AI-Powered Math Tutoring: Platform for Personalized and Adaptive Education

Synthesis: Chudziak and Kostka (2025) propose a multi-agent AI math tutoring platform that moves beyond the reactive answer-giving of current LLM tutors toward structured, individualized, tool-assisted learning. It combines adaptive Socratic tutoring agents, dual-memory (long-term + working) personalization, GraphRAG-based textbook retrieval, and Directed Acyclic Graph (DAG) course planning, letting students learn new topics, target their weaknesses, revise for exams, and practice on unlimited personalized exercises. On the MathDial benchmark, a pedagogically informed "Tutor Prompt" significantly beat a base prompt on guided tutoring (higher Success@N, lower Telling@N), and o3-mini(high) was selected for task creation.

Motivation

The authors identify a core gap: current AI tutoring systems, particularly LLM-based tutors, tend to provide direct answers without encouraging deep reflection or incorporating structured pedagogical tools and strategies. This "reactive nature" is most problematic in mathematics, where AI tutoring systems remain underdeveloped. The research question is: How can AI tutoring systems move beyond reactive assistance to enable structured, individualized, and tool-assisted learning experiences?

System Architecture

Built on LangGraph, the multi-agent system's main interaction loop centers on a Tutor Agent (GPT-4o, chosen for conversational ability, tool use, and low latency) that orchestrates components via a ReAct-style framework. A Memory Dispatcher oversees personalization:

• Dual-memory framework. Long-Term Memory (LTM) stores persistent student data (prior knowledge, misconceptions, learning preferences, goals); Working Memory (WM) holds current-session context (topic, problem state, recent interactions).
• Guided tutoring. Instead of solving problems directly, the Tutor Agent uses Socratic questioning that promotes self-explanation and metacognitive skills, dynamically adjusting support based on memory-tracked progress and grounding responses in textbook data.
• GraphRAG retrieval. Textbook material is represented as a knowledge graph, argued to better represent educational content relations than vector RAG for contextual tutoring.
• Task Creation. A dedicated module using o3-mini(high) generates personalized practice exercises based on topic, difficulty, and optionally GraphRAG data.
• Course creation. A pipeline of agents (Research → Planning → Step Handling → Coding) accesses memory and GraphRAG data to construct a structured DAG of prerequisite knowledge and optimal learning paths, stored in a database — supporting exam revision and structured learning.
• Auxiliary tools. SymPy-based Symbolic Solver, Matplotlib Function Plotter, and Course Graph Drawer.

Key Findings

• Guided prompting validates the approach. On the MathDial dataset, the "Tutor Prompt" (emphasizing Socratic questioning and scaffolding) significantly outperformed the "Base Prompt" for both GPT-4o and GPT-4o-mini, achieving superior Success@N and far lower Telling@N over interaction lengths — confirming the guided-tutoring strategy versus direct answer-giving in simulated dialogues.
• Model selection for task creation. o3-mini(high) and Claude 3.5 Sonnet tied at highest problem-solving accuracy (90.00%) with access to the SymPy tool; Gemini 2.0 Flash scored 88.67%, GPT-4o 78.67%, GPT-4o-mini 77.33%. o3-mini(high) was selected for Task Creation due to top performance and step-decomposition ability.
• Personalization is memory-driven. If LTM knows a student struggles with negative-sign distribution, the system proactively offers targeted hints, scaffolds problems differently, or gives corrective feedback; if a student prefers visual explanations, aids like function plotting are used — creating a responsive, individualized experience.

Limitations

• No evaluation with real students in actual learning environments (noted by reviewers).
• Personalization operates on a basic set of attributes.
• The pedagogical effectiveness of GraphRAG-generated courses has not yet been empirically evaluated.
• System performance depends fundamentally on underlying LLM capabilities and possible biases.

Future Work

Real-world user studies to assess learning gains, user experience, and practical utility of generated courses; advanced student modeling (e.g., affective state detection); spaced repetition; exploring different LLMs and RAG architectures; adaptability to other STEM domains, accessibility, and explainability.

Connected Concepts

• Intelligent Tutoring
• Math Education
• Adaptive Learning
• Personalized Learning
• Socratic Method
• Scaffolding
• LLM
• RAG
• Agentic AI

Connected Articles

• From Answer Generators To Reasoning Facilitators AI Tutors — Frameworks for shifting AI tutors away from answer generation toward reasoning facilitation, directly aligned with this paper's core motivation.
• Kar Mathbuddy Affective Math Tutoring 2025 — Another AI-based math tutoring system, offering a comparison point for affective and personalized math tutoring.
• Instructional Agents Multi Agent Course Gen — A parallel multi-agent LLM system for course material generation, relevant to this paper's course-creation pipeline.
• Retrieval Augmented Tutoring Algorithm Kite — Retrieval-augmented tutoring, complementing the paper's GraphRAG-based textbook retrieval.

Citation

Chudziak, J. A., & Kostka, A. (2025). AI-Powered Math Tutoring: Platform for Personalized and Adaptive Education. The 26th International Conference on Artificial Intelligence in Education (AIED 2025). arXiv:2507.12484.