Andrew Lan

Nigel Fernandez, Aritra Ghosh, Naiming Liu et al.

Automated scoring of open-ended student responses has the potential to significantly reduce human grader effort. Recent advances in automated scoring often leverage textual representations based on pre-trained language models such as BERT and GPT as input to scoring models. Most existing approaches train a separate model for each item/question, which is suitable for scenarios such as essay scoring where items can be quite different from one another. However, these approaches have two limitations: 1) they fail to leverage item linkage for scenarios such as reading comprehension where multiple items may share a reading passage; 2) they are not scalable since storing one model per item becomes difficult when models have a large number of parameters. In this paper, we report our (grand prize-winning) solution to the National Assessment of Education Progress (NAEP) automated scoring challenge for reading comprehension. Our approach, in-context BERT fine-tuning, produces a single shared scoring model for all items with a carefully-designed input structure to provide contextual information on each item. We demonstrate the effectiveness of our approach via local evaluations using the training dataset provided by the challenge. We also discuss the biases, common error types, and limitations of our approach.

Mengxue Zhang, Sami Baral, Neil Heffernan et al.

Automatic short answer grading is an important research direction in the exploration of how to use artificial intelligence (AI)-based tools to improve education. Current state-of-the-art approaches use neural language models to create vectorized representations of students responses, followed by classifiers to predict the score. However, these approaches have several key limitations, including i) they use pre-trained language models that are not well-adapted to educational subject domains and/or student-generated text and ii) they almost always train one model per question, ignoring the linkage across a question and result in a significant model storage problem due to the size of advanced language models. In this paper, we study the problem of automatic short answer grading for students' responses to math questions and propose a novel framework for this task. First, we use MathBERT, a variant of the popular language model BERT adapted to mathematical content, as our base model and fine-tune it for the downstream task of student response grading. Second, we use an in-context learning approach that provides scoring examples as input to the language model to provide additional context information and promote generalization to previously unseen questions. We evaluate our framework on a real-world dataset of student responses to open-ended math questions and show that our framework (often significantly) outperforms existing approaches, especially for new questions that are not seen during training.

Yun-Wei Chu, Seyyedali Hosseinalipour, Elizabeth Tenorio et al.

Traditional learning-based approaches to student modeling generalize poorly to underrepresented student groups due to biases in data availability. In this paper, we propose a methodology for predicting student performance from their online learning activities that optimizes inference accuracy over different demographic groups such as race and gender. Building upon recent foundations in federated learning, in our approach, personalized models for individual student subgroups are derived from a global model aggregated across all student models via meta-gradient updates that account for subgroup heterogeneity. To learn better representations of student activity, we augment our approach with a self-supervised behavioral pretraining methodology that leverages multiple modalities of student behavior (e.g., visits to lecture videos and participation on forums), and include a neural network attention mechanism in the model aggregation stage. Through experiments on three real-world datasets from online courses, we demonstrate that our approach obtains substantial improvements over existing student modeling baselines in predicting student learning outcomes for all subgroups. Visual analysis of the resulting student embeddings confirm that our personalization methodology indeed identifies different activity patterns within different subgroups, consistent with its stronger inference ability compared with the baselines.

Hunter McNichols, Wanyong Feng, Jaewook Lee et al.

Multiple-choice questions (MCQs) are ubiquitous in almost all levels of education since they are easy to administer, grade, and are a reliable form of assessment. An important aspect of MCQs is the distractors, i.e., incorrect options that are designed to target specific misconceptions or insufficient knowledge among students. To date, the task of crafting high-quality distractors has largely remained a labor-intensive process for teachers and learning content designers, which has limited scalability. In this work, we explore the task of automated distractor and corresponding feedback message generation in math MCQs using large language models. We establish a formulation of these two tasks and propose a simple, in-context learning-based solution. Moreover, we propose generative AI-based metrics for evaluating the quality of the feedback messages. We conduct extensive experiments on these tasks using a real-world MCQ dataset. Our findings suggest that there is a lot of room for improvement in automated distractor and feedback generation; based on these findings, we outline several directions for future work.

