Learning to Make MISTAKEs: Modeling Incorrect Student Thinking And Key Errors
On the map: LLM reasoning → Mathematical reasoning
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).
Key facts. Cited by 19 papers in the map (data through 7 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.
Builds on
20 of 32 references.
Closest ancestors · 2
Same direction, newest first
- 2024Stepwise Verification and Remediation of Student Reasoning Errors with Large Language Model Tutors12 Jul
- 2023MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems23 May
Other references · 18
- 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,084
- 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
- 2022STaR: Bootstrapping Reasoning With Reasoningcited by 895
- 2021Show Your Work: Scratchpads for Intermediate Computation with Language Modelscited by 871
- 2022One Embedder, Any Task: Instruction-Finetuned Text Embeddingscited by 329
- 2024Quiet-STaR: Language Models Can Teach Themselves to Think Before Speakingcited by 292
- 2024LLM Agents Grounded in Self-Reports Enable General-Purpose Simulation of Individualscited by 235
- 2024Generative Students: Using LLM-Simulated Student Profiles to Support Question Item Evaluationcited by 56
- 2024Exploring Knowledge Tracing in Tutor-Student Dialogues using LLMscited by 44
- 2023Automated Distractor and Feedback Generation for Math Multiple-choice Questions via In-context Learningcited by 24
- 2025DrawEduMath: Evaluating Vision Language Models with Expert-Annotated Students' Hand-Drawn Math Imagescited by 17
- 2025Training Turn-by-Turn Verifiers for Dialogue Tutoring Agents: The Curious Case of LLMs as Your Coding Tutorscited by 17
6 more
- 2024LLM-based Cognitive Models of Students with Misconceptionscited by 16
- 2024Exploring Automated Distractor Generation for Math Multiple-choice Questions via Large Language Modelscited by 15
- 2024Toward In-Context Teaching: Adapting Examples to Students' Misconceptionscited by 12
- 2024Improving Automated Distractor Generation for Math Multiple-choice Questions with Overgenerate-and-rankcited by 12
- 2024MalAlgoQA: Pedagogical Evaluation of Counterfactual Reasoning in Large Language Models and Implications for AI in Educationcited by 8
- 2022Language Modeling with Latent Situationscited by 6
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Citing papers per year: 2026: 19.
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- 2026τ-Knowledge: Evaluating Conversational Agents over Unstructured Knowledgecited by 35
- 2026HumanLM: Simulating Users with State Alignment Beats Response Imitationcited by 31
- 2026Simulated Students in Tutoring Dialogues: Substance or Illusion?cited by 14
- 2026OdysSim: Building Foundation Models for Human Behavior Simulationcited by 8
- 2026Towards Valid Student Simulation with Large Language Modelscited by 7
- 2026Reinforcing Human Behavior Simulation via Verbal Feedbackcited by 4
- 2026LLMs Struggle to Measure What Distinguishes Students of Different Proficiency Levels: A Study of Item Discrimination in Reading Comprehension Assessmentcited by 2
- 2026Steer Model beyond Assistant: Controlling System Prompt Strength via Contrastive Decodingcited by 1
- 2026Misconception Diagnosis From Student-Tutor Dialogue: Generate, Retrieve, Rerankcited by 1
- 2026The Aftermath of DrawEduMath: Vision Language Models Underperform with Struggling Students and Misdiagnose Errorscited by 1
- 2026Can LLMs Model Incorrect Student Reasoning? A Case Study on Distractor Generationcited by 1
- 2026INSIDE the Student's Mind: Jointly Modeling Latent Reasoning and Action in LLM Student Simulatorscited by 1
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- 2026XYBench: Can LLMs Respond Pragmatically to Queries with Misconceptions?cited by 1
- 2026CustomerSim: Benchmarking and Aligning Multimodal Language Models as Retail User Simulatorscited by 0
- 2026Simulating Students or Sycophantic Problem Solving? On Misconception Faithfulness of LLM Simulatorscited by 0
- 2026Taxonomy-Targeted Error Generation for Quantitative Reasoningcited by 0
- 2026AI Assistants Overassistcited by 0
- 2026KnowSim: Evaluating Information Calibration in LLM Assistants with User Simulators that Learncited by 0
- 2026A Dataset for Modeling Iterative Problem-Solvingcited by 0
- 2026XYBench: Can LLMs Respond Pragmatically to Queries with Misconceptions?6 Sep 2026
- 2026A Dataset for Modeling Iterative Problem-Solving1 Sep 2026
