Evaluating GPT-4 at Grading Handwritten Solutions in Math Exams

Recent advances in generative artificial intelligence (AI) have shown promise in accurately grading open-ended student responses. However, few prior works have explored grading handwritten responses due to a lack of data and the challenge of combining visual and textual information. In this work, we leverage state-of-the-art multi-modal AI models, in particular GPT-4o, to automatically grade handwritten responses to college-level math exams. Using real student responses to questions in a probability theory exam, we evaluate GPT-4o's alignment with ground-truth scores from human graders using various prompting techniques. We find that while providing rubrics improves alignment, the model's overall accuracy is still too low for real-world settings, showing there is significant room for growth in this task.

Exploring Knowledge Tracing in Tutor-Student Dialogues

Recent advances in large language models (LLMs) have led to the development of artificial intelligence (AI)-powered tutoring chatbots, showing promise in providing broad access to high-quality personalized education. Existing works have primarily studied how to make LLMs follow tutoring principles but not how to model student behavior in dialogues. However, analyzing student dialogue turns can serve as a formative assessment, since open-ended student discourse may indicate their knowledge levels and reveal specific misconceptions. In this work, we present a first attempt at performing knowledge tracing (KT) in tutor-student dialogues. We propose LLM prompting methods to identify the knowledge components/skills involved in each dialogue turn and diagnose whether the student responds correctly to the tutor, and verify the LLM's effectiveness via an expert human evaluation. We then apply a range of KT methods on the resulting labeled data to track student knowledge levels over an entire dialogue. We conduct experiments on two tutoring dialogue datasets, and show that a novel yet simple LLM-based method, LLMKT, significantly outperforms existing KT methods in predicting student response correctness in dialogues. We perform extensive qualitative analyses to highlight the challenges in dialogue KT and outline multiple avenues for future work.

Exploring Automated Keyword Mnemonics Generation with Large Language Models via Overgenerate-and-Rank

In this paper, we study an under-explored area of language and vocabulary learning: keyword mnemonics, a technique for memorizing vocabulary through memorable associations with a target word via a verbal cue. Typically, creating verbal cues requires extensive human effort and is quite time-consuming, necessitating an automated method that is more scalable. We propose a novel overgenerate-and-rank method via prompting large language models (LLMs) to generate verbal cues and then ranking them according to psycholinguistic measures and takeaways from a pilot user study. To assess cue quality, we conduct both an automated evaluation of imageability and coherence, as well as a human evaluation involving English teachers and learners. Results show that LLM-generated mnemonics are comparable to human-generated ones in terms of imageability, coherence, and perceived usefulness, but there remains plenty of room for improvement due to the diversity in background and preference among language learners.

DiVERT: Distractor Generation with Variational Errors Represented as Text for Math Multiple-choice Questions

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.

Interpreting Latent Student Knowledge Representations in Programming Assignments

Recent advances in artificial intelligence for education leverage generative large language models, including using them to predict open-ended student responses rather than their correctness only. However, the black-box nature of these models limits the interpretability of the learned student knowledge representations. In this paper, we conduct a first exploration into interpreting latent student knowledge representations by presenting InfoOIRT, an Information regularized Open-ended Item Response Theory model, which encourages the latent student knowledge states to be interpretable while being able to generate student-written code for open-ended programming questions. InfoOIRT maximizes the mutual information between a fixed subset of latent knowledge states enforced with simple prior distributions and generated student code, which encourages the model to learn disentangled representations of salient syntactic and semantic code features including syntactic styles, mastery of programming skills, and code structures. Through experiments on a real-world programming education dataset, we show that InfoOIRT can both accurately generate student code and lead to interpretable student knowledge representations.

Can Large Language Models Replicate ITS Feedback on Open-Ended Math Questions?

