Zachary A. Pardos

dblp:45/6140 · also Zach A. Pardos · DBLP profile ↗
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99ranked-venue papers
25as first author
39since 2021 · last 2026
0000-0002-6016-7051ORCID · verified

Domains — the database's venue-derived domains; a paper can count in several

Applied, interdisciplinary, general and emerging computing · 81 · 20 first-author · 32 since 2021Human-computer interaction and ubiquitous computing · 41 · 16 first-author · 17 since 2021Artificial intelligence and machine learning · 23 · 3 first-author · 13 since 2021Systems, architecture and hardware · 15 · 3 first-author · 8 since 2021Graphics, computer vision, multimedia, augmented reality and games · 3 · 2 since 2021Databases, data management, data science and information retrieval · 1
YearPublicationVenuePosition
2026 Toward Trait-Aware Learning Analytics
abstract
Learning analytics (LA) draws from the learning sciences to interpret learner behavior and inform system design. Yet, past personalization remains largely at the content or performance level (during learner-system interactions), overlooking relatively stable individual differences such as personality (unfolding over long-term learning trajectories such as college degrees). The latter could bring underappreciated benefits to the design, implementation, and impact of LA. In this position paper, we conduct an ad hoc literature review and argue for an expanded framing of LA that centers on learner traits as key to both interpreting and designing close-the-loop experiments in LA. We show that personality traits are relevant to LA's central outcomes (e.g., engagement and achievement) and conducive to action, as their established ties to human-computer interaction (HCI) inform how systems time, frame, and personalize support. Drawing inspiration from HCI, where psychometrics inform personalization strategies, we propose that LA can evolve by treating traits not only as predictive features but as design resources and moderators of analytics efficacy. In line with past position papers published at LAK, we present a research agenda grounded in the LA cycle and discuss methodological and ethical challenges.
Conrad Borchers, Hannah Deininger, Zachary A. Pardos
LAK3
2026 Strengthening Course Transfer Pathways Using Graph-Theoretic Articulation Networks
abstract
Academic pathway research investigates how students navigate their postsecondary education over time to support academic attainment and equitable learning experiences. In this context, upward transfer from two-year to four-year institutions is critical for bachelor’s degree attainment, yet the process of manually establishing course equivalencies (i.e., articulation) to facilitate this transfer remains labor-intensive. This study contributes systematic evaluations of how existing human-curated articulation agreements can be leveraged for data-assistive course-to-course articulation within an interpretable graph-theoretic framework. Specifically, we construct Articulation Networks using articulation data between California community colleges and universities to identify and rank candidate course equivalencies based on node-similarity measures. Analyzing data from over 56,000 courses, we find that among the evaluated similarity measures, Personalized PageRank achieves the highest accuracy–approaching the recall upper bound imposed by the graph structure–and outperforms course title text similarity baselines. Further, we demonstrate how the network approach can integrate additional information, such as the Course Identification Numbering (C-ID) system, to improve equivalency recommendations and support the assignment of appropriate C-ID designations for community college courses. Our findings highlight how network-based methods can serve as a valuable resource to support faculty and policymakers in streamlining course-equivalency decisions and strengthening pathways for transfer students.
Yerin Kwak, Robin Schmucker, Zachary A. Pardos
LAK3
2026 Push and Pull in Community College Cross-Enrollment: Remoteness, Articulation, and Student Mobility
abstract
Cross-enrollment across institutions can expand access to courses and support student progression. Still, little is known about how geographic constraints and institutional policies jointly shape cross-enrollment within community college (CC) systems. We adopt a push--pull framework: geographic remoteness constrains feasible cross-institution mobility, while credit mobility may attract enrollment expressed as articulation (CC-to-university: credit toward a four-year partner) and course equivalencies (CC-to-CC: equivalencies across the system). Using de-identified administrative records from a 12-institution community college system (100,547 students; 1,290,311 course enrollments), we quantify outgoing and incoming cross-enrollment and relate these patterns to institutional remoteness and credit mobility. We find that less remote colleges exhibit higher outgoing and incoming cross-enrollment than more remote colleges. Further, cross-enrolled students are more likely to take articulated courses, and institutions with higher equivalency ratios receive higher incoming cross-enrollment (8.62% vs. 6.70%). This association was slightly stronger at more remote colleges. This study demonstrates how analysis of complex college systems can surface factors shaping student mobility and inform the design of cross-enrollment and articulation policies in CC systems.
