# Learning to Make MISTAKEs: Modeling Incorrect Student Thinking And Key Errors

arXiv: https://arxiv.org/abs/2510.11502 · HTML: https://mlsanity.com/paper/2510.11502/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 20 of 20)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [One Embedder, Any Task: Instruction-Finetuned Text Embeddings](https://mlsanity.com/paper/2212.09741/) (2022)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [LLM Agents Grounded in Self-Reports Enable General-Purpose Simulation of Individuals](https://mlsanity.com/paper/2411.10109/) (2024)
- [MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems](https://mlsanity.com/paper/2305.14536/) (2023)
- [Generative Students: Using LLM-Simulated Student Profiles to Support Question Item Evaluation](https://mlsanity.com/paper/2405.11591/) (2024)
- [Exploring Knowledge Tracing in Tutor-Student Dialogues using LLMs](https://mlsanity.com/paper/2409.16490/) (2024)
- [Stepwise Verification and Remediation of Student Reasoning Errors with Large Language Model Tutors](https://mlsanity.com/paper/2407.09136/) (2024)
- [Automated Distractor and Feedback Generation for Math Multiple-choice Questions via In-context Learning](https://mlsanity.com/paper/2308.03234/) (2023)
- [Training Turn-by-Turn Verifiers for Dialogue Tutoring Agents: The Curious Case of LLMs as Your Coding Tutors](https://mlsanity.com/paper/2502.13311/) (2025)
- [DrawEduMath: Evaluating Vision Language Models with Expert-Annotated Students' Hand-Drawn Math Images](https://mlsanity.com/paper/2501.14877/) (2025)
- [LLM-based Cognitive Models of Students with Misconceptions](https://mlsanity.com/paper/2410.12294/) (2024)
- [Exploring Automated Distractor Generation for Math Multiple-choice Questions via Large Language Models](https://mlsanity.com/paper/2404.02124/) (2024)
- [Toward In-Context Teaching: Adapting Examples to Students' Misconceptions](https://mlsanity.com/paper/2405.04495/) (2024)
- [Improving Automated Distractor Generation for Math Multiple-choice Questions with Overgenerate-and-rank](https://mlsanity.com/paper/2405.05144/) (2024)
- [MalAlgoQA: Pedagogical Evaluation of Counterfactual Reasoning in Large Language Models and Implications for AI in Education](https://mlsanity.com/paper/2407.00938/) (2024)
- [Language Modeling with Latent Situations](https://mlsanity.com/paper/2212.10012/) (2022)

## Built on by (most cited first, 20 of 20)

- [τ-Knowledge: Evaluating Conversational Agents over Unstructured Knowledge](https://mlsanity.com/paper/2603.04370/) (2026)
- [HumanLM: Simulating Users with State Alignment Beats Response Imitation](https://mlsanity.com/paper/2603.03303/) (2026)
- [Simulated Students in Tutoring Dialogues: Substance or Illusion?](https://mlsanity.com/paper/2601.04025/) (2026)
- [OdysSim: Building Foundation Models for Human Behavior Simulation](https://mlsanity.com/paper/2606.14199/) (2026)
- [Towards Valid Student Simulation with Large Language Models](https://mlsanity.com/paper/2601.05473/) (2026)
- [Reinforcing Human Behavior Simulation via Verbal Feedback](https://mlsanity.com/paper/2605.20506/) (2026)
- [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)
- [Steer Model beyond Assistant: Controlling System Prompt Strength via Contrastive Decoding](https://mlsanity.com/paper/2601.06403/) (2026)
- [Misconception Diagnosis From Student-Tutor Dialogue: Generate, Retrieve, Rerank](https://mlsanity.com/paper/2602.02414/) (2026)
- [The Aftermath of DrawEduMath: Vision Language Models Underperform with Struggling Students and Misdiagnose Errors](https://mlsanity.com/paper/2603.00925/) (2026)
- [Can LLMs Model Incorrect Student Reasoning? A Case Study on Distractor Generation](https://mlsanity.com/paper/2603.15547/) (2026)
- [INSIDE the Student's Mind: Jointly Modeling Latent Reasoning and Action in LLM Student Simulators](https://mlsanity.com/paper/2608.10492/) (2026)
- [KnowSim: Evaluating Information Calibration in LLM Assistants with User Simulators that Learn](https://mlsanity.com/paper/2608.17150/) (2026)
- [XYBench: Can LLMs Respond Pragmatically to Queries with Misconceptions?](https://mlsanity.com/paper/2609.06842/) (2026)
- [CustomerSim: Benchmarking and Aligning Multimodal Language Models as Retail User Simulators](https://mlsanity.com/paper/2605.08334/) (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)
- [AI Assistants Overassist](https://mlsanity.com/paper/2607.21306/) (2026)
- [A Dataset for Modeling Iterative Problem-Solving](https://mlsanity.com/paper/2609.00940/) (2026)
- [Socio-Foundation: A Model for Generalizable Individual Behavior Simulation via Hierarchical Capability Distillation](https://mlsanity.com/paper/2610.08967/) (2026)

## Abstract (arXiv)

Research on reasoning in language models (LMs) predominantly focuses on improving the correctness of their outputs. But some important applications require modeling reasoning patterns that are incorrect. For example, automated systems that can reason about and simulate student errors are useful for providing real-time feedback in the classroom or offline practice for educators-in-training. This paper presents a new method, MISTAKE, that (1) constructs high-quality synthetic examples of reasoning errors by leveraging cycle consistency between incorrect answers and latent misconceptions; and (2) uses the generated data to learn models for student simulation, misconception classification, and answer generation. We evaluate MISTAKE on three educational tasks and find that it results in (1) higher accuracy when simulating incorrect student answers based on specific misconceptions, (2) increased performance inferring latent misconceptions from observed incorrect answers, and (3) higher alignment with expert-written distractor answers when generating incorrect answers (e.g., for multiple-choice tests).