arXiv subjects

Andrew Lan

Publications and source records attributed to Andrew Lan.

At least 37 records · Page 2Linked to original sources

arXiv2026

Mathematics Teachers Interactions with a Multi-Agent System for Personalized Problem Generation

Large language models can increasingly adapt educational tasks to learners characteristics. In the present study, we examine a multi-agent teacher-in-the-loop system for personalizing middle school math problems. The teacher enters a base problem and desired topic, the LLM generates the problem, and then four AI agents evaluate the problem using criteria that each specializes in (mathematical accuracy, authenticity, readability, and realism). Eight middle school mathematics teachers created 212 problems in ASSISTments using the system and assigned these problems to their students. We find that both teachers and students wanted to modify the fine-grained personalized elements of the real-world context of the problems, signaling issues with authenticity and fit. Although the agents detected many issues with realism as the problems were being written, there were few realism issues noted by teachers and students in the final versions. Issues with readability and mathematical hallucinations were also somewhat rare. Implications for multi-agent systems for personalization that support teacher control are given.

cs.AI↗

arXiv2026

Pattern-based Knowledge Component Extraction from Student Code Using Representation Learning

Personalized instruction aims to provide learners with support that adapts to their individual knowledge and progress toward learning objectives. Discovering and tracing Knowledge Components (KCs) is an important step in building accurate models of student learning. However, KC discovery in computer science education is challenging due to the open-ended nature of programming, wide variability in student solutions, and intertwined use of programming structures in code. We address these challenges with a pattern-based KC discovery method that uses a data-driven approach to define KCs as recurring structural patterns in student code that reveal persistent patterns of struggle and mastery in students' solutions. We then evaluate the discovered KCs using expert evaluation and statistical student modeling to demonstrate their effectiveness in capturing student learning and struggles. We propose a framework for modeling students' learning by deriving pattern-based KCs from student code through a three-stage process. First, an attention-based code representation model identifies Abstract Syntax Tree subtrees most relevant to code correctness. Second, a Variational Autoencoder abstracts these subtrees into a smooth latent space, capturing structural similarity across student submissions. Third, the resulting representations are clustered into pattern-based KCs. To assess the effectiveness of pattern-based KCs for modeling students' learning, we adapt the Deep Knowledge Tracing model to incorporate these KCs, demonstrating significant improvements in predictive performance over baseline KT methods. Additionally, the learning curve analysis showed alignment between the derived KCs and learning theory.

cs.LG↗

arXiv2026

Using LLMs for Knowledge Component-level Correctness Labeling in Open-ended Coding Problems

Fine-grained skill representations, commonly referred to as knowledge components (KCs), are fundamental to many approaches in student modeling and learning analytics. However, KC-level correctness labels are rarely available in real-world datasets, especially for open-ended programming tasks where solutions typically involve multiple KCs simultaneously. Simply propagating problem-level correctness to all associated KCs obscures partial mastery and often leads to poorly fitted learning curves. To address this challenge, we propose an automated framework that leverages large language models (LLMs) to label KC-level correctness directly from student-written code. Our method assesses whether each KC is correctly applied and further introduces a temporal context-aware Code-KC mapping mechanism to better align KCs with individual student code. We evaluate the resulting KC-level correctness labels in terms of learning curve fit and predictive performance using the power law of practice and the Additive Factors Model. Experimental results show that our framework leads to learning curves that are more consistent with cognitive theory and improves predictive performance, compared to baselines. Human evaluation further demonstrates substantial agreement between LLM and expert annotations.

cs.CL↗

arXiv2026

The StudyChat Dataset: Analyzing Student Dialogues With ChatGPT in an Artificial Intelligence Course

The widespread availability of large language models (LLMs), such as ChatGPT, has significantly impacted education, raising both opportunities and challenges. Students can frequently interact with LLM-powered, interactive learning tools, but their usage patterns need to be observed and understood. We introduce StudyChat, a publicly available dataset capturing real-world student interactions with an LLM-powered tutoring chatbot in a semester-long, university-level artificial intelligence (AI) course. We deploy a web application that replicates ChatGPT's core functionalities, and use it to log student interactions with the LLM while working on programming assignments. We collect 16,851 interactions, which we annotate using a dialogue act labeling schema inspired by observed interaction patterns and prior research. We analyze these interactions, highlight usage trends, and analyze how specific student behavior correlates with their course outcome. We find that students who prompt LLMs for conceptual understanding and coding help tend to perform better on assignments and exams. Moreover, students who use LLMs to write reports and circumvent assignment learning objectives have lower outcomes on exams than others. StudyChat serves as a shared resource to facilitate further research on the evolving role of LLMs in education.

