# Simulating Students or Sycophantic Problem Solving? On Misconception Faithfulness of LLM Simulators

arXiv: https://arxiv.org/abs/2605.12748 · HTML: https://mlsanity.com/paper/2605.12748/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Deep Knowledge Tracing](https://mlsanity.com/paper/1506.05908/) (2015)
- [MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems](https://mlsanity.com/paper/2305.14536/) (2023)
- [qDKT: Question-centric Deep Knowledge Tracing](https://mlsanity.com/paper/2005.12442/) (2020)
- [Learning to Make MISTAKEs: Modeling Incorrect Student Thinking And Key Errors](https://mlsanity.com/paper/2510.11502/) (2025)
- [Simulated Students in Tutoring Dialogues: Substance or Illusion?](https://mlsanity.com/paper/2601.04025/) (2026)
- [Prompt Chaining or Stepwise Prompt? Refinement in Text Summarization](https://mlsanity.com/paper/2406.00507/) (2024)
- [Leveraging generative artificial intelligence to simulate student learning behavior](https://mlsanity.com/paper/2310.19206/) (2023)
- [LLM-based Cognitive Models of Students with Misconceptions](https://mlsanity.com/paper/2410.12294/) (2024)
- [Novice Learner and Expert Tutor: Evaluating Math Reasoning Abilities of Large Language Models with Misconceptions](https://mlsanity.com/paper/2310.02439/) (2023)
- [TutorUp: What If Your Students Were Simulated? Training Tutors to Address Engagement Challenges in Online Learning](https://mlsanity.com/paper/2502.16178/) (2025)
- [DiVERT: Distractor Generation with Variational Errors Represented as Text for Math Multiple-choice Questions](https://mlsanity.com/paper/2406.19356/) (2024)
- [LookAlike: Consistent Distractor Generation in Math MCQs](https://mlsanity.com/paper/2505.01903/) (2025)
- [Exploring Iterative Controllable Summarization with Large Language Models](https://mlsanity.com/paper/2411.12460/) (2024)
- [MalruleLib: Large-Scale Executable Misconception Reasoning with Step Traces for Modeling Student Thinking in Mathematics](https://mlsanity.com/paper/2601.03217/) (2026)

## Abstract (arXiv)

Large language models (LLMs) can fluently generate student-like responses, making them attractive as simulated students for training and evaluating AI tutors and human educators. Yet such simulators are typically evaluated by output similarity to real students, not by whether they behave like students with coherent misconceptions during interaction. We introduce a controlled framework for evaluating misconception faithfulness, whether a simulator maintains a misconception-driven belief state and updates selectively when feedback addresses the underlying misconception. Central to our framework is a misconception-contrastive feedback protocol that compares targeted feedback against two controls: misaligned feedback (targeting a different but plausible misconception) and generic feedback (only identifying answer is wrong). We propose Selective Flip Score (SFS), which quantifies how much more often a simulator flips its answer under targeted feedback than under contrastive controls. Across seven LLMs (4B-120B), multiple datasets, and prompting strategies, simulators exhibit near-zero SFS, correcting their answers at similarly high rates regardless of feedback relevance. Further analyses reveal a sycophantic failure mode: models behave less like students with misconceptions but more like problem-solvers who treat any corrective signal as a cue to abandon the simulated belief and re-solve from internal knowledge. To address this, we develop a post-training pipeline spanning supervised fine-tuning (SFT), preference optimization, and reinforcement learning (RL) with an SFS-aligned reward; SFT yields notable gains up to +0.56, and SFS-aligned RL provides more consistent improvements than preference optimization. Our results establish misconception faithfulness as a challenging yet trainable property, motivating a shift from static output matching toward interactive, belief-aware student modeling.