Conrad Borchers, Robin Schmucker, Zachary A. Pardos
L@S4
2026 Survey of Computerized Adaptive Testing: A Machine Learning Perspective
abstract
Computerized Adaptive Testing (CAT) offers an efficient and personalized method for assessing examinee proficiency by dynamically adjusting test questions based on individual performance. Compared to traditional, non-personalized testing methods, CAT requires fewer questions and provides more accurate assessments. As a result, CAT has been widely adopted across various fields, including education, healthcare, sports, sociology, and the evaluation of AI models. While traditional methods rely on psychometrics and statistics, the increasing complexity of large-scale testing has spurred the integration of machine learning techniques. This paper aims to provide a machine learning-focused survey on CAT, presenting a fresh perspective on this adaptive testing paradigm. We delve into measurement models, question selection algorithm, bank construction, and test control within CAT, exploring how machine learning can optimize these components. Through an analysis of current methods, strengths, limitations, and challenges, we strive to develop robust, fair, and efficient CAT systems. By bridging psychometric-driven CAT research with machine learning, this survey advocates for a more inclusive and interdisciplinary approach to the future of adaptive testing.
Yan Zhuang 0001, Qi Liu 0003, Haoyang Bi, Zhenya Huang, Weizhe Huang, Jiatong Li 0002, Junhao Yu, Zirui Liu 0010, Zirui Hu, Yuting Hong, Zachary A. Pardos, Haiping Ma, Mengxiao Zhu 0001, Shijin Wang 0001, Enhong Chen
IEEE Trans. Pattern Anal. Mach. Intell.11
2025 PromptHive: Bringing Subject Matter Experts Back to the Forefront with Collaborative Prompt Engineering for Educational Content Creation
Mohi Reza, Ioannis Anastasopoulos, Shreya Bhandari, Zachary A. Pardos
CHI4
2025 Generating Change: AI as an Opportunity to Address Long-Standing OER Challenges
Ioannis Anastasopoulos, Zachary A. Pardos
EC-TEL (2)2
2025 Designing the Course Load Analytics Platform
Conrad Borchers, Shreya K. Sheel, Anirudh Pai, Sher Shah, Zachary A. Pardos
EC-TEL (2)5
2025 Temperature is All You Need: Approximating Human Mathematics Hint Efficacy with LLMs
Zachary A. Pardos, Shreya Bhandari
EC-TEL (2)1
2025 PromptHive: Demonstrating Collaborative, Human-Centered OER Creation with LLMs
Zachary A. Pardos, Shreya Bhandari, Ioannis Anastasopoulos
EC-TEL (2)1
2025 Can Language Models Grade Algebra Worked Solutions? Evaluating LLM-Based Autograders Against Human Grading
Shreya Bhandari, Zachary A. Pardos
EDM2
2025 When LLMs Hallucinate: Examining the Effects of Erroneous Feedback in Math Tutoring Systems
Marlene Steinbach, Shreya Bhandari, Jennifer Meyer, Zachary A. Pardos
EDM4
2025 PromptHive: Demonstrating Collaborative, Human-Centered OER Creation with LLMs
Shreya Bhandari, Ioannis Anastasopoulos, Zachary A. Pardos
L@S3
2025 Automating Academic Transcript Evaluation: A Comparative Study of OCR Techniques for Course and Grade Evaluation
abstract
As higher education institutions manage increasing volumes of student transcripts, the demand for efficient and accurate transcript evaluation has become more urgent. In the transfer admissions process, aligning courses and grades from diverse institutions remains a labor-intensive and error-prone task. A major challenge lies in extracting structured academic data from heterogeneous transcript formats, often in scanned or printed form. Recent advancements in Optical Character Recognition (OCR) and vision-language models (VLMs) offer promising avenues for automation. In this study, we evaluate three automated extraction pipelines: AWS Textract, a traditional OCR engine, and two multimodal large language model --- GPT-4o1 and Claude 3.7 --- that perform direct visual understanding of transcript documents. Through comparative analysis, we assess each method's effectiveness in extracting course and grade information across varied transcript layouts. Our findings indicate that combining OCR with semantic reasoning via VLMs significantly improves extraction accuracy, offering scalable solutions to streamline transcript evaluation workflows in transfer admissions.
