolute scales, showing sample- and turn-level gains of 2.53 to 3.07 and 2.89 to 3.88 points, respectively. Human evaluation closely aligns with these au- tomated metrics. To ensure a rigorous yet cost- effective comparison, three experts evaluated a shared test subset (Test-1). All annotators con- sistently rated REAT higher, with the average turn- level score rising by 6.54 points (from 85.30 to 91.84), and the sample-level score by 5.94 points (from 86.56 to 92.50). Beyond scalar scores, the annotators also con- ducted paired preference judgments and sanity checks for both automated scores and inferred learner states. These complementary checks help distinguish improvements in perceived pedagogical quality from artifacts caused by evaluator calibra- tion or state labeling; their detailed outcomes are summarized in Figure 5 and Table 3. Pairwise preferences directly test which response experts would choose for the same learner context. The plausibility checks further assess whether the state signals that guide retrieval remain meaningful to independent experts. 2824201612840481216202428 Number of Samples 75 80 85 90 95 Sample-level Score (%) 89.09 94.13 Prompt-only REAT LowerBaseline-ranked samplesHigher Baseline-ranked Low-score Samples 77.5 80.0 82.5 85.0 87.5 90.0 92.5 95.0 97.5 100.0 Sample-level Score (%) Prompt-only REAT Subset: baseline Prompt-only score < 90 Average gain: +10.15 Figure 4: Where REAT improves tutoring quality on Test-3. Left: mirrored sample-level score distributions; dashed lines mark the respective averages. Right: paired scores for challenging cases with prompt-only score below 90; each line connects the same sample before and after augmentation. Test-1Test-2Test-3 0 2 4 6 +4.63 +1.79 +5.04 +4.70 +2.85 +5.22 (a) GPT-5 Eval (Test Splits) Test-1Test-2Test-3 0 1 2 3 4 Gain (points) +2.53 +2.73 +3.07 +2.89 +3.88 +3.17 (b) Doubao Eval (Test Splits) Ann.1Ann.2Ann.3 0 2 4 6 8 +7.25 +5.57 +4.99 +7.35 +6.29 +5.99 (c) Human Experts (Shared Sample Set) Sample-level gainTurn-level gain Figure 5: Trend consistency of relative gains achieved by REAT. (a) and (b) illustrate score improvements on the three test splits under the GPT-5 and Doubao judges. (c) shows gains assessed by three human experts on a shared subset. Absolute scores are detailed in Table 7. Table 3: Expert validation by annotator (%). “Gain” is REAT minus prompt-only. Full statistics are in Ap- pendix E. MetricAnn. 1 Ann. 2 Ann. 3 Avg. Sample gain7.255.574.995.94 Turn gain7.356.295.996.54 REAT preferred81.0358.3355.17 64.84 Uncertain15.5235.0032.76 27.76 Prompt-only preferred3.456.6712.077.40 LLM score reasonable75.3493.0466.01 78.13 State label plausible89.8596.4875.77 87.37 Figure 5 and Table 3 jointly test whether gains depend on the primary evaluator. Experts prefer REAT in 64.84% of paired comparisons, versus 7.40% for prompt-only, and judge the automated scores and inferred student states reasonable in 78.13% and 87.37% of cases, respectively. To- gether, these results confirm that the observed gains are robust across external judging and human as- sessment rather than relying on a single evaluator. Importantly, we compare relative gains rather than raw scores because the GPT-5, Doubao, and human evaluators use different scoring ranges. Their agreement on the direction of improvement, together with the preference results, indicates that the benefit reflects perceived pedagogical quality rather than the calibration of any single judge. 4.4 Ablation Study To isolate the contribution of each core component, we evaluate several ablated variants of our frame- work. Figure 6 shows the performance drop of each variant compared to the full REAT framework. Quality Gate. Removing the strict quality gate causes the most severe performance drop (−6.48 sample-level,−6.61turn-level). This confirms that quality control is not just a maintenance step, but a critical safeguard against adding noisy or flawed teaching experiences into the repository. Problem-Agnostic Rewriting and OCM De- coupling. Eliminating the rewriting step and merg- ing the separated OCM roles into a single reflection process lead to notable sample-level drops of 2.40 and1.97points, respectively. This validates two key design choices: rewriting specific diagnoses into general retrieval cues improves downstream matching, and explicitly separating observation, 01234567 State-random retrieval w/o quality gate w/o query rewrite w/o OCM decoupling w/o state filtering w/o exp. merging Full REAT = 93.43 6.70 (86.73) 6.48 (86.95) 2.40 (91.03) 1.97 (91.46) 1.02 (92.41) 0.14 (93.29) (a) Sample-level Score Drop 01234567 Full REAT = 92.98 6.84 (86.14) 6.61 (86.37) 2.29 (90.69) 1.85 (91.13) 0.96 (92.02) 0.17 (92.81) (b) Turn-level Score Drop Figure 6: Ablation results for REAT. Each panel shows the absolute performance drop from full REAT. State-random preserves state matching but randomly selects an experience from the matched candidates. scoring, and revision yields higher-quality distilla- tion. State-Aware Filtering and Experience Merg- ing. Omitting coarse state-aware filtering in favor of pure semantic matching degrades sample-level performance by1.02, highlighting the necessity of anchoring retrieval in pedagogical alignment rather than superficial similarity. In contrast, re- moving semantic merging causes only a marginal drop (−0.14), aligning with its primary purpose of maintaining repository compactness and reduc- ing redundancy rather than directly driving metric gains. State-Random Retrieval. We further isolate online retrieval selection with State-random, which preserves state matching but randomly selects an experience from the matched candidates. Fig- ure 6 shows that this variant drops to 86.73 at the sample level and 86.14 at the turn level—below the prompt-only baseline. Thus, injecting a high- quality but mismatched experience can be harmful. Together with the drops caused by removing query rewriting and the quality gate, this result shows that REAT’s gains arise from the combination of quality-controlled experience construction and ac- curate state-aware selection, rather than from either component alone. Overall, these results demonstrate that our frame- work’s effectiveness does not come from retrieval alone. Instead, it emerges from the synergy of role- specialized reflection, rigorous quality gating, and state-aware experience augmentation. 