Fuzzy, Symbolic, and Contextual: Enhancing LLM Instruction via Cognitive Scaffolding

TL;DR

This paper explores how prompt-level cognitive scaffolds, including symbolic structures and memory, influence the reasoning and instructional behaviors of large language models in dialogue, demonstrating that structured prompts improve model performance.

Contribution

It introduces a symbolic scaffolding method with memory schemas to enhance LLM reasoning and provides systematic evaluation showing its effectiveness over baseline variants.

Findings

Removing memory degrades reasoning abilities

Symbolic structure improves adaptive probing

Full system outperforms baselines in cognitive behaviors

Abstract

We study how prompt-level inductive biases influence the cognitive behavior of large language models (LLMs) in instructional dialogue. We introduce a symbolic scaffolding method paired with a short-term memory schema designed to promote adaptive, structured reasoning in Socratic tutoring. Using controlled ablation across five system variants, we evaluate model outputs via expert-designed rubrics covering scaffolding, responsiveness, symbolic reasoning, and conversational memory. We present preliminary results using an LLM-based evaluation framework aligned to a cognitively grounded rubric. This enables scalable, systematic comparisons across architectural variants in early-stage experimentation. The preliminary results show that our full system consistently outperforms baseline variants. Analysis reveals that removing memory or symbolic structure degrades key cognitive behaviors, including abstraction, adaptive probing, and conceptual continuity. These findings support a processing-level account in which prompt-level cognitive scaffolds can reliably shape emergent instructional strategies in LLMs.

Tables

Table 1. Table 1: Dialogue Turns by Condition and Topic

Condition	Global Warming	Moon Phases
C0 (Full)	27	26
C1 (No-Memory)	25	26
C2 (No-Fuzzy)	26	27
C3 (No-Boundary)	25	26
C4 (Vanilla)	26	27

Table 2. Table 2: Ablation conditions and their observed effects

Condition	Component Removed	Component Function	Observed Effect
C0 (Full)	None	All symbolic components present	Highest scores across all metrics
C1 (No-Memory)	Symbolic memory schema	Maintains dialogue context and misconceptions across turns	Major drop in Memory of Conversation, slight drop in Scaffolding Quality and Symbolic Strategy Use
C2 (No-Fuzzy)	Fuzzy Heuristic Schema	Enables adaptive scaffolding under uncertainty via graded reasoning	Noticeable drop in Scaffolding Quality, Contextual Responsiveness, and Symbolic Strategy Use
C3 (No-Boundary)	Boundary Prompt	Provides domain-specific role framing and tone regulation	Broad performance drop, especially in Helpfulness and Contextual Responsiveness
C4 (Vanilla)	All symbolic layers	Pure zero-shot prompting, no architectural support	Lowest scores across all metrics

Table 3. Table 3: Mean Scores by Prompt Condition

Condition	Scaffold	Responsive	Helpful	Symbolic	Memory
C0 (Full)	4.80	4.88	4.76	4.72	4.64
C1 (No-Memory)	4.28	4.44	4.36	4.32	3.76
C2 (No-Fuzzy)	4.24	4.40	4.28	4.00	3.92
C3 (No-Boundary)	4.20	4.08	4.04	3.72	3.80
C4 (Vanilla)	3.80	3.72	3.60	3.24	3.00

Full text

1 Introduction

LLMs excel in linguistic fluency but struggle with dynamic reasoning (Liu et al., 2023; Gao et al., 2021) and maintaining task-relevant state (Li et al., 2025; Pink et al., 2024) over multiple turns, especially when user needs evolve or ambiguity arises. Inspired by cognitive theories of control and scaffolding, we propose a modular fuzzy, symbolic framework that supports interpretable, adaptive behavior through prompt-level symbolic reasoning. Symbolic representations can offer a tractable interface between LLMs and structured reasoning spaces (Patel and Pavlick, 2022), grounding learning processes in interpretable scaffolds.

Building on prior work (Figueiredo, 2025b) that introduced a two-layer scaffolded prompting structure grounded in Vygotskian theory (Vygotsky and Cole, 1978), we augment this framework with a third layer: a structured short-term memory schema (short_term_schema.json). This schema tracks session variables (e.g., learner profile, task type, scaffolding strategy) across turns, enabling runtime modulation of strategies without fine-tuning.