cs.AI↗

arXiv2026

Toward LLM-Supported Automated Assessment of Critical Thinking Subskills

As the world becomes increasingly saturated with AI-generated content, disinformation, and algorithmic persuasion, critical thinking - the capacity to evaluate evidence, detect unreliable claims, and exercise independent judgment - is becoming a defining human skill. Developing critical thinking skills through timely assessment and feedback is crucial; however, there has not been extensive work in educational data mining on defining, measuring, and supporting critical thinking. In this paper, we investigate the feasibility of measuring "subskills" that underlie critical thinking. We ground our work in an authentic task where students operationalize critical thinking by writing argumentative essays. We developed a coding rubric based on an established skills progression and completed human coding for a corpus of student essays. We then evaluated three distinct approaches to automated scoring: zero-shot prompting, few-shot prompting, and supervised fine-tuning, implemented across three large language models (GPT-5, Llama 3.1 8B, and ModernBERT). Fine-tuning Llama 3.1 8B achieved the best results and demonstrated particular strength on subskills with highly separable proficiency levels with balanced labels across levels, while lower performance was observed for subskills that required detection of subtle distinctions between proficiency levels or imbalanced labels. Our exploratory work represents an initial step toward scalable assessment of critical thinking skills across authentic educational contexts. Future research should continue to combine automated critical thinking assessment with human validation to more accurately detect and measure dynamic, higher-order thinking skills.

cs.CY↗

arXiv2026

CATTO: Balancing Preferences and Confidence in Language Models

Large language models (LLMs) often make accurate next token predictions but their confidence in these predictions can be poorly calibrated: high-confidence predictions are frequently wrong, and low-confidence predictions may be correct. This miscalibration is exacerbated by preference-based alignment methods breaking the link between predictive probability and correctness. We introduce a Calibration Aware Token-level Training Objective (CATTO), a calibration-aware objective that aligns predicted confidence with empirical prediction correctness, which can be combined with the original preference optimization objectives. Empirically, CATTO reduces Expected Calibration Error (ECE) by 2.22%-7.61% in-distribution and 1.46%-10.44% out-of-distribution compared to direct preference optimization (DPO), and by 0.22%-1.24% in-distribution and 1.23%-5.07% out-of-distribution compared to the strongest DPO baseline. This improvement in confidence does not come at a cost of losing task accuracy, where CATTO maintains or slightly improves multiple-choice question-answering accuracy on five datasets. We also introduce Confidence@k, a test-time scaling mechanism leveraging calibrated token probabilities for Bayes-optimal selection of output tokens.

cs.LG↗

arXiv2026

Should There be a Teacher In-the-Loop? A Study of Generative AI Personalized Tasks Middle School

Adapting instruction to the fine-grained needs of individual students is a powerful application of recent advances in large language models. These generative AI models can create tasks that correspond to students' interests and enact context personalization, enhancing students' interest in learning academic content. However, when there is a teacher in-the-loop creating or modifying tasks with generative AI, it is unclear how efficient this process might be, despite commercial generative AI tools' claims that they will save teachers time. In the present study, we teamed 7 middle school mathematics teachers with ChatGPT to create personalized versions of problems in their curriculum, to correspond to their students' interests. We look at the prompting moves teachers made, their efficiency when creating problems, and the reactions of their 521 7th grade students who received the personalized assignments. We find that having a teacher-in-the-loop results in generative AI-enhanced personalization being enacted at a relatively broad grain size, whereas students tend to prefer a smaller grain size where they receive specific popular culture references that interest them. Teachers spent a lot of effort adjusting popular culture references and addressing issues with the depth or realism of the problems generated, giving higher or lower levels of ownership to the generative AI. Teachers were able to improve in their ability to craft interesting problems in partnership with generative AI, but this process did not appear to become particularly time efficient as teachers learned and reflected on their students' data, iterating their approaches.