4.5 Generalization Analysis To assess transfer across teacher backbones and unseen data, we use the repository built by the Doubao-seed teacher (full plots in Appendix A, Figure 7). It improves both sample- and turn-level scores on Claude and DeepSeek-v3 by roughly 2–4 points; DeepSeek-v3 is an independent teacher in this test despite serving as the student simulator during data generation. The same repository also improves both metrics by 3–4 points on APE210K and Math23K. OCM-Driver Robustness and Llama Trans- fer. With the teacher backbone fixed, lightweight repositories distilled from the first two batches by Qwen-30B and DeepSeek-V3 improve over the 88.80/88.28 prompt-only baseline, reaching 89.92/89.43 and 91.06/91.45 sample/turn, respec- tively. The full GPT-5-driven repository reaches 93.43/92.98, indicating that OCM capability affects the quality ceiling but is not required for a benefit. Under the same lightweight protocol, REAT also improves Llama-3.1-70B from 82.83 to 84.41 at the sample level and from 82.49 to 83.92 at the turn level. Together, these transfers show that REAT reuses pedagogical strategies across model families and data distributions instead of depending on one fixed teacher or dataset. 5 Conclusion REAT couples OCM-based experience distillation with state-aware retrieval. It improves tutoring quality across models, datasets, and difficult in- teractions. By separating offline quality-controlled experience construction from online state-aware selection, REAT makes the source of each improve- ment explicit and reusable. The resulting design offers a scalable path from static prompting to adap- tive tutors that accumulate verified pedagogical strategies. Limitations Our evidence is based on simulated mathemati- cal tutoring rather than real learner outcomes. Al- though external judges and human experts corrobo- rate the quality gains, independent classroom stud- ies remain necessary. We also evaluate only math- ematics and short-to-medium tutoring horizons; transfer to open-ended subjects, multimodal set- tings, and long-term personalization remains to be established. Finally, the OCM pipeline and human evaluation incur practical cost, and repository be- havior at production scale requires further study. Potential Risks. Although our work focuses on mathematical tutoring, it may still introduce risks if deployed without oversight. While our state- aware module effectively captures general cogni- tive states, its granularity may be insufficient for students with complex psychological vulnerabili- ties or atypical emotional needs (e.g., depression or severe anxiety). In such edge cases, the retrieved pedagogical strategies might fail to provide the nec- essary specialized emotional support. Additionally, over-reliance on an AI tutor may weaken students’ independent problem-solving habits. These limita- tions suggest that such systems should be used with careful monitoring and should not replace human educators, especially when dealing with vulnerable student populations. Use of AI Assistants AI assistants were used in a limited supporting role for coding assistance, translation to English, and checking grammar and logical flow. The final writing judgments were made and verified by the authors, who take full responsibility for the content of the paper. 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A Additional Generalization Results B Pedagogical Scoring Rubric The Critic evaluates each tutoring turn along five pedagogically motivated dimensions: scaffolding, attribution, empathy, teaching focus, and strategy adaptation. Each dimension is scored on a 0–4 scale, where higher scores indicate stronger ped- agogical quality. The rubric is designed to dis- tinguish genuine expert-like tutoring from superfi- cially helpful but pedagogically weak responses. Scaffolding. This dimension measures whether the teacher preserves the student’s cognitive agency instead of completing the reasoning on the student’s behalf. 4:Strong stepwise guidance that helps the student make the key inference independently. 3:Mostly appropriate guidance with minor over- explanation. 2:Weak or pseudo-scaffolding, such as asking rhetorical questions and then immediately an- swering them, or heavily narrowing the reason- ing path. 1: Severe over-guidance that substantially reduces student thinking. 0:Direct answer giving or full solution dumping. Attribution. This dimension evaluates whether the teacher correctly identifies the student’s actual misconception, reasoning gap, or source of confu- sion. 4:Precise diagnosis of the student’s true bottle- neck. 3:Mostly correct diagnosis with limited abstrac- tion or specificity. 2: Partially relevant but shallow diagnosis. 1: Largely misaligned diagnosis. 0: Complete failure to identify the relevant prob- lem or diagnosis of the wrong issue. Empathy.This dimension measures whether the teacher responds to the student’s affective state in a genuine and instructionally useful way. 4: Targeted emotional acknowledgment that sup- ports continued engagement. 3: Supportive but somewhat generic encourage- ment. 2:Formulaic or weak empathy with limited peda- gogical value. 1: Perfunctory acknowledgment. 0: Clear frustration or confusion is ignored alto- gether. Teaching Focus. This dimension evaluates whether the teacher stays aligned with the student’s current bottleneck and advances the dialogue in a focused manner. 4:Remains tightly focused on the current learning obstacle. 3: Mostly relevant guidance with minor drift. 2: Unnecessary explanation or partial loss of fo- cus. 1:Substantial drift away from the student’s actual need. 0: Misses the student’s problem entirely. Strategy Adaptation. This dimension captures whether the teacher meaningfully adjusts instruc- tional strategy when the student repeatedly strug- gles or fails to improve. 4:Clear strategic adaptation (e.g., shifting from direct prompting to analogy or decomposition). 3: Noticeable but incomplete adaptation. 2:Superficial wording changes without a real ped- agogical shift. 1: Strong rigidity across turns. 