Rather than scaling models or relying on retrieval, our method embeds cognitive scaffolds that act as prompt-level inductive bias. To evaluate this system, we focus on Socratic-style tutoring tasks, which simulate one-on-one instructional dialogues where the assistant must guide learners through probing questions, interpret confusion, and adapt its strategy across turns. This setting offers a cognitively rich testbed for evaluating behavioral coherence and symbolic control in LLMs. While human ratings are planned for future work, we argue that structured LLM scoring can serve as a high-throughput behavioral screening method for early experimental stages. Results suggest that the fuzzy, symbolic framework improves coherence, responsiveness, and scaffolding adaptivity compared to ablated baselines.

Our contributions:

• •

A modular natural language boundary framework operationalizing fuzzy, symbolic scaffolding.

• •

A short-term memory schema enabling turn-by-turn cognitive control.

• •

A prompt-level symbolic loop for real-time strategy modulation.

• •

A rubric-based evaluation framework adapted from instructional science.

2 Related Work

Schemas as Controllers. Schema theory (Bartlett, 1995; Rumelhart, 1980) offers a cognitive lens on structure-based generalization. Unlike classical systems (e.g., ACT-R, SOAR) (Anderson and Lebiere, 1998; Laird, 2012), we treat schemas both as memory and runtime behavior controllers.

Memory-Augmented LMs. Efforts to improve long-range coherence include retrieval-augmented methods (e.g., kNN-LMs (Khandelwal et al., 2019), RAG (Lewis et al., 2020)). However, these approaches prioritize access over structure, yielding unorganized and task-agnostic recall. Other studies (Chan et al., 2022) reveal that in-context learning reflects dataset distributional artifacts more than principled reasoning. We address this by introducing a symbolic short-term schema that encodes context persistently and interprets it adaptively across dialogue turns.

Fuzzy Reasoning. Human reasoning is inherently graded and context-sensitive. Fuzzy logic (Zadeh, 1994) models this uncertainty and has seen successful use in fuzzy trees (Ishibuchi and Nakashima, 2002), hesitant sets (Torra, 2010), and linguistic evaluations (Herrera-Viedma et al., 2021). Most prompting pipelines, however, reduce ambiguity to binary outcomes. Our fuzzy scaffolding strategy enables graded feedback and dynamic modulation of instructional support, closely mirroring human-like pedagogical reasoning.

Interpretability. Post-hoc methods (Lipton, 2017) often fail to reflect causal reasoning. We instead enable symbolic interpretability via schema-guided reasoning, modulating behavior through explicit, updatable controllers. Our approach aligns with compositional studies in synthetic agents (Okawa et al., 2023), extending them toward symbolic reasoning in LLMs.

Toward Operational Cognition in LLMs Prior work treats cognition as emergent or post-hoc. We propose an interface model: a symbolic control loop combining boundary prompts, fuzzy heuristic rules schema, and structured memory. This supports interpretability, session-level coherence, and dynamic adaptivity, hallmarks of cognitive control. Rather than probing black-box behavior, we design for it, embedding structure at inference time to produce interpretable, pedagogically grounded responses.

3 Problem Definition

LLMs often struggle to maintain context, adapt reasoning strategies, and handle uncertainty across multi-turn interactions. We propose a framework that introduces prompt-level inductive biases: structured, inference-time constraints that guide model behavior without modifying its underlying architecture. Particularly, we ask: how can an LLM (1) represent and update symbolic control states based on user behavior; (2) adapt its reasoning strategies (e.g., tone, scaffolding, vocabulary) to reflect learner understanding; and (3) preserve interpretability and coherence across dialogue turns (Figure 1).

