The flexible and generalized nature of large language models has allowed for their application in a wide array of language-based domains.Much like their human contemporaries, these models are capable of engaging in discussions and debates as a means of improving answer quality.We first take a theoretical approach to analyzing debate and provide a framework through which debate can be mathematically examined.Building on this framework, we provide several theoretical results for multi-agent debate.In particular, we demonstrate that similar model capabilities, or similar model responses, can result in static debate dynamics where the debate procedure simply converges to the majority opinion. When this majority opinion is the result of a common misconception (ingrained in the models through shared training data) debate is likely to converge to answers associated with that common misconception.Using insights from our theoretical results we then propose three interventions which improve the efficacy of debate. For each intervention, we provide theoretical results demonstrating how debate is improved.We also demonstrate that these interventions result in better performance on four common benchmark tasks.

We first take a theoretical approach to analyzing debate and provide a framework through which debate can be mathematically examined. Building on this framework, we provide several theoretical results for multi-agent debate.

Generating high-quality MCQs, especially those targeting diverse cognitive levels and incorporating common misconceptions into distractor design, is time-consuming and expertise-intensive, making manual creation impractical at scale. Current automated approaches typically generate questions at lower cognitive levels and fail to incorporate domain-specific misconceptions. This paper presents a hierarchical concept map-based framework that provides structured knowledge to guide LLMs in generating MCQs with distractors. We chose high-school physics as our test domain and began by developing a hierarchical concept map covering major Physics topics and their interconnections with an efficient database design. Next, through an automated pipeline, topic-relevant sections of these concept maps are retrieved to serve as a structured context for the LLM to generate questions and distractors that specifically target common misconceptions. Lastly, an automated validation is completed to ensure that the generated MCQs meet the requirements provided. We evaluate our framework against two baseline approaches: a base LLM and a RAG-based generation. We conducted expert evaluations and student assessments of the generated MCQs. Expert evaluation shows that our method significantly outperforms the baseline approaches, achieving a success rate of 75.20% in meeting all quality criteria compared to approximately 37% for both baseline methods. Student assessment data reveal that our concept map-driven approach achieved a significantly lower guess success rate of 28.05% compared to 37.10% for the baselines, indicating a more effective assessment of conceptual understanding. The results demonstrate that our concept map-based approach enables robust assessment across cognitive levels and instant identification of conceptual gaps, facilitating faster feedback loops and targeted interventions at scale.

In the aftermath of COVID-19, many universities implemented supplementary "reinforcement" roles to support students in demanding courses. Although the name for such roles may differ between institutions, the underlying idea of providing structured supplementary support is common. However, these roles were often poorly defined, lacking structured materials, pedagogical oversight, and integration with the core teaching team. This paper reports on the redesign of reinforcement sessions in a challenging undergraduate course on formal methods and computational models, using a large language model (LLM) as a reflective planning tool. The LLM was prompted to simulate the perspective of a second-year student, enabling the identification of conceptual bottlenecks, gaps in intuition, and likely reasoning breakdowns before classroom delivery. These insights informed a structured, repeatable session format combining targeted review, collaborative examples, independent student work, and guided walkthroughs. Conducted over a single semester, the intervention received positive student feedback, indicating increased confidence, reduced anxiety, and improved clarity, particularly in abstract topics such as the pumping lemma and formal language expressive power comparisons. The findings suggest that reflective, instructor-facing use of LLMs can enhance pedagogical design in theoretically dense domains and may be adaptable to other cognitively demanding computer science courses.

Detecting student misconceptions in open-ended responses is a longstanding challenge, demanding semantic precision and logical reasoning. We propose MiRAGE - Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion, a novel framework for automated misconception detection in mathematics. MiRAGE operates in three stages: (1) a Retrieval module narrows a large candidate pool to a semantically relevant subset; (2) a Reasoning module employs chain-of-thought generation to expose logical inconsistencies in student solutions; and (3) a Reranking module refines predictions by aligning them with the reasoning. These components are unified through an ensemble-fusion strategy that enhances robustness and interpretability. On mathematics datasets, MiRAGE achieves Mean Average Precision scores of 0.82/0.92/0.93 at levels 1/3/5, consistently outperforming individual modules. By coupling retrieval guidance with multi-stage reasoning, MiRAGE reduces dependence on large-scale language models while delivering a scalable and effective solution for educational assessment.

