Neil T. Heffernan

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.

Fareya Ikram, Nischal Ashok Kumar, Junyang Lu et al.

Students benefit from math problems contextualized to their interests. Large language models (LLMs) offer promise for efficient personalization at scale. However, LLM-generated personalized problems may often have problems such as unrealistic quantities and contexts, poor readability, limited authenticity with respect to students' experiences, and occasional mathematical inconsistencies. To alleviate these problems, we propose a multi-agent framework that formalizes personalization as an iterative generate--validate--revise process; we use four specialized validator agents targeting the criteria of solvability, realism, readability, and authenticity, respectively. We evaluate our framework on 600 problems drawn from a popular online mathematics homework platform, ASSISTments, personalizing each problem to a fixed set of 20 student interest topics. We compare three refinement strategies that differ in how validation feedback is coordinated into revisions. Results show that authenticity and realism are the most frequent failure modes in initial LLM-personalized problems, but that a single refinement iteration substantially reduces these failures. We further find that different refinement strategies have different strengths on different criteria. We also assess validator reliability via human evaluation. Results show that reliability is highest on realism and lowest on authenticity, highlighting the need for better evaluation protocols that consider teachers' and students' personal characteristics.

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.

Jia Tracy Shen, Michiharu Yamashita, Ethan Prihar et al.

Since the introduction of the original BERT (i.e., BASE BERT), researchers have developed various customized BERT models with improved performance for specific domains and tasks by exploiting the benefits of transfer learning. Due to the nature of mathematical texts, which often use domain specific vocabulary along with equations and math symbols, we posit that the development of a new BERT model for mathematics would be useful for many mathematical downstream tasks. In this resource paper, we introduce our multi-institutional effort (i.e., two learning platforms and three academic institutions in the US) toward this need: MathBERT, a model created by pre-training the BASE BERT model on a large mathematical corpus ranging from pre-kindergarten (pre-k), to high-school, to college graduate level mathematical content. In addition, we select three general NLP tasks that are often used in mathematics education: prediction of knowledge component, auto-grading open-ended Q&A, and knowledge tracing, to demonstrate the superiority of MathBERT over BASE BERT. Our experiments show that MathBERT outperforms prior best methods by 1.2-22% and BASE BERT by 2-8% on these tasks. In addition, we build a mathematics specific vocabulary 'mathVocab' to train with MathBERT. We discover that MathBERT pre-trained with 'mathVocab' outperforms MathBERT trained with the BASE BERT vocabulary (i.e., 'origVocab'). MathBERT is currently being adopted at the participated leaning platforms: Stride, Inc, a commercial educational resource provider, and ASSISTments.org, a free online educational platform. We release MathBERT for public usage at: https://github.com/tbs17/MathBERT.

Jia Tracy Shen, Michiharu Yamashita, Ethan Prihar et al.

Educational content labeled with proper knowledge components (KCs) are particularly useful to teachers or content organizers. However, manually labeling educational content is labor intensive and error-prone. To address this challenge, prior research proposed machine learning based solutions to auto-label educational content with limited success. In this work, we significantly improve prior research by (1) expanding the input types to include KC descriptions, instructional video titles, and problem descriptions (i.e., three types of prediction task), (2) doubling the granularity of the prediction from 198 to 385 KC labels (i.e., more practical setting but much harder multinomial classification problem), (3) improving the prediction accuracies by 0.5-2.3% using Task-adaptive Pre-trained BERT, outperforming six baselines, and (4) proposing a simple evaluation measure by which we can recover 56-73% of mispredicted KC labels. All codes and data sets in the experiments are available at:https://github.com/tbs17/TAPT-BERT

Morgan Lee, Artem Frenk, Eamon Worden et al.

Knowledge Tracing (KT) has been an established problem in the educational data mining field for decades, and it is commonly assumed that the underlying learning process being modeled remains static. Given the ever-changing landscape of online learning platforms (OLPs), we investigate how concept drift and changing student populations can impact student behavior within an OLP through testing model performance both within a single academic year and across multiple academic years. Four well-studied KT models were applied to five academic years of data to assess how susceptible KT models are to concept drift. Through our analysis, we find that all four families of KT models can exhibit degraded performance, Bayesian Knowledge Tracing (BKT) remains the most stable KT model when applied to newer data, while more complex, attention based models lose predictive power significantly faster.

Paul Denny, Sumit Gulwani, Neil T. Heffernan et al.