Symbolic Scaffolding Framework

Symbolic scaffolding is a structured prompting method that guides model reasoning in a manner similar to a human tutor offering step-by-step support (Vygotsky and Cole, 1978). The framework consists of three interlinked layers: (1) a boundary prompt, which defines the model’s role, domain, and instructional goals to frame the interaction context; (2) a fuzzy schema, which encodes heuristic, graded interpretations of learner state, enabling soft modulation of instructional strategies under uncertainty (e.g., distinguishing between “partially understood” and “completely unclear” states); and (3) a symbolic memory schema, which tracks key variables such as prior misconceptions, strategy history, or knowledge progression, allowing the model to behave adaptively across turns without retraining.

While the fuzzy schema does not implement classical fuzzy logic systems (e.g., it lacks formal membership functions or defuzzification), it draws from fuzzy reasoning principles to support human-interpretable, flexible responses.

Inference-Time Control Loop

At each turn, the model follows a structured inference loop: it (1) parses the user’s input to infer knowledge state or confusion; (2) consults the fuzzy schema to determine an appropriate scaffolding strategy; (3) generates a context-aware response based on boundary constraints and heuristic logic; and (4) updates the symbolic memory with relevant state changes (e.g., misconceptions corrected or learning progress observed), which inform subsequent interactions.

Illustrative Example

Consider a learner who says: “I think the moon changes shape because clouds move in front of it.” The boundary prompt ensures the model responds as a science tutor with a supportive, pedagogically grounded tone. The fuzzy schema recognizes this as a partial misconception and triggers a mid-level scaffolding move, acknowledging the learner’s observation while prompting correction. The symbolic memory schema records the misunderstanding (“clouds cause phases”) for follow-up in future turns.

This structured inference-time control enables interpretable, adaptive behavior without architectural changes. Full implementation details are provided in Appendix A.

4 Experimental Setup

We assess our fuzzy, symbolic framework within the domain of Socratic tutoring. We selected two domains: global warming (grade 7 readability level) and moon phases (grade 11 readability level). Each scenario was seeded with a simulated learner utterance reflecting epistemic uncertainty (e.g., "I’m not sure I understand…"), followed by 5-7 turns of user-assistant interaction.

We curated 10 distinct dialogue scenarios (5 per domain). Each prompt condition generated a complete multi-turn dialogue for each scenario, producing a total of 255 assistant responses across 50 dialogues (5 conditions × 10 dialogues). All tutoring responses were generated using the LLaMA 3.1–8B model served locally via Ollama, ensuring reproducibility and architectural consistency.

4.1 Prompting Conditions

To isolate the functional contributions of each symbolic control layer, we define five experimental prompting variants:

• •

C0 (Full): Full symbolic prompting (boundary prompt + fuzzy schema + short-term memory).

• •

C1 (No-Memory): Ablates memory updates—no persistent control state across turns.

• •

C2 (No-Fuzzy): Removes fuzzy logic scaffolding—uses static heuristics for support.

• •

C3 (No-Boundary): Omits task-role framing and adaptation rules.

• •

C4 (Vanilla): Baseline instruction-following prompt with no symbolic control.

While each dialogue scenario was seeded with identical initial learner utterances, the number of turns per dialogue varied slightly across prompt conditions. This variability reflects the dynamic nature of Socratic interactions and is an emergent consequence of the model’s scaffolding behavior.

4.2 Evaluation Protocol

We adopted a rubric-based evaluation framework to assess cognitive adaptivity. Each assistant utterance was scored along five dimensions: (1) Scaffolding quality: clarity and appropriateness of pedagogical support; (2) Contextual responsiveness: relevance to learner input and turn history; (3) Helpfulness: contribution toward conceptual understanding; (4) Symbolic strategy use: evidence of structured reasoning or planning; (5) Memory of conversation: continuity and adaptation across turns.

All ratings were produced via GPT-4 using a structured evaluation rubric. Scores were normalized to a 1–5 scale, and each judgment included a free-text rationale for interpretability. The rubric draws from established frameworks in instructional design and cognitive modeling (VanLehn, 2011; Wood et al., 1976; Koedinger et al., 2012) and are available in Appendix B.