Mengxue Zhang, Zichao Wang, Zhichao Yang et al.

Solutions to math word problems (MWPs) with step-by-step explanations are valuable, especially in education, to help students better comprehend problem-solving strategies. Most existing approaches only focus on obtaining the final correct answer. A few recent approaches leverage intermediate solution steps to improve final answer correctness but often cannot generate coherent steps with a clear solution strategy. Contrary to existing work, we focus on improving the correctness and coherence of the intermediate solutions steps. We propose a step-by-step planning approach for intermediate solution generation, which strategically plans the generation of the next solution step based on the MWP and the previous solution steps. Our approach first plans the next step by predicting the necessary math operation needed to proceed, given history steps, then generates the next step, token-by-token, by prompting a language model with the predicted math operation. Experiments on the GSM8K dataset demonstrate that our approach improves the accuracy and interpretability of the solution on both automatic metrics and human evaluation.

Alexander Scarlatos, Andrew Lan

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.

Yun-Wei Chu, Seyyedali Hosseinalipour, Elizabeth Tenorio et al.

Conventional methods for student modeling, which involve predicting grades based on measured activities, struggle to provide accurate results for minority/underrepresented student groups due to data availability biases. In this paper, we propose a Multi-Layer Personalized Federated Learning (MLPFL) methodology that optimizes inference accuracy over different layers of student grouping criteria, such as by course and by demographic subgroups within each course. In our approach, personalized models for individual student subgroups are derived from a global model, which is trained in a distributed fashion via meta-gradient updates that account for subgroup heterogeneity while preserving modeling commonalities that exist across the full dataset. The evaluation of the proposed methodology considers case studies of two popular downstream student modeling tasks, knowledge tracing and outcome prediction, which leverage multiple modalities of student behavior (e.g., visits to lecture videos and participation on forums) in model training. Experiments on three real-world online course datasets show significant improvements achieved by our approach over existing student modeling benchmarks, as evidenced by an increased average prediction quality and decreased variance across different student subgroups. Visual analysis of the resulting students' knowledge state embeddings confirm that our personalization methodology extracts activity patterns clustered into different student subgroups, consistent with the performance enhancements we obtain over the baselines.

Nischal Ashok Kumar, Nigel Fernandez, Zichao Wang et al.

Reading comprehension is a crucial skill in many aspects of education, including language learning, cognitive development, and fostering early literacy skills in children. Automated answer-aware reading comprehension question generation has significant potential to scale up learner support in educational activities. One key technical challenge in this setting is that there can be multiple questions, sometimes very different from each other, with the same answer; a trained question generation method may not necessarily know which question human educators would prefer. To address this challenge, we propose 1) a data augmentation method that enriches the training dataset with diverse questions given the same context and answer and 2) an overgenerate-and-rank method to select the best question from a pool of candidates. We evaluate our method on the FairytaleQA dataset, showing a 5% absolute improvement in ROUGE-L over the best existing method. We also demonstrate the effectiveness of our method in generating harder, "implicit" questions, where the answers are not contained in the context as text spans.

Alexander Scarlatos, Christopher Brinton, Andrew Lan

Educational process data, i.e., logs of detailed student activities in computerized or online learning platforms, has the potential to offer deep insights into how students learn. One can use process data for many downstream tasks such as learning outcome prediction and automatically delivering personalized intervention. However, analyzing process data is challenging since the specific format of process data varies a lot depending on different learning/testing scenarios. In this paper, we propose a framework for learning representations of educational process data that is applicable across many different learning scenarios. Our framework consists of a pre-training step that uses BERT-type objectives to learn representations from sequential process data and a fine-tuning step that further adjusts these representations on downstream prediction tasks. We apply our framework to the 2019 nation's report card data mining competition dataset that consists of student problem-solving process data and detail the specific models we use in this scenario. We conduct both quantitative and qualitative experiments to show that our framework results in process data representations that are both predictive and informative.