Miha Bhaskaran, Zachary A. Pardos
L@S2
2025 Adaptive Tutoring Goes to Sweden: Machine Translation and Alignment of English OERs to a Swedish Calculus Course
abstract
Adaptive tutoring systems have demonstrated significant improvements in math learning, yet their adoption outside of the United States remains limited. The absence of these technologies, along with a lack of research on localizing tutoring systems to different educational contexts, presents a significant barrier for institutions seeking to integrate these tools into their classrooms to support students' math learning. This paper presents a case study on the localization and deployment of OATutor, an adaptive tutoring system developed in the U.S., for use in a math course at KTH Royal Institute of Technology in Sweden. Our study explores using artificial intelligence to automate and validate this process, focusing on translation and syllabus adaptation to ensure the content aligns with the course curriculum and the Swedish educational context. We successfully deployed the system in the course, demonstrating a novel method for translating math content and providing an analysis of syllabus adaptation tailored to the local context. By documenting this process, we contribute to the broader effort to make educational technologies more accessible to diverse learner populations by providing a scalable approach to localization.
Yerin Kwak, Nora Dunder, Olga Viberg, Zachary A. Pardos
L@S4
2025 When LLMs Hallucinate: Examining the Effects of Erroneous Feedback in Math Tutoring Systems
Marlene Steinbach, Shreya Bhandari, Jennifer Meyer, Zachary A. Pardos
L@S4
2024 Explainable Automatic Grading with Neural Additive Models
Aubrey Condor, Zachary A. Pardos
AIED (1)2
2024 AI for Adaptive Tutoring and Transfer Student Success
Zachary A. Pardos
CSEDU1
2024 Are You an Early Dropper or Late Shopper? Mining Enrollment Transaction Data to Study Procrastination in Higher Education
Conrad Borchers, Yinuo Xu, Zachary A. Pardos
EDM3
2024 Auditing an Automatic Grading Model with deep Reinforcement Learning
Aubrey Condor, Zachary A. Pardos
EDM2
2024 Leveraging Large Language Models for Next-Generation Educational Technologies
Neil T. Heffernan, Rose E. Wang, Christopher J. MacLellan, Arto Hellas, Chenglu Li, Candace A. Walkington, Joshua Littenberg-Tobias, David Joyner, Steven Moore, Adish Singla, Zachary A. Pardos, Maciej Pankiewicz, Juho Kim 0001, Shashank Sonkar, Clayton Cohn, Anthony Botelho, Andrew S. Lan, Mingyu Feng, Tanja Käser, Eamon Worden
EDM11
2024 Comparing Authoring Experiences with Spreadsheet Interfaces vs GUIs
abstract
There is little consensus over whether graphical user interfaces (GUIs) or programmatic systems are better for word processing. Even less is known about each interfaces’ affordances and limitations in the context of creating content for adaptive tutoring systems. In order to afford instructors the use of such systems with their own or adapted pedagogies, we must study their experiences in inputting their content. In this study, we conduct a between-subjects A/B test with two content authoring interfaces, a GUI and spreadsheet, to explore 32 instructors’ experiences in authoring algebra content with hints, scaffolds, images, and special characters. We study their experiences by measuring time taken, accuracy, and their perceptions of each interfaces’ usability. Our findings indicate no significant relationship between interface used and time taken authoring problems but significantly more accuracy in authoring problems in the spreadsheet interface over the GUI. Although both interfaces performed reasonably well in time taken and accuracy, both were perceived as average to low in usability, highlighting a dissonance between instructors’ perceptions and actual performances. Since both interfaces are reasonable in authoring content, other factors can be explored, such as cost and author incentive, when deciding which interface approach to take for authoring tutor content.
Shreya K. Sheel, Ioannis Anastasopoulos, Zachary A. Pardos
LAK3
2024 Extracting Course Similarity Signal using Subword Embeddings
abstract
Several studies have shown the utility of neural network models in learning course similarities and providing insightful course recommendations from enrollment data. In this study, we explore if additional signals can be found in the morphological structure of course names. We train skip-gram, FastText, and other combination models on these course sequence data from the past nine years and compare results with state-of-the-art models. We find a 97.95% improvement in model performance (as measured by recall @ 10 in similarity-based course recommendations) from skip-gram to FastText, and 80.75% improvement from the current best combination model to the previous state-of-the-art model, indicating that the naming convention of courses (e.g., PHYS_H101) carries valuable signals. We define attributes with which to categorize course pairs from our validation set and present an analysis of which models are strongest and weakest at predicting the similarity of which categories of course pairs. Additionally, we also explore course-taking culture, analyzing if courses with the same demographic features are learned to be more similar. Our approach could help students find alternatives to full courses, improve existing course recommendation systems and course articulations between institutions, and assist institutions in course policy-making.
