Modeling student misconceptions in a realistic manner is critical for AI in education. In this work, we examine how large language models (LLMs) reason about misconceptions when generating distractor answers for multiple-choice questions (MCQs), a task that requires producing answers that are incorrect, yet plausible. We introduce a taxonomy over reasoning strategies for distractor generation that is grounded in learning-science literature and empirical observation, which we apply to LLM-generated reasoning traces across math and science MCQs. On the math dataset, we find that models follow a misconception-based process with potentially high diagnostic value: they recover the correct solution, articulate student errors, simulate them, and select plausible candidates. On the science dataset, on the other hand, they tend to follow a less robust approach based on semantic similarity to the correct answer. We find the most frequent failure modes to be that the model is unable to generate a correct solution or that it discards plausible distractor candidates when performing selection. Providing the correct solution in the prompt yields a relative improvement of 6.4% in alignment with human-authored distractors, highlighting the critical role of anchoring distractor generation to the correct solution. Together, our findings offer an interpretable view of how LLMs model incorrect student reasoning.
Personalized tutoring, teacher training, and education research need access to \emph{targeted} synthetic misconceptions, but privacy and IRB constraints make labelled corpora of real student errors scarce. LLMs could in principle generate synthetic errors at scale, but producing an arbitrary wrong answer is easy for a modern LLM while producing one that matches a specified cognitive failure mode is much harder. We present a framework that generates errors targeted to a five-class taxonomy adapted from the revised Bloom's taxonomy, evaluated on questions from the TheoremQA dataset. A Generation Agent (GA) drafts a candidate erroneous solution conditioned on a target class, and an Examination Agent (EA) judges whether the draft is incorrect and class-consistent. The framework yields a reusable recipe for building class-stratified synthetic error datasets where authentic student corpora are unavailable. As a secondary diagnostic, targeted error generation is substantially harder than free-form incorrect-answer generation, and answer-grounding contributes more than expanded examples or external textbook content.
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.
Distractor generation (DG) remains a labor-intensive task that still significantly depends on domain experts. The task focuses on generating plausible yet incorrect options, known as distractors, for multiple-choice questions. A reliable distractor must be contextually relevant to the question and able to mislead examinees through implicit reasoning when identifying the correct answer. While a recent method integrates fine-tuning pre-trained encoder-decoder models with contrastive learning to generate semantically relevant distractors for a given question-answer, it often fails to capture the underlying reasoning process that experts utilize when selecting distractors in benchmarks. In this paper, we explore large language models (LLMs) reasoning for DG through in-context learning with unsupervised semantic retrieval for selecting few-shot examples. We design a rationale-augmented DG framework that jointly generates distractors and their rationales for a given question-answer. Extensive experiments on six benchmarks, with varying average distractor lengths and domains, demonstrate that prompting LLMs with few-shot examples substantially improves the performance compared to recent DG models. It outperforms recent approaches and achieves state-of-the-art results in generating reasoned distractors that align with human-labeled benchmarks.