Mengxue Zhang, Neil Heffernan, Andrew Lan

Automated scoring of student responses to open-ended questions, including short-answer questions, has great potential to scale to a large number of responses. Recent approaches for automated scoring rely on supervised learning, i.e., training classifiers or fine-tuning language models on a small number of responses with human-provided score labels. However, since scoring is a subjective process, these human scores are noisy and can be highly variable, depending on the scorer. In this paper, we investigate a collection of models that account for the individual preferences and tendencies of each human scorer in the automated scoring task. We apply these models to a short-answer math response dataset where each response is scored (often differently) by multiple different human scorers. We conduct quantitative experiments to show that our scorer models lead to improved automated scoring accuracy. We also conduct quantitative experiments and case studies to analyze the individual preferences and tendencies of scorers. We found that scorers can be grouped into several obvious clusters, with each cluster having distinct features, and analyzed them in detail.

Alexander Scarlatos, Digory Smith, Simon Woodhead et al.

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.

Nischal Ashok Kumar, Andrew Lan

The Socratic method is a way of guiding students toward solving a problem independently without directly revealing the solution to the problem. Although this method has been shown to significantly improve student learning outcomes, it remains a complex labor-intensive task for instructors. Large language models (LLMs) can be used to augment human effort by automatically generating Socratic questions for students. However, existing methods that involve prompting these LLMs sometimes produce invalid outputs, e.g., those that directly reveal the solution to the problem or provide irrelevant or premature questions. To alleviate this problem, inspired by reinforcement learning with AI feedback (RLAIF), we first propose a data augmentation method to enrich existing Socratic questioning datasets with questions that are invalid in specific ways. Next, we propose a method to optimize open-source LLMs such as LLama 2 to prefer ground-truth questions over generated invalid ones, using direct preference optimization (DPO). Our experiments on a Socratic questions dataset for student code debugging show that a DPO-optimized 7B LLama 2 model can effectively avoid generating invalid questions, and as a result, outperforms existing state-of-the-art prompting methods.

Jaewook Lee, Hunter McNichols, Andrew Lan

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.

Zhangqi Duan, Nigel Fernandez, Alexander Hicks et al.

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.

Alexander Scarlatos, Naiming Liu, Jaewook Lee et al.

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.

Nigel Fernandez, Alexander Scarlatos, Andrew Lan

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.

Hunter McNichols, Jaewook Lee, Stephen Fancsali et al.

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.

Marisa C. Peczuh, Nischal Ashok Kumar, Ryan Baker et al.

Critical thinking represents a fundamental competency in today's education landscape. Developing critical thinking skills through timely assessment and feedback is crucial; however, there has not been extensive work in the learning analytics community on defining, measuring, and supporting critical thinking. In this paper, we investigate the feasibility of measuring core "subskills" that underlie critical thinking. We ground our work in an authentic task where students operationalize critical thinking: student-written 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, GPT-5-mini, and ModernBERT). GPT-5 with few-shot prompting achieved the strongest results and demonstrated particular strength on subskills with separable, frequent categories, while lower performance was observed for subskills that required detection of subtle distinctions or rare categories. Our results underscore critical trade-offs in automated critical thinking assessment: proprietary models offer superior reliability at higher cost, while open-source alternatives provide practical accuracy with reduced sensitivity to minority categories. Our work represents an initial step toward scalable assessment of higher-order reasoning skills across authentic educational contexts.

Nigel Fernandez, Alexander Scarlatos, Wanyong Feng et al.

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.