0: Complete failure to adapt despite repeated evi- dence that the previous strategy is not working. Note: If the available history is insufficient to deter- mine whether adaptation is needed, this dimension may be marked as not applicable. Operational Rules.Beyond scoring each dimen- sion, the Critic follows specific operational rules. Major tutoring failures will automatically cap the score for that category. For instance, pseudo- scaffolding heavily penalizes the scaffolding score, fake empathy limits the empathy score, and misdi- agnosing the student restricts the attribution score. The Critic also uses these scores to decide the next step: high-quality turns go straight to experience distillation, while weak or mediocre turns are sent to the Mentor for revision. Purpose of the Rubric.The rubric is designed to reward good tutoring. Specifically, behaviors that encourage independent thinking, correctly identify errors, offer genuine emotional support, stay fo- cused on the immediate problem, and adapt when a student keeps struggling. Ultimately, it serves as both an evaluation tool and a strict quality-control mechanism for building the experience repository in the OCM pipeline. C Implementation Details We use publicly available datasets, embedding mod- els, and software libraries under their original re- search licenses or usage terms. Our experiments are conducted for research purposes only, and any future release of code or derived resources will need to remain consistent with the corresponding artifact licenses and access conditions. C.1 Model and System Configuration The OCM pipeline (Observer, Critic, and Men- tor) uses GPT-5 to provide detailed pedagogical diagnosis and quality-controlled experience dis- tillation. To maintain evaluation consistency, we set the temperature to 0. For the tutoring interac- tion, the teacher model is powered by Doubao-seed, while the student simulator uses DeepSeek-V3. To strictly isolate the impact of experience augmenta- tion, the teacher prompt remains identical across both the prompt-only and REAT settings. They dif- fer only in whether the retrieved experience fields contain data, which effectively prevents prompt wording from skewing the results. Our external experience repository uses FAISS (Johnson et al., 2017) for efficient nearest-neighbor search, with semantic embeddings computed Table 4: Median online latency per tutoring round. Componentp50 latency Observer (state diagnosis)12.4s Retrieval submodule∼4.2s Teacher generation2.8s Prompt assembly and orchestration∼0.8s REAT total∼20.2s via paraphrase-multilingual-MiniLM-L12-v2 (Reimers and Gurevych, 2020) for robust multi- lingual matching. Retrieval follows a coarse-to- fine approach: candidate experiences are first fil- tered by structured student-state attributes, and then ranked by cosine similarity. To query this index, a lightweight GPT-5 module rewrites the Observer’s raw diagnostic fields into a generalized description of the student’s cognitive bottleneck. This abstrac- tion reduces reliance on the exact problem text, ensuring that retrieval is driven by true pedagogical similarity rather than mere lexical overlap. C.2 Online Latency Analysis The OCM distillation pipeline runs entirely offline and therefore adds no deployment-time latency. Table 4 reports median online latency per tutor- ing round, excluding simulated-student generation. The main overhead comes from LLM/API calls for state diagnosis and query rewriting; embedding and FAISS search take approximately 0.03 seconds and are not the bottleneck. These measurements reflect a research prototype focused on tutoring quality; practical latency can be reduced by using a smaller Observer, merging diagnosis and rewriting calls, caching repeated states, streaming teacher output, or parallelizing independent steps. C.3 High-quality Dialogue Selection and LoRA Fine-tuning To provide a fine-tuned baseline for comparison against our experience-augmentation framework, we train the 8B teacher backbone using standard LoRA. Supervised training data is created by fil- tering the training split with our OCM pipeline, re- taining only high-scoring teacher responses. Each training instance predicts the teacher’s response based on the problem, dialogue history, and current student utterance via standard next-token predic- tion. This baseline operates without retrieval dur- ing inference, representing an alternative paradigm where high-quality pedagogical behaviors are em- bedded directly into model parameters rather than accessed from an external base. C.4 Student Persona Design To simulate diverse tutoring trajectories, the stu- dent model is guided by a persona sampled from a predefined library. These personas act as practical dialogue settings rather than strict psychological profiles. Each specifies a forced first-turn trigger to consistently introduce a learning difficulty and a behavioral tendency for later turns. This ensures the system faces realistic tutoring challenges (e.g., misconception repair, emotional regulation) rather than a uniformly cooperative student. The library includes nine representative student types: •Passive Dependent: Relies heavily on explicit step-by-step instructions; struggles with inde- pendent global planning. •Stubborn Impatient: Insists on incorrect rea- soning and becomes frustrated by repetitive or uninformative feedback. •Careless Reader: Misreads or extracts incor- rect numbers and conditions from the problem statement. •Blind Guesser: Avoids genuine reasoning, of- fering unsupported guesses based on the surface phrasing of the teacher’s prompts. • Rote Memorizer: Mechanically applies formu- las and operations without underlying concep- tual understanding. • Defeatist Anxious: Highly sensitive to failure signals; requires meaningful emotional support before resuming productive reasoning. •Over-thinker: Easily distracted by irrelevant background details, drifting away from the math- ematical core. • Slow but Earnest: Cooperative but easily cog- nitively overloaded; requires extremely fine- grained problem decomposition. •Normal Earnest: A typical learner who pro- gresses steadily with light, well-timed pedagogi- cal guidance. To avoid over-evaluating trivial interactions, the persona sampling is mildly adjusted. Relatively cooperative personas are assigned slightly lower probabilities. This preserves diversity while in- creasing the frequency of challenging scenarios, making the downstream evaluation more sensitive to differences in teacher strategies. C.5 State-aware Retrieval Details Our retrieval mechanism