This survey article has grown out of the GAIED (pronounced "guide") workshop organized by the authors at the NeurIPS 2023 conference. We organized the GAIED workshop as part of a community-building effort to bring together researchers, educators, and practitioners to explore the potential of generative AI for enhancing education. This article aims to provide an overview of the workshop activities and highlight several future research directions in the area of GAIED.

Sami Baral, Li Lucy, Ryan Knight et al. · allen-ai

In real-world settings, vision language models (VLMs) should robustly handle naturalistic, noisy visual content as well as domain-specific language and concepts. For example, K-12 educators using digital learning platforms may need to examine and provide feedback across many images of students' math work. To assess the potential of VLMs to support educators in settings like this one, we introduce DrawEduMath, an English-language dataset of 2,030 images of students' handwritten responses to K-12 math problems. Teachers provided detailed annotations, including free-form descriptions of each image and 11,661 question-answer (QA) pairs. These annotations capture a wealth of pedagogical insights, ranging from students' problem-solving strategies to the composition of their drawings, diagrams, and writing. We evaluate VLMs on teachers' QA pairs, as well as 44,362 synthetic QA pairs derived from teachers' descriptions using language models (LMs). We show that even state-of-the-art VLMs leave much room for improvement on DrawEduMath questions. We also find that synthetic QAs, though imperfect, can yield similar model rankings as teacher-written QAs. We release DrawEduMath to support the evaluation of VLMs' abilities to reason mathematically over images gathered with educational contexts in mind.

Sami Baral, Eamon Worden, Wen-Chiang Lim et al.

The effectiveness of feedback in enhancing learning outcomes is well documented within Educational Data Mining (EDM). Various prior research has explored methodologies to enhance the effectiveness of feedback. Recent developments in Large Language Models (LLMs) have extended their utility in enhancing automated feedback systems. This study aims to explore the potential of LLMs in facilitating automated feedback in math education. We examine the effectiveness of LLMs in evaluating student responses by comparing 3 different models: Llama, SBERT-Canberra, and GPT4 model. The evaluation requires the model to provide both a quantitative score and qualitative feedback on the student's responses to open-ended math problems. We employ Mistral, a version of Llama catered to math, and fine-tune this model for evaluating student responses by leveraging a dataset of student responses and teacher-written feedback for middle-school math problems. A similar approach was taken for training the SBERT model as well, while the GPT4 model used a zero-shot learning approach. We evaluate the model's performance in scoring accuracy and the quality of feedback by utilizing judgments from 2 teachers. The teachers utilized a shared rubric in assessing the accuracy and relevance of the generated feedback. We conduct both quantitative and qualitative analyses of the model performance. By offering a detailed comparison of these methods, this study aims to further the ongoing development of automated feedback systems and outlines potential future directions for leveraging generative LLMs to create more personalized learning experiences.

Mason DiCicco, Eamon Worden, Conner Olsen et al.

Understanding the mathematical reasoning capabilities of Large Language Models (LLMs) is a central topic in the study of artificial intelligence. This new domain necessitates the creation of datasets of reasoning tasks for both training and benchmarking the performance of LLMs. To this end, we introduce the Karp dataset: The first dataset composed of detailed proofs of NP-completeness reductions. The reductions vary in difficulty, ranging from simple exercises of undergraduate courses to more challenging reductions from academic papers. We compare the performance of state-of-the-art models on this task and demonstrate the effect of fine-tuning with the Karp dataset on reasoning capacity.

Adish Singla, Anna N. Rafferty, Goran Radanovic et al.

This survey article has grown out of the RL4ED workshop organized by the authors at the Educational Data Mining (EDM) 2021 conference. We organized this workshop as part of a community-building effort to bring together researchers and practitioners interested in the broad areas of reinforcement learning (RL) and education (ED). This article aims to provide an overview of the workshop activities and summarize the main research directions in the area of RL for ED.

Wen Huang, Kevin Labille, Xintao Wu et al.

