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 Large Language Models (LLMs) 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 about AI, 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 (Retrieval-Augmented Generation) 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.

What this means for practice

• Designers. Ship the prompt before the product: on MathDial a pedagogically informed Tutor Prompt significantly beat the base prompt for both GPT-4o and GPT-4o-mini, with higher Success@N and far lower Telling@N across interaction lengths.
• Designers. Route mathematical generation to the strongest reasoning model you can afford — o3-mini(high) and Claude 3.5 Sonnet tied at 90.00% problem-solving accuracy with the SymPy tool, ahead of Gemini 2.0 Flash (88.67%), GPT-4o (78.67%), and GPT-4o-mini (77.33%).
• Designers. Split personalization into two memories so support can be proactive: stable traits (prior knowledge, Misconceptions about AI, preferences, goals) in long-term memory and current-session context in working memory, letting the tutor offer a targeted hint or switch to a visual aid.
• Designers. Ground tutoring responses in the course textbook through GraphRAG rather than unindexed retrieval, and emit a prerequisite DAG of learning paths so students revising for an exam see an ordered route through topics.
• Designers. Give the tutoring agent callable tools — symbolic solver, function plotter, course-graph drawer — since tool access is what the model comparison granted and the guided dialogues assume.

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.

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).