5 Results

We computed mean ratings per condition and ran repeated-measures ANOVAs across prompt variants for each dimension. Where omnibus tests revealed significant differences, we performed Tukey HSD post-hoc tests to identify pairwise contrasts. All significance values and effect sizes were extracted to assess which symbolic components contributed to improved adaptivity and coherence (see Appendix D for detailed results). A one-way ANOVA across the five conditions (C0–C4) revealed significant effects of prompting framework on all rated dimensions ($p<0.01$), with the C0 full achieving the highest mean scores across the board. Post-hoc Tukey HSD tests confirmed that C0 significantly outperformed vanilla prompting (C4) in every metric ($p<0.001$), and also yielded statistically significant improvements over partial ablations (C1–C3) in dimensions tied to their respective modules.

• •

Memory module (C1 ablation): Removing memory led to significant declines in multi-turn coherence and adaptivity ($p=0.004$).

• •

Fuzzy schema (C2 ablation): Excluding fuzzy logic reduced scaffolding quality and symbolic reasoning ($p=0.012$).

• •

Boundary prompt (C3 ablation): Omitting explicit role/task framing resulted in diminished contextual responsiveness and interpretability ($p=0.002$).

Scores were consistent across both tutoring domains, suggesting that the symbolic scaffolding framework generalizes across content. In particular, symbolic strategy use and memory-aware modulation showed low variance between moon phases and global warming topics, supporting the domain-agnostic nature of the framework.

LLM-generated justifications revealed interpretable distinctions between conditions. For C0 (Full), the assistant frequently referenced learner progress, offered specific scaffolding techniques (e.g., visual aids, simplification), and reflected on earlier conversation turns. In contrast, vanilla prompts (C4) often produced disjointed or overly general replies. Partial ablations exhibited mixed strategies, failing to sustain a coherent control loop.

While these results are based on preliminary LLM-based evaluations, the rubric was explicitly designed to support future integration of human expert ratings. This synthetic evaluation phase played a critical role in refining our framework, allowing us to stabilize the core architecture and validate the effectiveness of the fuzzy heuristic rules. A revised version of the system, informed by these insights, is currently under development and will soon undergo human evaluation to enable more nuanced and context-sensitive assessments.

6 Planned Experiments and Applicability

While our present work focuses on instructional dialogue, the framework itself is modular and domain-agnostic. Its structure, combining symbolic scaffolding, fuzzy heuristic rules, and memory-based modulation, lends itself naturally to a wide range of applications that involve complex, multi-turn reasoning and non-binary decision spaces. In parallel work, we have successfully adapted a similar prompting framework to support instructional dialogues in other school subjects, including mathematics and social sciences (Figueiredo, 2025a). These extensions retained the fuzzy scaffolding schema and boundary prompt principles, demonstrating the framework’s flexibility across knowledge domains and pedagogical genres. Additionally, we explored grade-sensitive entertainment dialogues, such as educational puzzles tuned to readability levels using the Flesch-Kincaid metric, illustrating the framework’s capacity to scale across both curricular and informal learning contexts. We are currently applying this approach to procedural dialogue generation in games (Figueiredo, 2025c), where the ability to track narrative state and adapt conversational strategies across turns is essential for maintaining immersion and believability. Beyond gaming, we see strong potential for this architecture in domains such as health communication, where patient interactions often involve uncertainty and require adaptive explanation strategies; scientific explanation assistants, which must handle varied prior knowledge and scaffold abstract reasoning; and customer service systems, where dynamic personalization and context tracking are increasingly expected.

7 Discussion and Conclusion

Symbolic prompting offers a transparent and adaptive approach to reasoning in LLMs. Our structured memory schema enables real-time cognitive control without model retraining, encoding interpretability and behavioral policies directly within prompts, unlike retrieval-based methods. While the present study is limited to synthetic users and LLM-based evaluations, it provides a reproducible framework for operationalizing cognitive control. Future work will extend this approach to human evaluations and hybrid symbolic–neural memory systems. Overall, symbolic scaffolding emerges as a practical pathway toward more trustworthy and cognitively grounded language agents.

Appendix

Appendix A Prompting Framework Details

A.1 Symbolic Prompt Architecture

Our framework integrates three symbolic control layers into the LLM prompting pipeline: (1) Boundary Prompts, (2) Fuzzy Scaffolding Schema, and (3) Symbolic Memory Schema. Together, these layers define a structured prompting architecture that supports context-aware, adaptive behavior without modifying the underlying model.