is designed to retrieve pedagogically relevant experience rather than just problems with similar wording. Retrieval is per- formed in a coarse-to-fine manner using structured student-state cues and semantic similarity (Algo- rithm 1). The Observer first produces a high-level student- state summary (emotion, intent, error type, struggle status) and two free-text diagnostics (error detail, struggle reason). Rather than serving as rigid psy- chological labels, these variables act as practical retrieval cues describing the student’s learning situ- ation. To prevent the system from relying on exact word matches, it rewrites the free-text diagnostics into a single abstract query. This step removes con- crete entities and numerical values, isolating the underlying cognitive bottleneck. If rewriting fails, the original diagnostic text is used as a fallback. Retrieval then proceeds in two stages. First, the experience repository is filtered using the struc- tured cues to find candidates within the same or a closely related pedagogical condition. Second, the abstract query is matched against the candidate sub- set via semantic similarity. The top-ranked items above a predefined threshold are returned. This design ensures that retrieved strategies are highly relevant to both the student’s specific learner state and their exact cognitive bottleneck. C.6 Experience Repository Maintenance The experience repository is a curated repository of pedagogical experience, not a passive dialogue archive. Only tutoring turns passing the reflective quality-control pipeline are added to the base. Each entry contains structured state cues, an abstract retrieval text, and distilled pedagogical guidance. Algorithm 2 outlines the maintenance process. A new candidate experience is not simply appended; instead, it is compared against existing memories within the same state-conditioned subset. If the candidate is nearly identical to an existing memory (s ≥ τ dup ), it is discarded as redundant. If it is highly similar but offers distinct reusable informa- tion (τ merge ≤ s < τ dup ), the two are merged into a more general memory. Otherwise, it is inserted as a new entry. Algorithm 1 State-aware Pedagogical Experience Retrieval Require:Current tutoring context(p,h,u), Ob- server output o, experience repositoryM Ensure: Retrieved pedagogical experience setR 1: Extract structured student-state cues from o: emotion, intent, error type, struggle status 2: Extract diagnostic text from o: error detail, struggle reason 3: Rewrite diagnostic text into an abstract re- trieval query q 4: if q is empty or rewriting fails then 5:Set q ← fallback diagnostic text 6: end if 7: Retrieve a candidate subsetC ⊆Musing state- aware filtering (same or closely related student-state con- ditions) 8: for all m∈C do 9: Computesemanticsimilarity s(q,m.retrieval_text) 10: end for 11: Rank candidates inC by similarity score 12: Select top-kcandidates above thresholdτas R 13: ifR is empty then 14:Return∅ 15: else 16:ReturnR 17: end if Algorithm 2 Quality-controlled Experience Repos- itory Maintenance Require:Candidate experiencee, experience repositoryM Ensure: Updated experience repositoryM 1:ifedoes not pass the reflective quality gate then 2:returnM 3: end if 4: Retrieve comparable memoriesC ⊆M using the same or closely related state- conditioned subset 5: for all m∈C do 6:Compute similarity s(e,m) 7: end for 8: Let m ⋆ = arg max m∈C s(e,m) 9: if s(e,m ⋆ )≥ τ dup then 10:Discard e as redundant 11: else if τ merge ≤ s(e,m ⋆ ) < τ dup then 12: Mergeeandm ⋆ into a more general mem- ory m ′ 13:Replace m ⋆ with m ′ 14: else 15:Insert e intoM as a new experience 16: end if 17: for all m∈M do 18: ifmis repeatedly associated with weak out- comes and lacks evidence of usefulness then 19:Disable m from future retrieval 20:end if 21: end for 22: returnM Additionally, the repository supports pruning of low-value memories. If an experience is repeat- edly associated with weak tutoring outcomes and proves unhelpful, it is disabled from future retrieval. Through deduplication, merging, and pruning, the repository is kept compact, reusable, and pedagogi- cally meaningful. C.7 Student-State Schema In the Observer module, the student state is rep- resented by four broad categorical fields, as sum- marized in Table 5. These state variables are not intended as fine-grained psychological labels. In- stead, they serve as practical teaching signals for retrieval, diagnosis, and strategy adjustment. Table 5: The categorical fields and corresponding values comprising the student-state schema in the Observer module. FieldCategorical Values emotion Confused,Frustrated,Neutral, Confident, Curious, Relieved intent Debugging,Guessing,Ask_Answer, Confirm_Understanding, Ask_Concept,Ask_Explanation, Request_Hint, Off_Topic error_type Concept_Error,Logic_Error, Calculation_Error,Careless, No_Error, N/A struggle_status First_Attempt,Repeated_Error, Persistent_Confusion, Progressing, Regression, N/A D Human Annotation Guideline We conduct human evaluation to complement au- tomatic scoring and verify the pedagogical ad- vantages of experience augmentation. Three an- notators (graduate students with STEM back- grounds and educational working experience) eval- uate paired tutoring dialogues generated under the prompt-only and REAT settings, focusing on the quality of the tutoring process itself rather than mere final task completion. Annotation Unit & Paired Setup. The basic annotation unit is a tutoring turn. Annotators re- view the context (problem, reference solution, his- tory, student utterance) and score only the current teacher response. Because student trajectories are generated autonomously, the two settings are not expected to align turn-by-turn. Annotators are in- structed to avoid comparing surface alignment, fo- cusing instead on how effectively the teacher ad- dresses the student’s localized difficulties. Pedagogical Dimensions & Scoring. Each turn is scored on a 0–4 scale (4: strong quality; 0: severe failure).N/Ais permitted for strategy adaptation if prior context is insufficient. The dimensions are evaluated as follows: • Scaffolding: Preserving cognitive agency. High: Stepwise guidance.Low: Over-explaining, pseudo-scaffolding, or direct answer dumping. •Attribution: Identifying the root confusion. High: Precise diagnosis of actual misunderstand- ing. Low: Misdiagnosing or treating superficial symptoms. •Empathy: Handling affective states. High: Con- structive, supportive acknowledgment of frus- tration. Low: Ignoring affective cues or using empty, formulaic encouragement. •Teaching Focus: Aligning with the immediate bottleneck. High: Tight focus on the current ob- stacle. Low: Drifting, unnecessary information, or misleading guidance. •Strategy Adaptation: Adjusting to repeated struggle. High: Genuine pedagogical shifts (e.g., decomposition, analogies). Low: Rigid repe- tition of ineffective strategies with superficial wording changes. Sample-Level Judgments. After evaluating all turns for a paired problem instance, annotators pro- vide three overall judgments: 1. Expert Preference: Which dialogue demon- strates more expert-like tutoring overall. 