- 2026KnowSim: Evaluating Information Calibration in LLM Assistants with User Simulators that Learn17 Aug 2026
- 2026INSIDE the Student's Mind: Jointly Modeling Latent Reasoning and Action in LLM Student Simulators11 Aug 2026
- 2026AI Assistants Overassist23 Jul 2026
- 2026LLMs Struggle to Measure What Distinguishes Students of Different Proficiency Levels: A Study of Item Discrimination in Reading Comprehension Assessment17 Jun 2026
- 2026OdysSim: Building Foundation Models for Human Behavior Simulation12 Jun 2026
- 2026Taxonomy-Targeted Error Generation for Quantitative Reasoning27 May 2026
- 2026Reinforcing Human Behavior Simulation via Verbal Feedback19 May 2026
- 2026Simulating Students or Sycophantic Problem Solving? On Misconception Faithfulness of LLM Simulators12 May 2026
- 2026CustomerSim: Benchmarking and Aligning Multimodal Language Models as Retail User Simulators8 May 2026
- 2026Can LLMs Model Incorrect Student Reasoning? A Case Study on Distractor Generation16 Mar 2026
7 more
- 2026τ-Knowledge: Evaluating Conversational Agents over Unstructured Knowledge4 Mar 2026
- 2026The Aftermath of DrawEduMath: Vision Language Models Underperform with Struggling Students and Misdiagnose Errors1 Mar 2026
- 2026HumanLM: Simulating Users with State Alignment Beats Response Imitation7 Feb 2026
- 2026Misconception Diagnosis From Student-Tutor Dialogue: Generate, Retrieve, Rerank2 Feb 2026
- 2026Steer Model beyond Assistant: Controlling System Prompt Strength via Contrastive Decoding10 Jan 2026
- 2026Towards Valid Student Simulation with Large Language Models9 Jan 2026
- 2026Simulated Students in Tutoring Dialogues: Substance or Illusion?7 Jan 2026
- 2026τ-Knowledge: Evaluating Conversational Agents over Unstructured Knowledgecited by 35
- 2026HumanLM: Simulating Users with State Alignment Beats Response Imitationcited by 31
- 2026Simulated Students in Tutoring Dialogues: Substance or Illusion?cited by 14
- 2026OdysSim: Building Foundation Models for Human Behavior Simulationcited by 8
- 2026Towards Valid Student Simulation with Large Language Modelscited by 7
- 2026Reinforcing Human Behavior Simulation via Verbal Feedbackcited by 4
- 2026LLMs Struggle to Measure What Distinguishes Students of Different Proficiency Levels: A Study of Item Discrimination in Reading Comprehension Assessmentcited by 2
- 2026Steer Model beyond Assistant: Controlling System Prompt Strength via Contrastive Decodingcited by 1
- 2026Misconception Diagnosis From Student-Tutor Dialogue: Generate, Retrieve, Rerankcited by 1
- 2026XYBench: Can LLMs Respond Pragmatically to Queries with Misconceptions?cited by 1
- 2026CustomerSim: Benchmarking and Aligning Multimodal Language Models as Retail User Simulatorscited by 0
- 2026Simulating Students or Sycophantic Problem Solving? On Misconception Faithfulness of LLM Simulatorscited by 0
12 most cited of 15 All 15 (JSON)
- 2026XYBench: Can LLMs Respond Pragmatically to Queries with Misconceptions?6 Sep 2026
- 2026A Dataset for Modeling Iterative Problem-Solving1 Sep 2026
- 2026KnowSim: Evaluating Information Calibration in LLM Assistants with User Simulators that Learn17 Aug 2026
- 2026AI Assistants Overassist23 Jul 2026
- 2026LLMs Struggle to Measure What Distinguishes Students of Different Proficiency Levels: A Study of Item Discrimination in Reading Comprehension Assessment17 Jun 2026
- 2026OdysSim: Building Foundation Models for Human Behavior Simulation12 Jun 2026
- 2026Reinforcing Human Behavior Simulation via Verbal Feedback19 May 2026
- 2026Simulating Students or Sycophantic Problem Solving? On Misconception Faithfulness of LLM Simulators12 May 2026
- 2026CustomerSim: Benchmarking and Aligning Multimodal Language Models as Retail User Simulators8 May 2026
- 2026τ-Knowledge: Evaluating Conversational Agents over Unstructured Knowledge4 Mar 2026
- 2026HumanLM: Simulating Users with State Alignment Beats Response Imitation7 Feb 2026
- 2026Misconception Diagnosis From Student-Tutor Dialogue: Generate, Retrieve, Rerank2 Feb 2026
12 newest of 15 All 15 (JSON)
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- 2025From Correctness to Comprehension: AI Agents for Personalized Error Diagnosis in Education
- 2023Novice Learner and Expert Tutor: Evaluating Math Reasoning Abilities of Large Language Models with Misconceptions
- 2025No Need for Explanations: LLMs can implicitly learn from mistakes in-context
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- 2024Exposing the Achilles' Heel: Evaluating LLMs Ability to Handle Mistakes in Mathematical Reasoning