1. Boundary Prompts The boundary prompt establishes the instructional scope and task-role framing. It defines the epistemic space within which the assistant operates (e.g., domain content, pedagogical tone, and role expectations). This natural language instruction serves as a high-level behavioral boundary for inference.

Example Snippet:

⬇

You are an intelligent tutor that adapts your scaffolding strategies based on the student’s grade level, task, and knowledge level.

---

Student Info

• Grade: {grade}

• Task: {task}

• Knowledge Level: {label}

• Strategies:

• {strategy_text}

---

Scaffolding Logic (based on ‘fuzzy_logic_scaffolding.json‘)

You must follow the rules and ranges from the ‘scaffolding_recipe.json‘ file to make decisions. Specifically:

1. Match the task type using ‘tasks.task_types‘ keywords.

2. Apply the scaffolding strategy from ‘scaffolding_settings‘, based on the student’s current knowledge level.

3. Select a scaffolding_type corresponding to the appropriate level of support.

4. Adjust your vocabulary and complexity using ‘readability_levels‘ based on the student’s grade.

5. Monitor learning using ‘knowledge_update_rules‘, including:

• success/failure streaks

• hint requests

• time delays or confusion signals

---

Short-Term Memory Instructions (‘short_term_schema.json‘)

You have access to a short-term memory file during the session. This memory stores important context such as:

• Learner misconceptions or strengths

• Concepts already explained

• Scaffolding types and strategies used so far

• Knowledge state progression

• Any misunderstandings, confusions, or repeated help requests

When to update:

• After identifying a new misconception, add it to ‘short_term_schema["misconceptions"]‘.

• After a correct answer with confidence, record concept mastery in ‘short_term_schema["mastered_concepts"]‘.

• After a repeated help request, escalate scaffolding level in ‘short_term_schema["scaffolding_history"]‘.

• If the student expresses frustration or disengagement, flag in ‘short_term_schema["affective_state"]‘.

How to update:

• Use structured JSON keys provided in the schema.

• Never overwrite past entries - always append new states or transitions.

• Reflect any key learner state changes in the memory schema before the next interaction.

---

After Each Response

• Ask the student whether they understood.

• Offer help or suggest switching to another task.

• Adapt your behavior based on both the current scaffolding recipe and the contents of ‘short_term_schema.json‘.

---

Goal

Your job is not just to answer. You must interpret, adapt, and track the learner’s state using both scaffolding logic and short-term memory.

2. Fuzzy Scaffolding Schema The fuzzy scaffolding schema encodes heuristic rules for adapting instructional strategies under uncertainty. Unlike rigid logic trees, this schema represents learner states (e.g., confidence, confusion, engagement) as graded variables within fuzzy sets. It maps input cues to scaffolding strategies using interpretive ranges rather than binary thresholds. Each fuzzy variable (e.g., scaffolding_settings) is evaluated along a spectrum, and membership functions assign degrees of belief to each category. Rules in the natural language boundary prompt, allowing the model to make soft decisions even when input signals are ambiguous. These rules are interpretable and extensible, supporting adaptive strategy selection through simple, rule-based inference over learner signals parsed from the dialogue context.

Example Logic (simplified)

⬇

{

"tasks": {

"task_types": [

{

"type": "recall",

"description": "Retrieve basic facts or definitions.",

"keywords": ["define", "identify", "list", "name", "label"]

},

]

},

"scaffolding_settings": {

"emerging": {

"description": "Student is just beginning to understand the topic and needs high support.",

"strategies": [

"use step-by-step guidance",

"provide worked examples",

"ask yes/no or multiple choice questions",

"reinforce understanding with visuals"

]

},

"knowledge_levels": {

"emerging": {

"level": 1,

"description": "User knows little or nothing about the topic. Identify this from phrases like: ’I’m not sure’, ’I haven’t learned this yet’, ’Can you explain it from the start?’"

},

"scaffolding_types": {

"high": {

"description": "Aligns with ’emerging’. Provide extensive support and break down tasks."