Yinuo Xu, Zachary A. Pardos
LAK2
2024 Gaining Insights into Group-Level Course Difficulty via Differential Course Functioning
abstract
Curriculum Analytics (CA) studies curriculum structure and student data to ensure the quality of educational programs. One desirable property of courses within curricula is that they are not unexpectedly more difficult for students of different backgrounds. While prior work points to likely variations in course difficulty across student groups, robust methodologies for capturing such variations are scarce, and existing approaches do not adequately decouple course-specific difficulty from students' general performance levels. The present study introduces Differential Course Functioning (DCF) as an Item Response Theory (IRT)-based CA methodology. DCF controls for student performance levels and examines whether significant differences exist in how distinct student groups succeed in a given course. Leveraging data from over 20,000 students at a large public university, we demonstrate DCF's ability to detect inequities in undergraduate course difficulty across student groups described by grade achievement. We compare major pairs with high co-enrollment and transfer students to their non-transfer peers. For the former, our findings suggest a link between DCF effect sizes and the alignment of course content to student home department motivating interventions targeted towards improving course preparedness. For the latter, results suggest minor variations in course-specific difficulty between transfer and non-transfer students. While this is desirable, it also suggests that interventions targeted toward mitigating grade achievement gaps in transfer students should encompass comprehensive support beyond enhancing preparedness for individual courses. By providing more nuanced and equitable assessments of academic performance and difficulties experienced by diverse student populations, DCF could support policymakers, course articulation officers, and student advisors.
Frederik Baucks, Robin Schmucker, Conrad Borchers, Zachary A. Pardos, Laurenz Wiskott
L@S4
2023 OATutor: An Open-source Adaptive Tutoring System and Curated Content Library for Learning Sciences Research
abstract
Despite decades long establishment of effective tutoring principles, no adaptive tutoring system has been developed and open-sourced to the research community. The absence of such a system inhibits researchers from replicating adaptive learning studies and extending and experimenting with various tutoring system design directions. For this reason, adaptive learning research is primarily conducted on a small number of proprietary platforms. In this work, we aim to democratize adaptive learning research with the introduction of the first open-source adaptive tutoring system based on Intelligent Tutoring System principles. The system, we call Open Adaptive Tutor (OATutor), has been iteratively developed over three years with field trials in classrooms drawing feedback from students, teachers, and researchers. The MIT-licensed source code includes three creative commons (CC BY) textbooks worth of algebra problems, with tutoring supports authored by the OATutor project. Knowledge Tracing, an A/B testing framework, and LTI support are included.
Zachary A. Pardos, Matthew Tang, Ioannis Anastasopoulos, Shreya K. Sheel, Ethan Zhang
CHI1
2023 Mining Detailed Course Transaction Records for Semantic Information
Yinuo Xu, Zachary A. Pardos
EDM2
2023 Insights into undergraduate pathways using course load analytics
abstract
Course load analytics (CLA) inferred from LMS and enrollment features can offer a more accurate representation of course workload to students than credit hours and potentially aid in their course selection decisions. In this study, we produce and evaluate the first machine-learned predictions of student course load ratings and generalize our model to the full 10,000 course catalog of a large public university. We then retrospectively analyze longitudinal differences in the semester load of student course selections throughout their degree. CLA by semester shows that a student’s first semester at the university is among their highest load semesters, as opposed to a credit hour-based analysis, which would indicate it is among their lowest. Investigating what role predicted course load may play in program retention, we find that students who maintain a semester load that is low as measured by credit hours but high as measured by CLA are more likely to leave their program of study. This discrepancy in course load is particularly pertinent in STEM and associated with high prerequisite courses. Our findings have implications for academic advising, institutional handling of the freshman experience, and student-facing analytics to help students better plan, anticipate, and prepare for their selected courses.
Conrad Borchers, Zachary A. Pardos
LAK2
2023 Introducing an Open-source Adaptive Tutoring System to Accelerate Learning Sciences Experimentation
abstract
Learning @ Scale has embraced movements that spread access to education through open and free platforms of learning. In this tutorial, we introduce OATutor (recently published at CHI'23), the field's first free and open-source adaptive tutoring system based on ITS principles and designed for rapid experimentation. The MIT-licensed platform can be deployed to git-pages in only a few clicks and supports BKT mastery-based adaptive problem selection. We demonstrate how the system can be used to rapidly run A/B experiments, analyze the data, and publish the entire tutor, content, and analysis scripts to facilitate unprecedented ease of replication and transparency, as demonstrated in a recent study comparing ChatGPT generated hints to human-tutor hints. Our four-part tutorial will include how to add lessons to the system and link to them from assignments in a MOOC platform or LMS via LTI. The structured JSON format of the four CC BY courses worth of content released with OATutor opens up avenues for researchers to apply new and existing educational data mining and NLP techniques (e.g., KC tagging) and rapidly evaluate the impact of subsequent changes on learners.
