# LLM-based Cognitive Models of Students with Misconceptions

arXiv: https://arxiv.org/abs/2410.12294 · HTML: https://mlsanity.com/paper/2410.12294/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 17 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 2 of 2)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)

## Built on by (most cited first, 16 of 16)

- [Learning to Make MISTAKEs: Modeling Incorrect Student Thinking And Key Errors](https://mlsanity.com/paper/2510.11502/) (2025)
- [Embracing Imperfection: Simulating Students with Diverse Cognitive Levels Using LLM-based Agents](https://mlsanity.com/paper/2505.19997/) (2025)
- [Simulated Students in Tutoring Dialogues: Substance or Illusion?](https://mlsanity.com/paper/2601.04025/) (2026)
- [Do LLMs Make Mistakes Like Students? Exploring Natural Alignment between Language Models and Human Error Patterns](https://mlsanity.com/paper/2502.15140/) (2025)
- [Towards Valid Student Simulation with Large Language Models](https://mlsanity.com/paper/2601.05473/) (2026)
- [FoundationalASSIST: An Educational Dataset for Foundational Knowledge Tracing and Pedagogical Grounding of LLMs](https://mlsanity.com/paper/2602.00070/) (2026)
- [Can LLMs Reliably Simulate Real Students' Abilities in Mathematics and Reading Comprehension?](https://mlsanity.com/paper/2507.08232/) (2025)
- [Tailoring Diagnostic Modeling to Individual Learners: Personalized Distractor Generation via MCTS-Guided Reasoning Reconstruction](https://mlsanity.com/paper/2508.11184/) (2025)
- [LLMs Struggle to Measure What Distinguishes Students of Different Proficiency Levels: A Study of Item Discrimination in Reading Comprehension Assessment](https://mlsanity.com/paper/2606.18709/) (2026)
- [ParaStudent: Closing the Sim2Real Gap in User Simulators for AI Tutor Evaluation](https://mlsanity.com/paper/2507.12674/) (2025)
- [PEARL: Training Socratic Tutors with Pedagogically Aligned Reinforcement Learning](https://mlsanity.com/paper/2605.29582/) (2026)
- [When Helpfulness Becomes Sycophancy: Sycophancy is a Boundary Failure Between Social Alignment and Epistemic Integrity in Large Language Models](https://mlsanity.com/paper/2605.05403/) (2026)
- [Simulating Students or Sycophantic Problem Solving? On Misconception Faithfulness of LLM Simulators](https://mlsanity.com/paper/2605.12748/) (2026)
- [Taxonomy-Targeted Error Generation for Quantitative Reasoning](https://mlsanity.com/paper/2605.29007/) (2026)
- [From Triggers to Emotions: A CPM-Grounded Appraisal Multi-Agent for Dynamic Emotional Evolution in Persona-Based Dialogue](https://mlsanity.com/paper/2607.07824/) (2026)
- ["Act Like a 5th Grader" is Not Enough: Bounding Knowledge in LLM-Based User Simulators](https://mlsanity.com/paper/2608.30033/) (2026)

## Abstract (arXiv)

Accurately modeling student cognition is crucial for developing effective AI-driven educational technologies. A key challenge is creating realistic student models that satisfy two essential properties: (1) accurately replicating specific misconceptions, and (2) correctly solving problems where these misconceptions are not applicable. This dual requirement reflects the complex nature of student understanding, where misconceptions coexist with correct knowledge. This paper investigates whether Large Language Models (LLMs) can be instruction-tuned to meet this dual requirement and effectively simulate student thinking in algebra. We introduce MalAlgoPy, a novel Python library that generates datasets reflecting authentic student solution patterns through a graph-based representation of algebraic problem-solving. Utilizing MalAlgoPy, we define and examine Cognitive Student Models (CSMs) - LLMs instruction tuned to faithfully emulate realistic student behavior. Our findings reveal that LLMs trained on misconception examples can efficiently learn to replicate errors. However, the training diminishes the model's ability to solve problems correctly, particularly for problem types where the misconceptions are not applicable, thus failing to satisfy second property of CSMs. We demonstrate that by carefully calibrating the ratio of correct to misconception examples in the training data - sometimes as low as 0.25 - it is possible to develop CSMs that satisfy both properties. Our insights enhance our understanding of AI-based student models and pave the way for effective adaptive learning systems.