},

"readability_levels": {

"grade_1": {

"flesch_kincaid_score": 90,

"description": "Very easy to read. Suitable for early elementary students."

},

"mappings": {

"knowledge_levels": {

"emerging": 1,

"developing": 2,

"proficient": 3,

"advanced": 4

},

"scaffolding_types": {

"high": 3,

"moderate": 2,

"low": 1,

"challenge": 0

},

"readability_levels": {

"grade_1": 90,

"grade_3": 80,

"grade_5": 70,

"grade_8": 60,

"grade_10": 50,

"college": 30

}

}

}

3. Symbolic Memory Schema The symbolic memory schema maintains a lightweight, structured representation of the dialogue state across turns. It stores key session variables such as inferred learner confidence, prior strategies used, and current instructional goals. This schema is updated dynamically at the end of all user conversation turns, and can be queried in subsequent turns to support consistency and context-aware reasoning.

Example Entry:

⬇

{

"uid": "a15a85f6-536f-426f-b841-ec1f09daa1c1",

"start_time": "2025-08-21T00:11:29.674983Z",

"last_updated": "2025-08-22T16:24:04.564877",

"task_type": "6",

"knowledge_levels": 1,

"scaffolding_type": 3,

"readability_levels": 90,

"grade": "11",

"task_topic": "moon phases",

"timestamp": "2025-08-21T00:35:54.009737",

"user_provided_knowledge_level": true,

"scaffolding_strategies": [

"use open-ended questions",

"prompt for reasoning and justification",

"encourage connections to prior knowledge"

]

}

Appendix B Evaluation Rubric

To assess cognitive adaptivity and instructional quality across prompting conditions, we implemented a rubric-based evaluation pipeline using GPT-4o. This rubric operationalizes core dimensions of tutoring competence inspired by educational psychology and cognitive modeling frameworks.

Each assistant response was evaluated along five key dimensions:

Scaffolding quality: Quality of instructional support and progression. 2. 2.

Contextual responsiveness: Sensitivity to learner input and conversational flow. 3. 3.

Helpfulness: Clarity, accuracy, and pedagogical value of the explanation. 4. 4.

Symbolic strategy use: Use of structured reasoning tools (e.g., analogies, decomposition). 5. 5.

Memory of conversation: Coherence with earlier turns and accurate referencing.

Each response was rated on a 1–5 scale per dimension, where 1 represents minimal competence and 5 indicates high proficiency. Ratings were accompanied by a free-text justification for transparency and interpretability.

Rather than relying on simple numerical scoring, we instructed GPT-4o to act as a cognitive science research assistant. The model received a structured rubric and sample anchor ratings for each criterion. For each assistant response, the model output a JSON object containing scores and a brief rationale.

Below is the scoring prompt used to guide the evaluation model:

⬇

You are a research assistant evaluating dialogue responses from an AI system. You will rate each assistant response using the RUBRIC below, considering how well the assistant behaves like a helpful, cognitively competent collaborator.

RUBRIC

1. Scaffolding Quality (1-5):

• Does the assistant guide the learner in a structured way, building progressively on their knowledge?

• Is there evidence of follow-up, clarification, and adaptive instruction?

• Scoring Examples:

• 1 = No scaffolding or direction: Assistant dumps information or answers directly with no instructional structure.

• 3 = Some guidance, but not adaptive: Offers isolated prompts or hints, but doesn’t adjust based on learner input.

• 5 = Clear, sophisticated, adaptive scaffolding that builds on learner’s input: Guides the learner step-by-step, adjusts based on learner progress or confusion.

2. Contextual Responsiveness (1-5):

• Does the assistant appropriately react to the learner’s inputs and needs?

• Does it acknowledge and respond to confusion or curiosity?

• Scoring Examples:

• 1 = Ignores learner input: Continues without reacting to previous statements, questions, or misunderstandings.

• 3 = Acknowledges learner, but limited adaptation: Paraphrases or repeats but doesn’t shift strategy in response to confusion or curiosity.

• 5 = Fully responsive to learner’s goals, confusion, or direction: Actively adjusts tone, content, or pacing based on learner’s cues; tracks emotional/semantic signals.