Ioannis Anastasopoulos, Shreya K. Sheel, Zachary A. Pardos, Shreya Bhandari
L@S3
2023 Convincing the Expert: Reducing Algorithm Aversion in Administrative Higher Education Decision-making
abstract
Algorithm aversion can be described as the tendency of human decision-makers to discount algorithmic recommendations more heavily than similar recommendations made by humans. It has been a phenomenon observed to be most acutely exhibited by domain experts. In our work, we focus on expert administrators in higher education making course credit equivalency decisions that affect the academic planning and potential degree progress of millions of prospective transfer students. Using human-centered design, we construct an AI-based platform for recommending matches to courses on a student's transcript to courses offered at another institution. We conduct a 2 x 2, between-subject experiment to investigate potential aversion mitigation techniques by manipulating the presence of outliers and allowing users to provide feedback to the algorithm. Our findings indicate that intentional, human-centered design and careful presentation of algorithm-based recommendations can help improve Human-AI interaction and productivity with implications for various domains of expertise.
Lingrui Xu, Zachary A. Pardos, Anirudh Pai
L@S2
2023 A Bounded Ability Estimation for Computerized Adaptive Testing
abstract
Computerized adaptive testing (CAT), as a tool that can efficiently measure student's ability, has been widely used in various standardized tests (e.g., GMAT and GRE). The adaptivity of CAT refers to the selection of the most informative questions for each student, reducing test length. Existing CAT methods do not explicitly target ability estimation accuracy since there is no student's true ability as ground truth; therefore, these methods cannot be guaranteed to make the estimate converge to the true with such limited responses. In this paper, we analyze the statistical properties of estimation and find a theoretical approximation of the true ability: the ability estimated by full responses to question bank. Based on this, a Bounded Ability Estimation framework for CAT (BECAT) is proposed in a data-summary manner, which selects a question subset that closely matches the gradient of the full responses. Thus, we develop an expected gradient difference approximation to design a simple greedy selection algorithm, and show the rigorous theoretical and error upper-bound guarantees of its ability estimate. Experiments on both real-world and synthetic datasets, show that it can reach the same estimation accuracy using 15\% less questions on average, significantly reducing test length.
Yan Zhuang 0001, Qi Liu 0003, Guanhao Zhao, Zhenya Huang, Weizhe Huang, Zachary A. Pardos, Enhong Chen, Xin Li 0064
NeurIPS6
2022 Representing Scoring Rubrics as Graphs for Automatic Short Answer Grading
Aubrey Condor, Zachary A. Pardos, Marcia C. Linn
AIED (1)2
2022 A deep reinforcement learning approach to automatic formative feedback
Aubrey Condor, Zachary A. Pardos
EDM2
2022 Does chronology matter? Sequential vs contextual approaches to knowledge tracing
Zachary A. Pardos
EDM2
2021 Degree Planning with PLAN-BERT: Multi-Semester Recommendation Using Future Courses of Interest
abstract
Planning scenarios involving user pre-specified items present themselves frequently in recommender system domains. Although next-item and next-basket recommendation has been a focus of prior research, multiple consecutive item or basket approaches are needed for planning. No prior work has leveraged pre-specified future reference items to improve this type of challenging consecutive prediction task at inference time. PLAN-BERT is the first to accommodate this general planning scenario. It does so by contributing novel modifications that take inspiration from the masked training and contextual embedding of self-attention models. To test the model, we use the domain of student academic degree planning, in which students’ past course histories and future pre-specified courses of interest are used to fill in the remainder of their curriculum. Our offline analyses consist of 15 million historic course enrollments at 20 institutions and an online evaluation conducted at one of the institutions. Our results show that PLAN-BERT outperforms existing models including BERT, BiLSTM, and a UserKNN baseline, with small numbers of future reference items substantially improving accuracy. Significant results from our online evaluation show PLAN-BERT to be strongest in students' perceptions of personalization.