Aritra Ghosh, Andrew Lan

Deep neural network-based classifiers trained with the categorical cross-entropy (CCE) loss are sensitive to label noise in the training data. One common type of method that can mitigate the impact of label noise can be viewed as supervised robust methods; one can simply replace the CCE loss with a loss that is robust to label noise, or re-weight training samples and down-weight those with higher loss values. Recently, another type of method using semi-supervised learning (SSL) has been proposed, which augments these supervised robust methods to exploit (possibly) noisy samples more effectively. Although supervised robust methods perform well across different data types, they have been shown to be inferior to the SSL methods on image classification tasks under label noise. Therefore, it remains to be seen that whether these supervised robust methods can also perform well if they can utilize the unlabeled samples more effectively. In this paper, we show that by initializing supervised robust methods using representations learned through contrastive learning leads to significantly improved performance under label noise. Surprisingly, even the simplest method (training a classifier with the CCE loss) can outperform the state-of-the-art SSL method by more than 50\% under high label noise when initialized with contrastive learning. Our implementation will be publicly available at {\url{https://github.com/arghosh/noisy_label_pretrain}}.

Wanyong Feng, Jaewook Lee, Hunter McNichols et al.

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.

Jaewook Lee, Digory Smith, Simon Woodhead et al.

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.

Alexander Scarlatos, Wanyong Feng, Digory Smith et al.

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.

Nischal Ashok Kumar, Andrew Lan

In computer science education, test cases are an integral part of programming assignments since they can be used as assessment items to test students' programming knowledge and provide personalized feedback on student-written code. The goal of our work is to propose a fully automated approach for test case generation that can accurately measure student knowledge, which is important for two reasons. First, manually constructing test cases requires expert knowledge and is a labor-intensive process. Second, developing test cases for students, especially those who are novice programmers, is significantly different from those oriented toward professional-level software developers. Therefore, we need an automated process for test case generation to assess student knowledge and provide feedback. In this work, we propose a large language model-based approach to automatically generate test cases and show that they are good measures of student knowledge, using a publicly available dataset that contains student-written Java code. We also discuss future research directions centered on using test cases to help students.

Adriana Caraeni, Alexander Scarlatos, Andrew Lan

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.

Wanyong Feng, Peter Tran, Stephen Sireci et al.

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.

Hasnain Heickal, Andrew Lan

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.

Nischal Ashok Kumar, Chau Minh Pham, Mohit Iyyer et al.

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.

Nisarg Parikh, Nigel Fernandez, Alexander Scarlatos et al.

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.

Nigel Fernandez, Andrew Lan

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.

Alexander Scarlatos, Nigel Fernandez, Christopher Ormerod et al.

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.

Hunter McNichols, Fareya Ikram, Andrew Lan

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 monitored 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 ChatGPTs 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.

Fareya Ikram, Alexander Scarlatos, Andrew Lan

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.

Jaewook Lee, Alexander Scarlatos, Andrew Lan

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.

Hasnain Heickal, Andrew Lan

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.

Zhangqi Duan, Nigel Fernandez, Arun Balajiee Lekshmi Narayanan et al.

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 an 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 on two real-world student code submission datasets in different programming languages.We find that KCGen-KT outperforms existing KT methods and human-written KCs on future student response prediction. We investigate the learning curves of generated KCs and show that LLM-generated KCs result in a better fit than human written KCs under a cognitive model. We also conduct a human evaluation with course instructors to show that our pipeline generates reasonably accurate problem-KC mappings.

Alexander Scarlatos, Andrew Lan

Recent developments in large pre-trained language models have enabled unprecedented performance on a variety of downstream tasks. Achieving best performance with these models often leverages in-context learning, where a model performs a (possibly new) task given one or more examples. However, recent work has shown that the choice of examples can have a large impact on task performance and that finding an optimal set of examples is non-trivial. While there are many existing methods for selecting in-context examples, they generally score examples independently, ignoring the dependency between them and the order in which they are provided to the model. In this work, we propose Retrieval for In-Context Learning (RetICL), a learnable method for modeling and optimally selecting examples sequentially for in-context learning. We frame the problem of sequential example selection as a Markov decision process and train an example retriever using reinforcement learning. We evaluate RetICL on math word problem solving and scientific question answering tasks and show that it consistently outperforms or matches heuristic and learnable baselines. We also use case studies to show that RetICL implicitly learns representations of problem solving strategies.