Cancer patients are increasingly turning to large language models (LLMs) for medical information, making it critical to assess how well these models handle complex, personalized questions. However, current medical benchmarks focus on medical exams or consumer-searched questions and do not evaluate LLMs on real patient questions with patient details. In this paper, we first have three hematology-oncology physicians evaluate cancer-related questions drawn from real patients. While LLM responses are generally accurate, the models frequently fail to recognize or address false presuppositions in the questions, posing risks to safe medical decision-making. To study this limitation systematically, we introduce Cancer-Myth, an expert-verified adversarial dataset of 585 cancer-related questions with false presuppositions. On this benchmark, no frontier LLM -- including GPT-5, Gemini-2.5-Pro, and Claude-4-Sonnet -- corrects these false presuppositions more than $43\%$ of the time. To study mitigation strategies, we further construct a 150-question Cancer-Myth-NFP set, in which physicians confirm the absence of false presuppositions. We find typical mitigation strategies, such as adding precautionary prompts with GEPA optimization, can raise accuracy on Cancer-Myth to $80\%$, but at the cost of misidentifying presuppositions in $41\%$ of Cancer-Myth-NFP questions and causing a $10\%$ relative performance drop on other medical benchmarks. These findings highlight a critical gap in the reliability of LLMs, show that prompting alone is not a reliable remedy for false presuppositions, and underscore the need for more robust safeguards in medical AI systems.

We study how prompt-level inductive biases influence the cognitive behavior of large language models (LLMs) in instructional dialogue. We introduce a symbolic scaffolding method paired with a short-term memory schema designed to promote adaptive, structured reasoning in Socratic tutoring. Using controlled ablation across five system variants, we evaluate model outputs via expert-designed rubrics covering scaffolding, responsiveness, symbolic reasoning, and conversational memory. We present preliminary results using an LLM-based evaluation framework aligned to a cognitively grounded rubric. This enables scalable, systematic comparisons across architectural variants in early-stage experimentation. The preliminary results show that our full system consistently outperforms baseline variants. Analysis reveals that removing memory or symbolic structure degrades key cognitive behaviors, including abstraction, adaptive probing, and conceptual continuity. These findings support a processing-level account in which prompt-level cognitive scaffolds can reliably shape emergent instructional strategies in LLMs.

Programming assistants powered by large language models (LLMs) have become widely available, with conversational assistants like ChatGPT proving particularly accessible to less experienced programmers. However, the varied capabilities of these tools across model versions and the mixed availability of extensions that enable web search, code execution, or retrieval-augmented generation create opportunities for user misconceptions about what systems can and cannot do. Such misconceptions may lead to over-reliance, unproductive practices, or insufficient quality control in LLM-assisted programming. Here, we aim to characterize misconceptions that users of conversational LLM-based assistants may have in programming contexts. Using a two-phase approach, we first brainstorm and catalog user misconceptions that may occur, and then conduct a qualitative analysis to examine whether these conceptual issues surface in naturalistic Python-programming conversations with an LLM-based chatbot drawn from an openly available dataset. Indeed, we see evidence that some users have misplaced expectations about the availability of LLM-based chatbot features like web access, code execution, or non-text output generation. We also see potential evidence for deeper conceptual issues around the scope of information required to debug, validate, and optimize programs. Our findings reinforce the need for designing LLM-based tools that more clearly communicate their programming capabilities to users.

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).

When learning to code, students often develop misconceptions about various programming language concepts. These can not only lead to bugs or inefficient code, but also slow down the learning of related concepts. In this paper, we introduce McMining, the task of mining programming misconceptions from samples of code from a student. To enable the training and evaluation of McMining systems, we develop an extensible benchmark dataset of misconceptions together with a large set of code samples where these misconceptions are manifested. We then introduce two LLM-based McMiner approaches and through extensive evaluations show that models from the Gemini, Claude, and GPT families are effective at discovering misconceptions in student code.