High-quality distractors are crucial to both the assessment and pedagogical value of multiple-choice questions (MCQs), where manually crafting ones that anticipate knowledge deficiencies or misconceptions among real students is difficult. Meanwhile, automated distractor generation, even with the help of large language models (LLMs), remains challenging for subjects like math. It is crucial to not only identify plausible distractors but also understand the error behind them. In this paper, we introduce DiVERT (Distractor Generation with Variational Errors Represented as Text), a novel variational approach that learns an interpretable representation of errors behind distractors in math MCQs. Through experiments on a real-world math MCQ dataset with 1,434 questions used by hundreds of thousands of students, we show that DiVERT, despite using a base open-source LLM with 7B parameters, outperforms state-of-the-art approaches using GPT-4o on downstream distractor generation. We also conduct a human evaluation with math educators and find that DiVERT leads to error labels that are of comparable quality to human-authored ones.

Multiple-choice questions (MCQs) are ubiquitous in almost all levels of education since they are easy to administer, grade, and are a reliable format in assessments and practices. One of the most important aspects of MCQs is the distractors, i.e., incorrect options that are designed to target common errors or misconceptions among real students. To date, the task of crafting high-quality distractors largely remains a labor and time-intensive process for teachers and learning content designers, which has limited scalability. In this work, we study the task of automated distractor generation in the domain of math MCQs and explore a wide variety of large language model (LLM)-based approaches, from in-context learning to fine-tuning. We conduct extensive experiments using a real-world math MCQ dataset and find that although LLMs can generate some mathematically valid distractors, they are less adept at anticipating common errors or misconceptions among real students.

Multiple-choice questions (MCQs) are commonly used across all levels of math education since they can be deployed and graded at a large scale. A critical component of MCQs is the distractors, i.e., incorrect answers crafted to reflect student errors or misconceptions. Automatically generating them in math MCQs, e.g., with large language models, has been challenging. In this work, we propose a novel method to enhance the quality of generated distractors through overgenerate-and-rank, training a ranking model to predict how likely distractors are to be selected by real students. Experimental results on a real-world dataset and human evaluation with math teachers show that our ranking model increases alignment with human-authored distractors, although human-authored ones are still preferred over generated ones.

Automated teaching assistants and chatbots have significant potential to reduce the workload of human instructors, especially for logistics-related question answering, which is important to students yet repetitive for instructors. However, due to privacy concerns, there is a lack of publicly available datasets. We introduce SyllabusQA, an open-source dataset with 63 real course syllabi covering 36 majors, containing 5,078 open-ended course logistics-related question-answer pairs that are diverse in both question types and answer formats. Since many logistics-related questions contain critical information like the date of an exam, it is important to evaluate the factuality of answers. We benchmark several strong baselines on this task, from large language model prompting to retrieval-augmented generation. We introduce Fact-QA, an LLM-based (GPT-4) evaluation metric to evaluate the factuality of predicted answers. We find that despite performing close to humans on traditional metrics of textual similarity, there remains a significant gap between automated approaches and humans in terms of fact precision.

Mathematical language in scientific communications and educational scenarios is important yet relatively understudied compared to natural languages. Recent works on mathematical language focus either on representing stand-alone mathematical expressions, especially in their natural tree format, or mathematical reasoning in pre-trained natural language models. Existing works on jointly modeling and generating natural and mathematical languages simply treat mathematical expressions as text, without accounting for the rigid structural properties of mathematical expressions. In this paper, we propose a series of modifications to existing language models to jointly represent and generate text and math: representing mathematical expressions as sequences of node tokens in their operator tree format, using math symbol and tree position embeddings to preserve the semantic and structural properties of mathematical expressions, and using a constrained decoding method to generate mathematically valid expressions. We ground our modifications in GPT-2, resulting in a model MathGPT, and demonstrate that it outperforms baselines on mathematical expression generation tasks.

Patronizing and condescending language (PCL) is everywhere, but rarely is the focus on its use by media towards vulnerable communities. Accurately detecting PCL of this form is a difficult task due to limited labeled data and how subtle it can be. In this paper, we describe our system for detecting such language which was submitted to SemEval 2022 Task 4: Patronizing and Condescending Language Detection. Our approach uses an ensemble of pre-trained language models, data augmentation, and optimizing the threshold for detection. Experimental results on the evaluation dataset released by the competition hosts show that our work is reliably able to detect PCL, achieving an F1 score of 55.47% on the binary classification task and a macro F1 score of 36.25% on the fine-grained, multi-label detection task.