Wanyong Feng, Aritra Ghosh, Stephen Sireci et al.

Computerized adaptive testing (CAT) is a form of personalized testing that accurately measures students' knowledge levels while reducing test length. Bilevel optimization-based CAT (BOBCAT) is a recent framework that learns a data-driven question selection algorithm to effectively reduce test length and improve test accuracy. However, it suffers from high question exposure and test overlap rates, which potentially affects test security. This paper introduces a constrained version of BOBCAT to address these problems by changing its optimization setup and enabling us to trade off test accuracy for question exposure and test overlap rates. We show that C-BOBCAT is effective through extensive experiments on two real-world adult testing datasets.

Nischal Ashok Kumar, Wanyong Feng, Jaewook Lee et al.

In this paper, we take a preliminary step towards solving the problem of causal discovery in knowledge tracing, i.e., finding the underlying causal relationship among different skills from real-world student response data. This problem is important since it can potentially help us understand the causal relationship between different skills without extensive A/B testing, which can potentially help educators to design better curricula according to skill prerequisite information. Specifically, we propose a conceptual solution, a novel causal gated recurrent unit (GRU) module in a modified deep knowledge tracing model, which uses i) a learnable permutation matrix for causal ordering among skills and ii) an optionally learnable lower-triangular matrix for causal structure among skills. We also detail how to learn the model parameters in an end-to-end, differentiable way. Our solution placed among the top entries in Task 3 of the NeurIPS 2022 Challenge on Causal Insights for Learning Paths in Education. We detail preliminary experiments as evaluated on the challenge's public leaderboard since the ground truth causal structure has not been publicly released, making detailed local evaluation impossible.

Jaewook Lee, Andrew Lan

In second language vocabulary learning, existing works have primarily focused on either the learning interface or scheduling personalized retrieval practices to maximize memory retention. However, the learning content, i.e., the information presented on flashcards, has mostly remained constant. Keyword mnemonic is a notable learning strategy that relates new vocabulary to existing knowledge by building an acoustic and imagery link using a keyword that sounds alike. Beyond that, producing verbal and visual cues associated with the keyword to facilitate building these links requires a manual process and is not scalable. In this paper, we explore an opportunity to use large language models to automatically generate verbal and visual cues for keyword mnemonics. Our approach, an end-to-end pipeline for auto-generating verbal and visual cues, can automatically generate highly memorable cues. We investigate the effectiveness of our approach via a human participant experiment by comparing it with manually generated cues.

Hunter McNichols, Mengxue Zhang, Andrew Lan

Automated feedback as students answer open-ended math questions has significant potential in improving learning outcomes at large scale. A key part of automated feedback systems is an error classification component, which identifies student errors and enables appropriate, predefined feedback to be deployed. Most existing approaches to error classification use a rule-based method, which has limited capacity to generalize. Existing data-driven methods avoid these limitations but specifically require mathematical expressions in student responses to be parsed into syntax trees. This requirement is itself a limitation, since student responses are not always syntactically valid and cannot be converted into trees. In this work, we introduce a flexible method for error classification using pre-trained large language models. We demonstrate that our method can outperform existing methods in algebra error classification, and is able to classify a larger set of student responses. Additionally, we analyze common classification errors made by our method and discuss limitations of automated error classification.

Naiming Liu, Zichao Wang, Richard G. Baraniuk et al.