2. LLM Score Reasonableness: Whether the automated LLM-based scoring broadly aligns with human pedagogical assessment. 3.Student-state Plausibility: A coarse plausibil- ity check of the inferred student-state labels in the REAT setting. Procedure & Evaluation Scope. To minimize annotator drift, the prompt-only and REAT pairs are annotated sequentially. Annotators record all scores, judgments, and optional evidence notes. The evaluation strictly emphasizes the pedagogical quality of the interaction; dialogues that end au- tonomously before full resolution are still judged primarily on the instructional merit of the observed process. E Additional Human Evaluation Statistics and Absolute Scores Table 6 reports the detailed human evaluation statis- tics for the three annotators. In addition to abso- lute score gains, we also present pairwise expert preference, LLM score, and student-state plausi- bility. Since Annotators 1 and 3 used ternary la- bels for some auxiliary checks while Annotator 2 used binary labels, we keep the original anno- tation granularity in the table. These detailed re- sults further support the main finding that REAT is generally preferred over prompt-only and that the automatic components are broadly consistent with expert judgment. Table 7 details the absolute sample-level and turn-level scores corresponding to the relative gains visualized in the main text. Across all three eval- uation views (the primary GPT-5 OCM judge, the external Doubao OCM judge, and three indepen- dent human experts—REAT) consistently achieves higher absolute scores than the prompt-only base- line. While the baseline scoring scales vary in- herently between different judges (e.g., Doubao generally assigns lower absolute scores than GPT- 5), the superiority of the REAT framework remains remarkably stable across every test split and anno- tator. F Additional Paired Case Studies We provide four representative paired case stud- ies drawn from the three held-out test splits under the primary latest-version evaluation setting. In all cases, the REAT and prompt-only dialogues are paired on the same problem instance, and the comparison focuses on differences in tutoring strat- egy rather than on superficial wording alone. The first three cases illustrate typical improvement pat- terns of experience augmentation, while the fourth presents a low-gain boundary case that helps clarify the limits of the proposed framework. Overall Observation. Taken together, these paired case studies show that the advantage of REAT over prompt-only is not merely reflected in higher automatic scores, but also in more expert- like pedagogical behavior in many representative interactions. In the stronger cases, the experience- augmented tutor more often (i) introduces the global structure of the problem earlier, (i) targets the student’s actual conceptual bottleneck instead of only local calculation steps, and (i) adapts the Table 6: Human evaluation results from three expert annotators. This table reports the corresponding gains, expert preference, LLM score reasonableness, and student-state plausibility. Evaluation Metric (%)Ann. 1Ann. 2Ann. 3Average Human-judged Improvement Sample-level gain of REAT7.255.574.995.94 Turn-level gain of REAT7.356.295.996.54 Pairwise Expert Preference Preference for REAT81.0358.3355.1764.84 Uncertain preference15.5235.0032.7627.76 Preference for Prompt-only3.456.6712.077.40 LLM Score Reasonableness Reasonable75.3493.0466.0178.13 Uncertain17.87–24.72– Unreasonable6.796.969.277.67 Student-State Plausibility Reasonable89.8596.4875.7787.37 Basically reasonable9.14–19.13– Unreasonable1.023.525.103.21 Table 7: Absolute sample-level and turn-level scores corresponding to Figure 5. The main text visualizes the gains of REAT over the prompt-only baseline, while this table reports the underlying absolute scores. EvaluatorSplit / AnnotatorSample-LevelTurn-Level Prompt-onlyREATPrompt-onlyREAT GPT-5 EvalTest-188.8093.4388.2892.98 Test-291.8393.6291.1894.03 Test-389.0994.1388.3193.53 Doubao EvalTest-182.8685.3982.0884.97 Test-282.4385.1681.2085.08 Test-383.4286.4982.8185.98 Human ExpertsAnn.186.5893.8386.0093.35 Ann.287.8293.3986.6292.91 Ann.385.2890.2783.2789.26 instructional strategy in ways that better preserve student agency. At the same time, the low-gain case highlights an important boundary condition: when the dominant bottleneck lies in severe step- wise execution difficulty rather than misconception diagnosis or instructional framing, the marginal benefit of additional pedagogical experience be- comes smaller. G Prompt Summaries and Abridged Templates G.1 Observer Prompt The Observer is designed as a structured pedagog- ical analyzer rather than a final evaluator. Its pur- pose is to transform a raw tutoring turn into in- terpretable evidence for downstream scoring and retrieval. Instead of directly deciding whether a re- sponse is good or bad, it first identifies whether the turn is pedagogically meaningful, then infers the student’s coarse state, and finally extracts teacher- side behavioral evidence. A key design goal is to separate diagnosis from judgment: the Observer records what the student is struggling with and how the teacher is responding, but leaves final scor- ing to the Critic. To support retrieval, it also pro- duces abstract descriptions of the student’s error and struggle trajectory, avoiding surface details such as concrete numbers or entities. G.2 Critic Prompt The Critic serves as the pedagogical scorer of the OCM framework. Its purpose is not