Personalized recommendation based on multi-arm bandit (MAB) algorithms has shown to lead to high utility and efficiency as it can dynamically adapt the recommendation strategy based on feedback. However, unfairness could incur in personalized recommendation. In this paper, we study how to achieve user-side fairness in personalized recommendation. We formulate our fair personalized recommendation as a modified contextual bandit and focus on achieving fairness on the individual whom is being recommended an item as opposed to achieving fairness on the items that are being recommended. We introduce and define a metric that captures the fairness in terms of rewards received for both the privileged and protected groups. We develop a fair contextual bandit algorithm, Fair-LinUCB, that improves upon the traditional LinUCB algorithm to achieve group-level fairness of users. Our algorithm detects and monitors unfairness while it learns to recommend personalized videos to students to achieve high efficiency. We provide a theoretical regret analysis and show that our algorithm has a slightly higher regret bound than LinUCB. We conduct numerous experimental evaluations to compare the performances of our fair contextual bandit to that of LinUCB and show that our approach achieves group-level fairness while maintaining a high utility.

Aritra Ghosh, Neil Heffernan, Andrew S. Lan

Knowledge tracing (KT) refers to the problem of predicting future learner performance given their past performance in educational applications. Recent developments in KT using flexible deep neural network-based models excel at this task. However, these models often offer limited interpretability, thus making them insufficient for personalized learning, which requires using interpretable feedback and actionable recommendations to help learners achieve better learning outcomes. In this paper, we propose attentive knowledge tracing (AKT), which couples flexible attention-based neural network models with a series of novel, interpretable model components inspired by cognitive and psychometric models. AKT uses a novel monotonic attention mechanism that relates a learner's future responses to assessment questions to their past responses; attention weights are computed using exponential decay and a context-aware relative distance measure, in addition to the similarity between questions. Moreover, we use the Rasch model to regularize the concept and question embeddings; these embeddings are able to capture individual differences among questions on the same concept without using an excessive number of parameters. We conduct experiments on several real-world benchmark datasets and show that AKT outperforms existing KT methods (by up to $6\%$ in AUC in some cases) on predicting future learner responses. We also conduct several case studies and show that AKT exhibits excellent interpretability and thus has potential for automated feedback and personalization in real-world educational settings.

Nathaniel Swinger, Maria De-Arteaga, Neil Thomas Heffernan et al.

This paper presents an algorithm for enumerating biases in word embeddings. The algorithm exposes a large number of offensive associations related to sensitive features such as race and gender on publicly available embeddings, including a supposedly "debiased" embedding. These biases are concerning in light of the widespread use of word embeddings. The associations are identified by geometric patterns in word embeddings that run parallel between people's names and common lower-case tokens. The algorithm is highly unsupervised: it does not even require the sensitive features to be pre-specified. This is desirable because: (a) many forms of discrimination--such as racial discrimination--are linked to social constructs that may vary depending on the context, rather than to categories with fixed definitions; and (b) it makes it easier to identify biases against intersectional groups, which depend on combinations of sensitive features. The inputs to our algorithm are a list of target tokens, e.g. names, and a word embedding. It outputs a number of Word Embedding Association Tests (WEATs) that capture various biases present in the data. We illustrate the utility of our approach on publicly available word embeddings and lists of names, and evaluate its output using crowdsourcing. We also show how removing names may not remove potential proxy bias.

Shubhendu Trivedi, Zachary A. Pardos, Neil T. Heffernan

We explore the utility of clustering in reducing error in various prediction tasks. Previous work has hinted at the improvement in prediction accuracy attributed to clustering algorithms if used to pre-process the data. In this work we more deeply investigate the direct utility of using clustering to improve prediction accuracy and provide explanations for why this may be so. We look at a number of datasets, run k-means at different scales and for each scale we train predictors. This produces k sets of predictions. These predictions are then combined by a naïve ensemble. We observed that this use of a predictor in conjunction with clustering improved the prediction accuracy in most datasets. We believe this indicates the predictive utility of exploiting structure in the data and the data compression handed over by clustering. We also found that using this method improves upon the prediction of even a Random Forests predictor which suggests this method is providing a novel, and useful source of variance in the prediction process.

Joseph Jay Williams, Neil Heffernan

We explain and provide examples of a formalism that supports the methodology of discovering how to adapt and personalize technology by combining randomized experiments with variables associated with user models. We characterize a formal relationship between the use of technology to conduct A/B experiments and use of technology for adaptive personalization. The MOOClet Formalism [11] captures the equivalence between experimentation and personalization in its conceptualization of modular components of a technology. This motivates a unified software design pattern that enables technology components that can be compared in an experiment to also be adapted based on contextual data, or personalized based on user characteristics. With the aid of a concrete use case, we illustrate the potential of the MOOClet formalism for a methodology that uses randomized experiments of alternative micro-designs to discover how to adapt technology based on user characteristics, and then dynamically implements these personalized improvements in real time.