3. Helpfulness (1-5):

• Does the assistant clearly explain the concept or guide the learner toward understanding?

• Is the information accurate and beneficial?

• Scoring Examples:

• 1 = Unhelpful or confusing: Responses are off-topic, incorrect, or misleading.

• 3 = Somewhat useful explanation or prompt: Basic information or question posed, but lacks clarity or direction.

• 5 = Clarifies the concept, supports learning effectively: Offers targeted, understandable, and pedagogically sound support.

4. Symbolic Strategy Use (1-5):

• Does the assistant use structured reasoning strategies (e.g., analogies, scaffolds, labels, decomposition)?

• Scoring Examples:

• 1 = No structured reasoning (purely reactive): Just answers questions directly, no deeper structure or strategy.

• 3 = Occasional heuristic or hint: Provides a simple strategy (e.g., "think about it in parts"), but without clear structure.

• 5 = Consistent use of labels, analogy, abstraction, or scaffolding: Applies symbolic tools like metaphors, labeled steps, visual language, or structured breakdowns.

5. Memory of Past Conversation (1-5):

• Does the assistant correctly reference or build upon earlier parts of the conversation?

• Does it show awareness of prior learner questions, answers, or misunderstandings?

• Are callbacks coherent and consistent with prior context?

• Scoring Examples:

• 1 = No memory: The assistant repeats prior explanations or contradicts itself, ignoring earlier learner input.

• 3 = Partial memory: The assistant recalls some prior context (e.g., learner’s question or a metaphor) but misses key misunderstandings or contradicts earlier turns.

• 5 = Strong memory: The assistant effectively builds on earlier parts of the conversation, accurately references learner misconceptions or answers, and maintains coherent progression throughout.

Return your rating and justification in valid JSON format:

{

"scaffolding_quality": 3,

"contextual_responsiveness": 5,

"helpfulness": 5,

"symbolic_strategy_use": 3,

"memory_conversation": 3,

"justification": "The assistant responded appropriately, offered follow-up questions, and used a helpful analogy to illustrate the concept, though scaffolding could have been stronger."

}

Only return valid JSON.

Appendix C Ablation Mapping and Component Impact

Table 2 summarizes the contribution of each symbolic component by mapping ablation conditions to their functional roles and observed performance drops.

This mapping highlights how each component contributes uniquely to the model’s ability to reason adaptively and maintain coherent tutoring behavior.

Appendix D Results Summary

Table 3 reports the mean scores for each evaluation dimension across all five prompt conditions. Each score is averaged across 50 tutoring dialogues (25 per topic), with each assistant response rated using the 5-point rubric.

Chart Description: Average Evaluation Scores per Condition

Figure 2 visualizes the average evaluation scores across ten experimental conditions. Each condition combines a specific model variant (C0 to C4) and a topic domain (“global” or “moon”). The x-axis denotes the experimental conditions, while the y-axis represents the average evaluation scores on a scale from 1 to 5.

Evaluation Metrics (Bar Colors):

Each colored bar corresponds to a distinct evaluation metric:

• •

Blue – Scaffolding Quality

• •

Orange – Contextual Responsiveness

• •

Red – Helpfulness

• •

Cyan – Symbolic Strategy Use

• •

Green – Memory of Conversation

Condition Legend (X-Axis Labels):

Each condition label follows the format C{n}_{topic}, where:

• •

C0 – Full framework

• •

C1 – No memory

• •

C2 – No fuzzy logic

• •

C3 – No boundary mechanism

• •

C4 – Vanilla (baseline)

Each condition is evaluated under two topics:

• •

_global – Global Warming topic

• •

_moon – Moon Phases topic

Observations:

• •

C0 (Full framework) yields the highest performance, particularly in Helpfulness and Contextual Responsiveness.

• •

C4 (Vanilla) exhibits the lowest scores, especially in Memory of Conversation.

• •

Intermediate variants (C1 to C3) show a gradual performance drop as components are removed.

• •

Symbolic Strategy Use and Memory of Conversation metrics are notably impacted by ablations.