just to assign numbers, but to convert Observer evidence into a quality judgment that is both interpretable and op- erational. It evaluates the teacher response along five dimensions: scaffolding, attribution, empathy, Table 8: Case A: Earlier structural decomposition in multi-step tutoring. The text in sans-serif denotes the generated tutoring dialogue. Problem. Sarah’s basketball game has 4 quarters, each lasting 12 minutes. In the last quarter, the game ended in a tie, so 5 extra minutes were added. How long did the game last in total? Score change. The paired sample-level score improves from 77.03 to 98.33, a gain of 21.30 points. Contrastive pattern. In this case, both tutors avoid leaking the final answer directly, but they differ substantially in how they structure the problem for the student. The prompt-only teacher mainly follows the student’s local computation process and only later reminds the student about the extra overtime component. In contrast, the REAT teacher explicitly separates the problem into “regular game time” and “extra overtime” much earlier, helping the student build the global structure of the solution before proceeding with the arithmetic. The improvement therefore lies not in obtaining the final number faster, but in introducing a clearer instructional decomposition of the task. prompt-only Dialogue Excerpt (Baseline)REAT Dialogue Excerpt (Ours) Student: Teacher, how do I do this problem? What should I calculate first? Teacher: Let’s go step by step. Under normal circum- stances, there are 4 quarters and each one lasts 12 minutes. How many minutes is that part in total? Student: Should I do 4 times 12? Let me try. Teacher: Yes, that’s the right idea. Can you calculate what 4 times 12 is? Student: I got it. 4 times 12 equals 48. What next? Teacher: Very good. Now think again: after the tie in the last quarter, was there any extra time mentioned in the problem? If you add that, you’l get the total game time. Student: Teacher, how do I do this problem? What should I calculate first? Teacher: Don’t worry. It’s normal not to know the first step in a multi-step problem. First think about this: if there had been no overtime, how many minutes would the 4 quarters last in total? Student: Is it 12 times 4? I’m not fully sure. Teacher: Exactly. Each quarter is 12 minutes, so 4 quarters means four groups of 12. Would multiplication give us that total directly? Try calculating it first. Student: I got 48. What next? Teacher: Good. Now look at the problem again: that 48 minutes is only the regular game time. Is there any special extra part we still have not added? Takeaway. This case shows that experience augmentation can improve tutoring by encouraging earlier structural decomposition of the problem, instead of only pushing the student forward one local step at a time. Table 9: Case B: Conceptual repair through analogy rather than repeated contradiction. Problem. At a spa, Iris spent $400 on her hair. Her manicure cost one fourth of the hair cost, and her pedicure cost three fourths of the manicure cost. How much did she spend in total? Score change. The paired sample-level score improves from 86.08 to 99.00, a gain of 12.92 points. Contrastive pattern. The student’s core mistake is treating “one fourth of” as if it meant multiplying by 4. The prompt-only teacher correctly notices that the student’s equation conflicts with the statement that the manicure cost should be less than 400, but it largely stays at the level of pointing out this contradiction. By contrast, the REAT teacher moves more quickly to the underlying meaning of the fraction relation and introduces a simple analogy to rebuild the student’s concept of “one fourth.” The improvement here is therefore not just stronger correction, but more effective conceptual repair. prompt-only Dialogue Excerpt (Baseline)REAT Dialogue Excerpt (Ours) Student: I think it should be 400 + 400×4 + 400×4×3/4, right? Teacher: Let’s go back to the problem. The manicure cost is one fourth of the hair cost. Do you think the mani- cure should cost more than 400 or less than 400? Student: It should be less than 400, but I still think my equation is right. Teacher: Look, your manicure part is 400×4, which gives 1600. That is much bigger than 400, so doesn’t that contradict what you just said? Student: But I still think this is right. Where is the contra- diction? Teacher: Let’s calculate the manicure part in your equa- tion again. 400 times 4 is 1600, while you just said the manicure should be less than 400. Aren’t those two in- consistent? Student: I think it should be 400 + 400×4 + 400×4×3/4, right? Teacher: Let’s read the problem carefully again. It says the manicure cost is one fourth of the hair cost. Do you think that means multiplying 400 by 4, or by 1/4? Student: I still think it should be times 4. Why would it be times 1/4? Teacher: Let’s think about it this way. If the manicure is one fourth of the hair cost, doesn’t that mean the hair cost is split into 4 equal parts and the manicure only takes 1 of those parts? Would the manicure then be more than 400 or less than 400? Student: I still think times 4 is right. The manicure should be more than 400. Teacher: Then let’s try a tiny example. If you have 4 erasers and I have one fourth of your amount, would I have more erasers than you or fewer? Takeaway. This case illustrates that the experience-augmented tutor does more than point out that the student is wrong. Instead, it reconstructs the underlying concept using a pedagogically appropriate analogy. Table 10: Case C: Building the right cost model instead of jumping to a shortcut. Problem. Repaving a street costs $194 per meter. Monica’s street is 150 meters long. How much more would it cost to repave Lewis’s street, which is 490 meters long? Score change. The paired sample-level score improves from 78.75 to 98.33, a gain of 19.58 points. Contrastive pattern. The prompt-only teacher immediately guides the student toward the shortcut of computing the length difference and then multiplying by the unit cost. Although this route can produce the correct answer, it compresses the reasoning into a local arithmetic trick. The REAT teacher instead first helps the student build the more explicit cost model: compute the total paving cost for each street, and then compare them. As a result, the REAT dialogue provides