In education applications, knowledge tracing refers to the problem of estimating students' time-varying concept/skill mastery level from their past responses to questions and predicting their future performance. One key limitation of most existing knowledge tracing methods is that they treat student responses to questions as binary-valued, i.e., whether they are correct or incorrect. Response correctness analysis/prediction ignores important information on student knowledge contained in the exact content of the responses, especially for open-ended questions. In this paper, we conduct the first exploration into open-ended knowledge tracing (OKT) by studying the new task of predicting students' exact open-ended responses to questions. Our work is grounded in the domain of computer science education with programming questions. We develop an initial solution to the OKT problem, a student knowledge-guided code generation approach, that combines program synthesis methods using language models with student knowledge tracing methods. We also conduct a series of quantitative and qualitative experiments on a real-world student code dataset to validate OKT and demonstrate its promise in educational applications.

Aritra Ghosh, Saayan Mitra, Andrew Lan

In sequential recommender system applications, it is important to develop models that can capture users' evolving interest over time to successfully recommend future items that they are likely to interact with. For users with long histories, typical models based on recurrent neural networks tend to forget important items in the distant past. Recent works have shown that storing a small sketch of past items can improve sequential recommendation tasks. However, these works all rely on static sketching policies, i.e., heuristics to select items to keep in the sketch, which are not necessarily optimal and cannot improve over time with more training data. In this paper, we propose a differentiable policy for sketching (DiPS), a framework that learns a data-driven sketching policy in an end-to-end manner together with the recommender system model to explicitly maximize recommendation quality in the future. We also propose an approximate estimator of the gradient for optimizing the sketching algorithm parameters that is computationally efficient. We verify the effectiveness of DiPS on real-world datasets under various practical settings and show that it requires up to $50\%$ fewer sketch items to reach the same predictive quality than existing sketching policies.

Yun-Wei Chu, Elizabeth Tenorio, Laura Cruz et al.

We study the problem of predicting student knowledge acquisition in online courses from clickstream behavior. Motivated by the proliferation of eLearning lecture delivery, we specifically focus on student in-video activity in lectures videos, which consist of content and in-video quizzes. Our methodology for predicting in-video quiz performance is based on three key ideas we develop. First, we model students' clicking behavior via time-series learning architectures operating on raw event data, rather than defining hand-crafted features as in existing approaches that may lose important information embedded within the click sequences. Second, we develop a self-supervised clickstream pre-training to learn informative representations of clickstream events that can initialize the prediction model effectively. Third, we propose a clustering guided meta-learning-based training that optimizes the prediction model to exploit clusters of frequent patterns in student clickstream sequences. Through experiments on three real-world datasets, we demonstrate that our method obtains substantial improvements over two baseline models in predicting students' in-video quiz performance. Further, we validate the importance of the pre-training and meta-learning components of our framework through ablation studies. Finally, we show how our methodology reveals insights on video-watching behavior associated with knowledge acquisition for useful learning analytics.

Zichao Wang, Andrew S. Lan, Richard G. Baraniuk

We study the problem of generating arithmetic math word problems (MWPs) given a math equation that specifies the mathematical computation and a context that specifies the problem scenario. Existing approaches are prone to generating MWPs that are either mathematically invalid or have unsatisfactory language quality. They also either ignore the context or require manual specification of a problem template, which compromises the diversity of the generated MWPs. In this paper, we develop a novel MWP generation approach that leverages i) pre-trained language models and a context keyword selection model to improve the language quality of the generated MWPs and ii) an equation consistency constraint for math equations to improve the mathematical validity of the generated MWPs. Extensive quantitative and qualitative experiments on three real-world MWP datasets demonstrate the superior performance of our approach compared to various baselines.

Aritra Ghosh, Andrew Lan

Computerized adaptive testing (CAT) refers to a form of tests that are personalized to every student/test taker. CAT methods adaptively select the next most informative question/item for each student given their responses to previous questions, effectively reducing test length. Existing CAT methods use item response theory (IRT) models to relate student ability to their responses to questions and static question selection algorithms designed to reduce the ability estimation error as quickly as possible; therefore, these algorithms cannot improve by learning from large-scale student response data. In this paper, we propose BOBCAT, a Bilevel Optimization-Based framework for CAT to directly learn a data-driven question selection algorithm from training data. BOBCAT is agnostic to the underlying student response model and is computationally efficient during the adaptive testing process. Through extensive experiments on five real-world student response datasets, we show that BOBCAT outperforms existing CAT methods (sometimes significantly) at reducing test length.