Intelligent Tutoring Systems (ITSs) often contain an automated feedback component, which provides a predefined feedback message to students when they detect a predefined error. To such a feedback component, we often resort to template-based approaches. These approaches require significant effort from human experts to detect a limited number of possible student errors and provide corresponding feedback. This limitation is exemplified in open-ended math questions, where there can be a large number of different incorrect errors. In our work, we examine the capabilities of large language models (LLMs) to generate feedback for open-ended math questions, similar to that of an established ITS that uses a template-based approach. We fine-tune both open-source and proprietary LLMs on real student responses and corresponding ITS-provided feedback. We measure the quality of the generated feedback using text similarity metrics. We find that open-source and proprietary models both show promise in replicating the feedback they see during training, but do not generalize well to previously unseen student errors. These results suggest that despite being able to learn the formatting of feedback, LLMs are not able to fully understand mathematical errors made by students.

Generating Feedback-Ladders for Logical Errors in Programming using Large Language Models

In feedback generation for logical errors in programming assignments, large language model (LLM)-based methods have shown great promise. These methods ask the LLM to generate feedback given the problem statement and a student's (buggy) submission. There are several issues with these types of methods. First, the generated feedback messages are often too direct in revealing the error in the submission and thus diminish valuable opportunities for the student to learn. Second, they do not consider the student's learning context, i.e., their previous submissions, current knowledge, etc. Third, they are not layered since existing methods use a single, shared prompt for all student submissions. In this paper, we explore using LLMs to generate a "feedback-ladder", i.e., multiple levels of feedback for the same problem-submission pair. We evaluate the quality of the generated feedback-ladder via a user study with students, educators, and researchers. We have observed diminishing effectiveness for higher-level feedback and higher-scoring submissions overall in the study. In practice, our method enables teachers to select an appropriate level of feedback to show to a student based on their personal learning context, or in a progressive manner to go more detailed if a higher-level feedback fails to correct the student's error.

Math Multiple Choice Question Generation via Human-Large Language Model Collaboration

Multiple choice questions (MCQs) are a popular method for evaluating students' knowledge due to their efficiency in administration and grading. Crafting high-quality math MCQs is a labor-intensive process that requires educators to formulate precise stems and plausible distractors. Recent advances in large language models (LLMs) have sparked interest in automating MCQ creation, but challenges persist in ensuring mathematical accuracy and addressing student errors. This paper introduces a prototype tool designed to facilitate collaboration between LLMs and educators for streamlining the math MCQ generation process. We conduct a pilot study involving math educators to investigate how the tool can help them simplify the process of crafting high-quality math MCQs. We found that while LLMs can generate well-formulated question stems, their ability to generate distractors that capture common student errors and misconceptions is limited. Nevertheless, a human-AI collaboration has the potential to enhance the efficiency and effectiveness of MCQ generation.

Exploring Automated Distractor Generation for Math Multiple-choice Questions via Large Language Models

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.

Improving the Validity of Automatically Generated Feedback via Reinforcement Learning

Automatically generating feedback via large language models (LLMs) in intelligent tutoring systems and online learning platforms has the potential to improve the learning outcomes of many students. However, both feedback generation and evaluation are challenging: feedback content has to be valid especially in subjects like math, which requires models to understand the problem, the solution, and where the student's error lies. Feedback also has to be pedagogically valid to reflect effective tutoring strategies, such as explaining possible misconceptions and encouraging the student, among other desirable features. In this work, we address both problems of automatically generating and evaluating feedback while considering both correctness and alignment. First, we propose a rubric for evaluating math feedback and show that GPT-4 is able to effectively use it to annotate human-written and LLM-generated feedback. Second, we propose a framework for feedback generation that optimizes both correctness and alignment using reinforcement learning (RL). Specifically, we use GPT-4's annotations to create preferences over feedback pairs in an augmented dataset for training via direct preference optimization (DPO). We show that our methods significantly increase the correctness and alignment of generated feedback with Llama 2, an open-source LLM, qualitatively analyze our generation and evaluation systems using case studies, and outline several areas for future work.