cs.CY↗

arXiv2026

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

Personalization is critical for improving user experience in interactive writing and educational applications, yet remains understudied in story generation. We study the task of personalizing story generation, where our goal is to mimic an author's writing style, given other stories written by them. We collect Mythos, a dataset of 3.6k stories from 112 authors, with an average of 16 stories per author, across five distinct sources reflecting diverse story-writing settings. We propose a two-stage pipeline for personalized story generation: first, we infer authors' implicit writing characteristics and organize them into an Author Writing Sheet, which is validated by humans to be of high quality; second, we simulate the author's persona using tailored persona descriptions and personalized story rules. We find that stories personalized using the Author Writing Sheet outperform a non-personalized baseline, achieving a 78% win-rate in capturing authors' past style and 59% in similarity to ground-truth author stories. Human evaluation supports these findings and further highlights trends, such as Reddit stories being easier to personalize, and the Creativity and Language Use aspects of stories being easier to personalize than the Plot.

cs.CL↗

arXiv2025

PhoniTale: Phonologically Grounded Mnemonic Generation for Typologically Distant Language Pairs

Vocabulary acquisition poses a significant challenge for second-language (L2) learners, especially when learning typologically distant languages such as English and Korean, where phonological and structural mismatches complicate vocabulary learning. Recently, large language models (LLMs) have been used to generate keyword mnemonics by leveraging similar keywords from a learner's first language (L1) to aid in acquiring L2 vocabulary. However, most methods still rely on direct IPA-based phonetic matching or employ LLMs without phonological guidance. In this paper, we present PhoniTale, a novel cross-lingual mnemonic generation system that performs IPA-based phonological adaptation and syllable-aware alignment to retrieve L1 keyword sequence and uses LLMs to generate verbal cues. We evaluate PhoniTale through automated metrics and a short-term recall test with human participants, comparing its output to human-written and prior automated mnemonics. Our findings show that PhoniTale consistently outperforms previous automated approaches and achieves quality comparable to human-written mnemonics.

cs.CL↗

arXiv2025

SMART: Simulated Students Aligned with Item Response Theory for Question Difficulty Prediction

Item (question) difficulties play a crucial role in educational assessments, enabling accurate and efficient assessment of student abilities and personalization to maximize learning outcomes. Traditionally, estimating item difficulties can be costly, requiring real students to respond to items, followed by fitting an item response theory (IRT) model to get difficulty estimates. This approach cannot be applied to the cold-start setting for previously unseen items either. In this work, we present SMART (Simulated Students Aligned with IRT), a novel method for aligning simulated students with instructed ability, which can then be used in simulations to predict the difficulty of open-ended items. We achieve this alignment using direct preference optimization (DPO), where we form preference pairs based on how likely responses are under a ground-truth IRT model. We perform a simulation by generating thousands of responses, evaluating them with a large language model (LLM)-based scoring model, and fit the resulting data to an IRT model to obtain item difficulty estimates. Through extensive experiments on two real-world student response datasets, we show that SMART outperforms other item difficulty prediction methods by leveraging its improved ability alignment.

cs.CL↗

arXiv2025

Interpretable Mnemonic Generation for Kanji Learning via Expectation-Maximization

Learning Japanese vocabulary is a challenge for learners from Roman alphabet backgrounds due to script differences. Japanese combines syllabaries like hiragana with kanji, which are logographic characters of Chinese origin. Kanji are also complicated due to their complexity and volume. Keyword mnemonics are a common strategy to aid memorization, often using the compositional structure of kanji to form vivid associations. Despite recent efforts to use large language models (LLMs) to assist learners, existing methods for LLM-based keyword mnemonic generation function as a black box, offering limited interpretability. We propose a generative framework that explicitly models the mnemonic construction process as driven by a set of common rules, and learn them using a novel Expectation-Maximization-type algorithm. Trained on learner-authored mnemonics from an online platform, our method learns latent structures and compositional rules, enabling interpretable and systematic mnemonics generation. Experiments show that our method performs well in the cold-start setting for new learners while providing insight into the mechanisms behind effective mnemonic creation.

cs.CL↗

arXiv2025

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.

