From Text to Visuals: Using LLMs to Generate Math Diagrams with Vector Graphics

Advances in large language models (LLMs) offer new possibilities for enhancing math education by automating support for both teachers and students. While prior work has focused on generating math problems and high-quality distractors, the role of visualization in math learning remains under-explored. Diagrams are essential for mathematical thinking and problem-solving, yet manually creating them is time-consuming and requires domain-specific expertise, limiting scalability. Recent research on using LLMs to generate Scalable Vector Graphics (SVG) presents a promising approach to automating diagram creation. Unlike pixel-based images, SVGs represent geometric figures using XML, allowing seamless scaling and adaptability. Educational platforms such as Khan Academy and IXL already use SVGs to display math problems and hints. In this paper, we explore the use of LLMs to generate math-related diagrams that accompany textual hints via intermediate SVG representations. We address three research questions: (1) how to automatically generate math diagrams in problem-solving hints and evaluate their quality, (2) whether SVG is an effective intermediate representation for math diagrams, and (3) what prompting strategies and formats are required for LLMs to generate accurate SVG-based diagrams. Our contributions include defining the task of automatically generating SVG-based diagrams for math hints, developing an LLM prompting-based pipeline, and identifying key strategies for improving diagram generation. Additionally, we introduce a Visual Question Answering-based evaluation setup and conduct ablation studies to assess different pipeline variations. By automating the math diagram creation, we aim to provide students and teachers with accurate, conceptually relevant visual aids that enhance problem-solving and learning experiences.

Training LLM-based Tutors to Improve Student Learning Outcomes in Dialogues

Generative artificial intelligence (AI) has the potential to scale up personalized tutoring through large language models (LLMs). Recent AI tutors are adapted for the tutoring task by training or prompting LLMs to follow effective pedagogical principles, though they are not trained to maximize student learning throughout the course of a dialogue. Therefore, they may engage with students in a suboptimal way. We address this limitation by introducing an approach to train LLMs to generate tutor utterances that maximize the likelihood of student correctness, while still encouraging the model to follow good pedagogical practice. Specifically, we generate a set of candidate tutor utterances and score them using (1) an LLM-based student model to predict the chance of correct student responses and (2) a pedagogical rubric evaluated by GPT-4o. We then use the resulting data to train an open-source LLM, Llama 3.1 8B, using direct preference optimization. We show that tutor utterances generated by our model lead to significantly higher chances of correct student responses while maintaining the pedagogical quality of GPT-4o. We also conduct qualitative analyses and a human evaluation to demonstrate that our model generates high quality tutor utterances.

Learning Code-Edit Embedding to Model Student Debugging Behavior

Providing effective feedback for programming assignments in computer science education can be challenging: students solve problems by iteratively submitting code, executing it, and using limited feedback from the compiler or the auto-grader to debug. Analyzing student debugging behavior in this process may reveal important insights into their knowledge and inform better personalized support tools. In this work, we propose an encoder-decoder-based model that learns meaningful code-edit embeddings between consecutive student code submissions, to capture their debugging behavior. Our model leverages information on whether a student code submission passes each test case to fine-tune large language models (LLMs) to learn code editing representations. It enables personalized next-step code suggestions that maintain the student's coding style while improving test case correctness. Our model also enables us to analyze student code-editing patterns to uncover common student errors and debugging behaviors, using clustering techniques. Experimental results on a real-world student code submission dataset demonstrate that our model excels at code reconstruction and personalized code suggestion while revealing interesting patterns in student debugging behavior.

Automated Knowledge Component Generation and Knowledge Tracing for Coding Problems

Knowledge components (KCs) mapped to problems help model student learning, tracking their mastery levels on fine-grained skills thereby facilitating personalized learning and feedback in online learning platforms. However, crafting and tagging KCs to problems, traditionally performed by human domain experts, is highly labor-intensive. We present a fully automated, LLM-based pipeline for KC generation and tagging for open-ended programming problems. We also develop an LLM-based knowledge tracing (KT) framework to leverage these LLM-generated KCs, which we refer to as KCGen-KT. We conduct extensive quantitative and qualitative evaluations validating the effectiveness of KCGen-KT. On a real-world dataset of student code submissions to open-ended programming problems, KCGen-KT outperforms existing KT methods. We investigate the learning curves of generated KCs and show that LLM-generated KCs have a comparable level-of-fit to human-written KCs under the performance factor analysis (PFA) model. We also conduct a human evaluation to show that the KC tagging accuracy of our pipeline is reasonably accurate when compared to that by human domain experts.

Whose story is it? Personalizing story generation by inferring author styles

Personalization has become essential for improving user experience in interactive writing and educational applications, yet its potential in story generation remains largely unexplored. In this work, we propose a novel two-stage pipeline for personalized story generation. Our approach first infers an author's implicit story-writing characteristics from their past work and organizes them into an Author Writing Sheet, inspired by narrative theory. The second stage uses this sheet to simulate the author's persona through tailored persona descriptions and personalized story writing rules. To enable and validate our approach, we construct Mythos, a dataset of 590 stories from 64 authors across five distinct sources that reflect diverse story-writing settings. A head-to-head comparison with a non-personalized baseline demonstrates our pipeline's effectiveness in generating high-quality personalized stories. Our personalized stories achieve a 75 percent win rate (versus 14 percent for the baseline and 11 percent ties) in capturing authors' writing style based on their past works. Human evaluation highlights the high quality of our Author Writing Sheet and provides valuable insights into the personalized story generation task. Notable takeaways are that writings from certain sources, such as Reddit, are easier to personalize than others, like AO3, while narrative aspects, like Creativity and Language Use, are easier to personalize than others, like Plot.

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.