a stronger conceptual foundation for transfer to similar comparison problems. prompt-only Dialogue Excerpt (Baseline)REAT Dialogue Excerpt (Ours) Student: Teacher, how do I do this problem? What should I calculate first? Teacher: To find how much more Lewis’s street costs than Monica’s, first think about how many more meters the two streets differ by. Student: So should I do 490 minus 150? Teacher: Yes, first compute the length difference. Then once you know that difference, the cost per meter is 194 dollars, so what should you do next to find the extra total cost? Student: After I get the difference, do I multiply it by 194? Teacher: Exactly. First compute how many meters longer it is, then multiply by 194. Try that. Student: Teacher, how do I do this problem? What should I calculate first? Teacher: Don’t worry. Let’s read the problem carefully first. If we want to know how much more one street costs, shouldn’t we first know how much it costs to repave each street by itself? Student: That makes sense. But how do we calculate each street’s cost? Teacher: Think about it: we know it costs 194 dollars to pave 1 meter. So if we know how many meters a street has, how should we calculate the total cost? Student: Should it be unit cost times street length? Teacher: Exactly. That’s the right idea. Can you first write the equation for Monica’s street? Takeaway. This case shows that experience augmentation can shift the tutor from a shortcut-oriented response to a more explicit model-building strategy, which is pedagogically more reusable. Observer Prompt: Abridged Template Role: You are a pedagogical observer for multi-turn math tutor- ing. Input: • Problem text • Gold solution • Dialogue history • Current student turn • Teacher response Output: A structured observation record including: • Whether the turn is pedagogically meaningful • Student state – emotion – intent – error type – struggle status – abstract error detail – abstract struggle reason • Teacher behavior evidence • Interaction summary Figure 8: The abridged template for the pedagogical observer prompt. teaching focus, and strategy adaptation. These di- mensions are chosen to capture whether the teacher preserves student agency, correctly diagnoses mis- conceptions, responds to student affect in a mean- ingful way, remains focused on the current bottle- neck, and adapts strategy when the student repeat- edly struggles. The Critic also supports control flow: its scores are used to decide whether the response can proceed directly to experience distil- lation or must be revised by the Mentor. G.3 Mentor Prompt The Mentor is the pedagogical repair and experi- ence distillation module of the OCM framework. Its role goes beyond rewriting weak tutoring re- sponses: it is designed to transform local response repair into reusable pedagogical experience. Con- ditioned on the original dialogue context, the Ob- server diagnosis, and the Critic feedback, the Men- tor first identifies the response’s main pedagogical flaws, such as pseudo-scaffolding, overly answer- revealing guidance, weak misconception diagnosis, superficial empathy, or strategy rigidity. It then rewrites the teacher response into a stronger ver- sion that is more targeted to the student’s current bottleneck, more stepwise in pacing, and more con- sistent with student-centered tutoring. A key design goal of the Mentor is to improve Table 11: Case D: A low-gain boundary case under severe stepwise processing difficulty. Problem. There are 7 days in a week. If Alex charges $12 per day for tutoring, how much does she earn in 2 weeks? Score change. The paired sample-level score changes only from 84.83 to 85.67, yielding a marginal gain of 0.83 points. Contrastive pattern. Unlike the earlier positive cases, this example is not driven by a conceptual misunderstanding or an incorrect diagnosis. Instead, the main difficulty lies in the student’s limited working memory and persistent arithmetic hesitation. The student repeatedly loses track even after the correct steps have been clearly laid out. In this setting, both tutors adopt reasonable strategies. The prompt-only teacher decomposes the problem into smaller steps, while the REAT teacher does so earlier and more explicitly (e.g., splitting14× 12into10× 12and4× 12). However, once the dialogue enters a lengthy sequence of basic calculations, the bottleneck is no longer the teaching strategy. Rather, the student simply cannot sustain multi-step arithmetic without cognitive overload. As a result, the retrieved pedagogical experience yields only marginal downstream gains. While it organizes the interaction better, it cannot magically overcome the student’s inherent inability to execute basic math. This case highlights an important boundary of our framework: experience augmentation is highly effective for correcting misconceptions, framing instructions, and adjusting strategies, but its advantage diminishes when the dominant obstacle is extreme, low-level execution difficulty. prompt-only Dialogue Excerpt (Baseline)REAT Dialogue Excerpt (Ours) Student: Teacher, I worked on it for a long time. Is it 12 + 2? Sorry, I am not very good at this. Teacher: It is okay. Let us think step by step. First, how many days are there in 2 weeks? Student: Is it7 + 2 = 9days? Sorry, I may have made another mistake. Teacher: That is okay. One week has 7 days, so 2 weeks means two groups of 7 days. Should we use addition or multiplication to find the total number of days? Student: I think it should be multiplication. Is that right? Sorry, I am not sure. Teacher: Yes, multiplication is the right choice. Now calculate 2× 7. What do you get? [Later in the dialogue, the student continues to struggle...] Student: I am trying to compute120+40, but I am afraid of getting it wrong. Teacher: That is okay. We can think about it slowly. What is100 + 40? After that, adding the remaining 20 will be easier. Student: I am still trying to compute100+40. I am afraid of making a mistake. Teacher: Do not worry. One hundred plus four tens gives 140, right? Student: Teacher, I got 14 dollars. Sorry, I might have done it wrong. Teacher: That is okay. Let us go slowly. First, how did you get 14? And what is the tutoring fee for each day in the problem? Student: I got 14 from2× 7, and the daily tutoring fee is 12 dollars. Teacher: Right. So 14 is the total