Mengxue Zhang, Zichao Wang, Richard Baraniuk et al.

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually constructing cognitive models and anticipating student errors for each question. This process requires significant human effort and does not scale to most questions used in homework and practices that do not come with this information. In this paper, we analyze students' step-by-step solution processes to equation solving questions in an attempt to scale up error diagnostics and feedback mechanisms developed for a small number of questions to a much larger number of questions. Leveraging a recent math expression encoding method, we represent each math operation applied in solution steps as a transition in the math embedding vector space. We use a dataset that contains student solution steps in the Cognitive Tutor system to learn implicit and explicit representations of math operations. We explore whether these representations can i) identify math operations a student intends to perform in each solution step, regardless of whether they did it correctly or not, and ii) select the appropriate feedback type for incorrect steps. Experimental results show that our learned math operation representations generalize well across different data distributions.

Aritra Ghosh, Andrew Lan

Learning with labels noise has gained significant traction recently due to the sensitivity of deep neural networks under label noise under common loss functions. Losses that are theoretically robust to label noise, however, often makes training difficult. Consequently, several recently proposed methods, such as Meta-Weight-Net (MW-Net), use a small number of unbiased, clean samples to learn a weighting function that downweights samples that are likely to have corrupted labels under the meta-learning framework. However, obtaining such a set of clean samples is not always feasible in practice. In this paper, we analytically show that one can easily train MW-Net without access to clean samples simply by using a loss function that is robust to label noise, such as mean absolute error, as the meta objective to train the weighting network. We experimentally show that our method beats all existing methods that do not use clean samples and performs on-par with methods that use gold samples on benchmark datasets across various noise types and noise rates.

Aritra Ghosh, Jay Raspat, Andrew Lan

Knowledge tracing refers to a family of methods that estimate each student's knowledge component/skill mastery level from their past responses to questions. One key limitation of most existing knowledge tracing methods is that they can only estimate an \emph{overall} knowledge level of a student per knowledge component/skill since they analyze only the (usually binary-valued) correctness of student responses. Therefore, it is hard to use them to diagnose specific student errors. In this paper, we extend existing knowledge tracing methods beyond correctness prediction to the task of predicting the exact option students select in multiple choice questions. We quantitatively evaluate the performance of our option tracing methods on two large-scale student response datasets. We also qualitatively evaluate their ability in identifying common student errors in the form of clusters of incorrect options across different questions that correspond to the same error.

Shalini Pandey, Andrew Lan, George Karypis et al.

In recent years, Massive Open Online Courses (MOOCs) have witnessed immense growth in popularity. Now, due to the recent Covid19 pandemic situation, it is important to push the limits of online education. Discussion forums are primary means of interaction among learners and instructors. However, with growing class size, students face the challenge of finding useful and informative discussion forums. This problem can be solved by matching the interest of students with thread contents. The fundamental challenge is that the student interests drift as they progress through the course, and forum contents evolve as students or instructors update them. In our paper, we propose to predict future interest trajectories of students. Our model consists of two key operations: 1) Update operation and 2) Projection operation. Update operation models the inter-dependency between the evolution of student and thread using coupled Recurrent Neural Networks when the student posts on the thread. The projection operation learns to estimate future embedding of students and threads. For students, the projection operation learns the drift in their interests caused by the change in the course topic they study. The projection operation for threads exploits how different posts induce varying interest levels in a student according to the thread structure. Extensive experimentation on three real-world MOOC datasets shows that our model significantly outperforms other baselines for thread recommendation.