# Embracing Imperfection: Simulating Students with Diverse Cognitive Levels Using LLM-based Agents

arXiv: https://arxiv.org/abs/2505.19997 · HTML: https://mlsanity.com/paper/2505.19997/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 26 May 2025.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 22 of 22)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [CodeNet: A Large-Scale AI for Code Dataset for Learning a Diversity of Coding Tasks](https://mlsanity.com/paper/2105.12655/) (2021)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [Bridging the Novice-Expert Gap via Models of Decision-Making: A Case Study on Remediating Math Mistakes](https://mlsanity.com/paper/2310.10648/) (2023)
- [Clicks can be Cheating: Counterfactual Recommendation for Mitigating Clickbait Issue](https://mlsanity.com/paper/2009.09945/) (2020)
- [simpleKT: A Simple But Tough-to-Beat Baseline for Knowledge Tracing](https://mlsanity.com/paper/2302.06881/) (2023)
- [Stepwise Verification and Remediation of Student Reasoning Errors with Large Language Model Tutors](https://mlsanity.com/paper/2407.09136/) (2024)
- [MathVC: An LLM-Simulated Multi-Character Virtual Classroom for Mathematics Education](https://mlsanity.com/paper/2404.06711/) (2024)
- [Large Language Models for Education: A Survey](https://mlsanity.com/paper/2405.13001/) (2024)
- [AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understanding](https://mlsanity.com/paper/2409.09039/) (2024)
- [LLM-based Cognitive Models of Students with Misconceptions](https://mlsanity.com/paper/2410.12294/) (2024)
- [Towards Transformer-Based Aligned Generation with Self-Coherence Guidance](https://mlsanity.com/paper/2503.17675/) (2025)
- [Evaluating and Optimizing Educational Content with Large Language Model Judgments](https://mlsanity.com/paper/2403.02795/) (2024)
- [Toward In-Context Teaching: Adapting Examples to Students' Misconceptions](https://mlsanity.com/paper/2405.04495/) (2024)
- [MPCODER: Multi-user Personalized Code Generator with Explicit and Implicit Style Representation Learning](https://mlsanity.com/paper/2406.17255/) (2024)
- [Instruction Tuning-free Visual Token Complement for Multimodal LLMs](https://mlsanity.com/paper/2408.05019/) (2024)
- [Disentangled Knowledge Tracing for Alleviating Cognitive Bias](https://mlsanity.com/paper/2503.02539/) (2025)
- [Knowledge is Power: Harnessing Large Language Models for Enhanced Cognitive Diagnosis](https://mlsanity.com/paper/2502.05556/) (2025)
- [Graphusion: Leveraging Large Language Models for Scientific Knowledge Graph Fusion and Construction in NLP Education](https://mlsanity.com/paper/2407.10794/) (2024)
- [Large Language Model-Driven Curriculum Design for Mobile Networks](https://mlsanity.com/paper/2405.18039/) (2024)

## Built on by (most cited first, 19 of 19)

- [SMART: Simulated Students Aligned with Item Response Theory for Question Difficulty Prediction](https://mlsanity.com/paper/2507.05129/) (2025)
- [TeachLM: Post-Training LLMs for Education Using Authentic Learning Data](https://mlsanity.com/paper/2510.05087/) (2025)
- [Mnemis: Dual-Route Retrieval on Hierarchical Graphs for Long-Term LLM Memory](https://mlsanity.com/paper/2602.15313/) (2026)
- [Towards Valid Student Simulation with Large Language Models](https://mlsanity.com/paper/2601.05473/) (2026)
- [Tailoring Diagnostic Modeling to Individual Learners: Personalized Distractor Generation via MCTS-Guided Reasoning Reconstruction](https://mlsanity.com/paper/2508.11184/) (2025)
- [IntelliCode: A Multi-Agent LLM Tutoring System with Centralized Learner Modeling](https://mlsanity.com/paper/2512.18669/) (2025)
- [DrawSim-PD: Simulating Student Science Drawings to Support NGSS-Aligned Teacher Diagnostic Reasoning](https://mlsanity.com/paper/2602.01578/) (2026)
- [StudentSim: Training LLM-based Student Simulators](https://mlsanity.com/paper/2609.01591/) (2026)
- [Tackling Device Data Distribution Real-time Shift via Prototype-based Parameter Editing](https://mlsanity.com/paper/2509.06552/) (2025)
- [Cognitive-Level Adaptive Generation via Capability-Aware Retrieval and Style Adaptation](https://mlsanity.com/paper/2509.19336/) (2025)
- [DebugTA: An LLM-Based Agent for Simplifying Debugging and Teaching in Programming Education](https://mlsanity.com/paper/2510.11076/) (2025)
- [CogEvolution: A Human-like Generative Educational Agent to Simulate Student's Cognitive Evolution](https://mlsanity.com/paper/2604.14786/) (2026)
- [CustomerSim: Benchmarking and Aligning Multimodal Language Models as Retail User Simulators](https://mlsanity.com/paper/2605.08334/) (2026)
- [Are Agents Ready to Teach? A Multi-Stage Benchmark for Real-World Teaching Workflows](https://mlsanity.com/paper/2605.14322/) (2026)
- [Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems](https://mlsanity.com/paper/2606.08030/) (2026)
- [Simulating Students' Java Programming Errors with Large Language Models](https://mlsanity.com/paper/2606.14113/) (2026)
- [CogGuard: Cognitive and Operational Profiling for Proactive Warning in Edge Intelligent Services](https://mlsanity.com/paper/2606.15199/) (2026)
- [Aligning LLM-Simulated and Human Examinees for Psychometric Calibration: A Cognitive Diagnostic Profiling Approach](https://mlsanity.com/paper/2607.26317/) (2026)
- [From Learner Behavior to Reusable Skills for Effective and Efficient Learner Simulation](https://mlsanity.com/paper/2609.37157/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are revolutionizing education, with LLM-based agents playing a key role in simulating student behavior. A major challenge in student simulation is modeling the diverse learning patterns of students at various cognitive levels. However, current LLMs, typically trained as ``helpful assistants'', target at generating perfect responses. As a result, they struggle to simulate students with diverse cognitive abilities, as they often produce overly advanced answers, missing the natural imperfections that characterize student learning and resulting in unrealistic simulations. To address this issue, we propose a training-free framework for student simulation. We begin by constructing a cognitive prototype for each student using a knowledge graph, which captures their understanding of concepts from past learning records. This prototype is then mapped to new tasks to predict student performance. Next, we simulate student solutions based on these predictions and iteratively refine them using a beam search method to better replicate realistic mistakes. To validate our approach, we construct the textttStudent100 dataset, consisting of 100 students working on Python programming and 5,000 learning records. Experimental results show that our method consistently outperforms baseline models, achieving 100% improvement in simulation accuracy.