cs.CL↗

arXiv2025

Exploring LLMs for Predicting Tutor Strategy and Student Outcomes in Dialogues

Tutoring dialogues have gained significant attention in recent years, given the prominence of online learning and the emerging tutoring abilities of artificial intelligence (AI) agents powered by large language models (LLMs). Recent studies have shown that the strategies used by tutors can have significant effects on student outcomes, necessitating methods to predict how tutors will behave and how their actions impact students. However, few works have studied predicting tutor strategy in dialogues. Therefore, in this work we investigate the ability of modern LLMs, particularly Llama 3 and GPT-4o, to predict both future tutor moves and student outcomes in dialogues, using two math tutoring dialogue datasets. We find that even state-of-the-art LLMs struggle to predict future tutor strategy while tutor strategy is highly indicative of student outcomes, outlining a need for more powerful methods to approach this task.

cs.CL↗

arXiv2025

LookAlike: Consistent Distractor Generation in Math MCQs

Large language models (LLMs) are increasingly used to generate distractors for multiple-choice questions (MCQs), especially in domains like math education. However, existing approaches are limited in ensuring that the generated distractors are consistent with common student errors. We propose LookAlike, a method that improves error-distractor consistency via preference optimization. Our two main innovations are: (a) mining synthetic preference pairs from model inconsistencies, and (b) alternating supervised fine-tuning (SFT) with Direct Preference Optimization (DPO) to stabilize training. Unlike prior work that relies on heuristics or manually annotated preference data, LookAlike uses its own generation inconsistencies as dispreferred samples, thus enabling scalable and stable training. Evaluated on a real-world dataset of 1,400+ math MCQs, LookAlike achieves 51.6% accuracy in distractor generation and 57.2% in error generation under LLM-as-a-judge evaluation, outperforming an existing state-of-the-art method (45.6% / 47.7%). These improvements highlight the effectiveness of preference-based regularization and inconsistency mining for generating consistent math MCQ distractors at scale.

cs.LG↗

arXiv2025

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.

cs.SE↗

arXiv2025

Reasoning and Sampling-Augmented MCQ Difficulty Prediction via LLMs

The difficulty of multiple-choice questions (MCQs) is a crucial factor for educational assessments. Predicting MCQ difficulty is challenging since it requires understanding both the complexity of reaching the correct option and the plausibility of distractors, i.e., incorrect options. In this paper, we propose a novel, two-stage method to predict the difficulty of MCQs. First, to better estimate the complexity of each MCQ, we use large language models (LLMs) to augment the reasoning steps required to reach each option. We use not just the MCQ itself but also these reasoning steps as input to predict the difficulty. Second, to capture the plausibility of distractors, we sample knowledge levels from a distribution to account for variation among students responding to the MCQ. This setup, inspired by item response theory (IRT), enable us to estimate the likelihood of students selecting each (both correct and incorrect) option. We align these predictions with their ground truth values, using a Kullback-Leibler (KL) divergence-based regularization objective, and use estimated likelihoods to predict MCQ difficulty. We evaluate our method on two real-world \emph{math} MCQ and response datasets with ground truth difficulty values estimated using IRT. Experimental results show that our method outperforms all baselines, up to a 28.3\% reduction in mean squared error and a 34.6\% improvement in the coefficient of determination. We also qualitatively discuss how our novel method results in higher accuracy in predicting MCQ difficulty.

cs.AI↗

arXiv2025

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.

cs.AI↗

arXiv2024

Test Case-Informed Knowledge Tracing for Open-ended Coding Tasks

Open-ended coding tasks, which ask students to construct programs according to certain specifications, are common in computer science education. Student modeling can be challenging since their open-ended nature means that student code can be diverse. Traditional knowledge tracing (KT) models that only analyze response correctness may not fully capture nuances in student knowledge from student code. In this paper, we introduce Test case-Informed Knowledge Tracing for Open-ended Coding (TIKTOC), a framework to simultaneously analyze and predict both open-ended student code and whether the code passes each test case. We augment the existing CodeWorkout dataset with the test cases used for a subset of the open-ended coding questions, and propose a multi-task learning KT method to simultaneously analyze and predict 1) whether a student's code submission passes each test case and 2) the student's open-ended code, using a large language model as the backbone. We quantitatively show that these methods outperform existing KT methods for coding that only use the overall score a code submission receives. We also qualitatively demonstrate how test case information, combined with open-ended code, helps us gain fine-grained insights into student knowledge.

cs.CY↗