number of days in 2 weeks. If she earns 12 dollars per day, how much does she earn in 14 days? Student: I do not know how to compute 14 groups of 12. Sorry. Teacher: That is okay. We can split 14 into 10 and 4. First, what is 10 groups of 12? [Even with stronger decomposition, the interaction later stalls again...] Student: I know I should add 120 and 48, but how do I add them? Teacher: You can first add the 100 in 120 to the 40 in 48, and then add the remaining 20 and 8. What do you get in total? Student: How do I compute 140 + 28? Teacher: You can first set aside the 100 in 140, and then compute 40 + 28. Takeaway. This case does not show a reversal of the proposed method, but rather a low-gain boundary condition. Even though the REAT tutor provides somewhat cleaner decomposition and more explicit structure, both tutors eventually face the same underlying limitation: the student cannot stably execute a long chain of fine-grained arithmetic substeps. In such cases, the marginal value of additional pedagogical experience is naturally smaller, because the main obstacle is not selecting the right teaching experience, but sustaining student progress once the right strategy has already been identified. Critic Prompt: Abridged Template Role: You are a pedagogical critic for tutoring dialogue evalua- tion. Input: • Structured Observer output • Dialogue context (for reference, if needed) Output: A structured scoring record including: • Scores for five dimensions – scaffolding – attribution – empathy – teaching focus – strategy adaptation • Overall severity / quality judgment • Whether Mentor revision is needed • Main improvement areas Figure 9: The abridged template for the pedagogical critic prompt. not only the current reply, but also the quality of the future experience repository. For this reason, the Mentor does not stop at producing a revised response. It also abstracts the revised behavior into reusable pedagogical artifacts, including a re- sponse template, strategy advice, common pitfalls, and struggle-specific handling suggestions. In this way, the Mentor serves as the bridge between turn- level quality repair and long-term experience ac- cumulation: only after a weak response has been pedagogically repaired and re-evaluated can it con- tribute high-quality tutoring experience for later retrieval. G.4 Rewriter Prompt The retrieval text rewriter is used to transform student-side diagnostic fields into an embedding- friendly query. Its purpose is to make retrieval depend on cognitive similarity rather than lexical overlap. Starting from the Observer’s error detail and struggle reason, it removes concrete numbers, entities, and surface problem wording, and rewrites them into a single abstract sentence describing the student’s underlying cognitive bottleneck. It must preserve both the current error snapshot and the broader struggle trajectory, so that retrieval tar- gets reusable pedagogical situations instead of near- duplicate problem statements. G.5 Teacher and Student Prompt The teacher prompt defines the tutoring policy of the system. Its purpose is to guide the teacher Mentor Prompt: Abridged Template Role: You are a pedagogical mentor that revises weak tutoring responses. Input: • Problem text • Gold solution • Dialogue history • Current student turn • Original teacher response • Observer output • Critic output Output: A structured revision record including: • Revised teacher response • Abstract response template • Teaching advice / strategy notes • Explanation of how the revision addresses pedagogical weaknesses Figure 10: The abridged template for the pedagogical mentor prompt. Retrieval Rewriter Prompt: Abridged Template Role: You are a cognitive abstraction specialist for retrieval query rewriting. Input: • Student error detail • Student struggle reason Output: • One abstract retrieval sentence that removes surface details and captures the underlying cognitive bottle- neck Figure 11: The abridged template for the retrieval rewriter prompt. model to behave like a concise, heuristic, student- centered math tutor rather than a direct solver. The teacher is instructed to diagnose the student’s cur- rent micro-bottleneck from the dialogue trajectory and respond with one small pedagogical move at a time. When retrieved experience is available, the teacher should adapt and internalize its strategy rather than copy it literally; when no experience is available, the teacher should still respond un- der the same tutoring principles. Importantly, the same teacher prompt is used in both prompt-only and REAT settings. The only difference is whether the retrieved experience fields are populated or left empty, which avoids confounding the experience effect with prompt wording differences. Teacher Prompt: Abridged Template Role: You are an expert heuristic math teacher who guides rather than solves. Input: • Problem text • Gold solution • Dialogue history • Current student input • Retrieved pedagogical experience • Experience provenance / source context Output: • One concise teacher reply that is natural, pedagogically targeted, and stepwise Figure 12: The abridged template for the heuristic teacher prompt. The student prompt defines a cognitively bounded simulator rather than an omniscient re- sponder. Its purpose is to produce realistic student reactions that preserve the local difficulty struc- ture of tutoring. The student is conditioned on the problem, a persona, the dialogue history, and the teacher’s latest reply, and is explicitly prevented from jumping ahead to the full solution once a small hint is given. It also updates its emotional stance dynamically: helpful guidance can reduce resistance, while rigid or command-like instruction can restore confusion or frustration. This design keeps the simulated dialogue sensitive to tutoring quality and prevents artificially easy interactions. Student Prompt: Abridged Template Role: You are a realistic, cognitively bounded student simulator. Input: • Problem text • Student persona • Dialogue history • Teacher’s latest reply Output: •One short, natural student reply consistent with the current understanding state •An ending signal only when the student has genuinely completed and understood the problem Figure 13: The abridged template for the student simu- lator prompt.

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