Erzhuo Shao, Shiyuan Guo, Zachary A. Pardos
AAAI3
2021 Towards Equity and Algorithmic Fairness in Student Grade Prediction
abstract
Equity of educational outcome and fairness of AI with respect to race have been topics of increasing importance in education. In this work, we address both with empirical evaluations of grade prediction in higher education, an important task to improve curriculum design, plan interventions for academic support, and offer course guidance to students. With fairness as the aim, we trial several strategies for both label and instance balancing to attempt to minimize differences in algorithm performance with respect to race. We find that an adversarial learning approach, combined with grade label balancing, achieved by far the fairest results. With equity of educational outcome as the aim, we trial strategies for boosting predictive performance on historically underserved groups and find success in sampling those groups in inverse proportion to their historic outcomes. With AI-infused technology supports increasingly prevalent on campuses, our methodologies fill a need for frameworks to consider performance trade-offs with respect to sensitive student attributes and allow institutions to instrument their AI resources in ways that are attentive to equity and fairness.
Weijie Jiang 0007, Zachary A. Pardos
AIES2
2021 pyBKT: An Accessible Library of Bayesian Knowledge Tracing Models
Anirudhan Badrinath, Frédéric Wang, Zachary A. Pardos
EDM3
2021 Automatic short answer grading with SBERT on out-of-sample questions
Aubrey Condor, Max Litster, Zachary A. Pardos
EDM3
2021 Item Response Ranking for Cognitive Diagnosis
abstract
Cognitive diagnosis, a fundamental task in education area, aims at providing an approach to reveal the proficiency level of students on knowledge concepts. Actually, monotonicity is one of the basic conditions in cognitive diagnosis theory, which assumes that student's proficiency is monotonic with the probability of giving the right response to a test item. However, few of previous methods consider the monotonicity during optimization. To this end, we propose Item Response Ranking framework (IRR), aiming at introducing pairwise learning into cognitive diagnosis to well model the monotonicity between item responses. Specifically, we first use an item specific sampling method to sample item responses and construct response pairs based on their partial order, where we propose the two-branch sampling methods to handle the unobserved responses. After that, we use a pairwise objective function to exploit the monotonicity in the pair formulation. In fact, IRR is a general framework which can be applied to most of contemporary cognitive diagnosis models. Extensive experiments demonstrate the effectiveness and interpretability of our method.
Shiwei Tong, Qi Liu 0003, Runlong Yu, Wei Huang 0002, Zhenya Huang, Zachary A. Pardos, Weijie Jiang 0007
IJCAI6
2021 Which one's more work? Predicting effective credit hours between courses
abstract
University students select courses for an upcoming term in part based on expected workload. Course credit hours is often the only metric given by the institution relevant to how much work a course will be and does not serve as a precise estimate due to the lack of granularity of the metric which can lead to student under or overestimation. We define a novel task of predicting relative effective course credit hours, or time load; essentially, determining which courses take more time than others. For this task, we draw from institutional data sources including course catalog descriptions, student enrollment histories and ratings from a popular course rating website. To validate this work, we design a personalized survey for university students to collect ground truth labels, presenting them with pairs of courses they had taken and asking which course took more time per week on average. We evaluate which sources of data using which machine representation techniques provide the best prediction of these course time load ratings. We establish a benchmark accuracy of 0.71 on this novel task and find skip-grams applied to enrollment data (i.e., course2vec), not catalog descriptions, to be most useful in predicting the time demands of a course.
Shruthi Chockkalingam, Run Yu 0002, Zachary A. Pardos
LAK3
2021 Learning Skill Equivalencies Across Platform Taxonomies
abstract
Assessment and reporting of skills is a central feature of many digital learning platforms. With students often using multiple platforms, cross-platform assessment has emerged as a new challenge. While technologies such as Learning Tools Interoperability (LTI) have enabled communication between platforms, reconciling the different skill taxonomies they employ has not been solved at scale. In this paper, we introduce and evaluate a methodology for finding and linking equivalent skills between platforms by utilizing problem content as well as the platform’s clickstream data. We propose six models to represent skills as continuous real-valued vectors, and leverage machine translation to map between skill spaces. The methods are tested on three digital learning platforms: ASSISTments, Khan Academy, and Cognitive Tutor. Our results demonstrate reasonable accuracy in skill equivalency prediction from a fine-grained taxonomy to a coarse-grained one, achieving an average [email protected] of 0.8 between the three platforms. Our skill translation approach has implications for aiding in the tedious, manual process of taxonomy to taxonomy mapping work, also called crosswalks, within the tutoring as well as standardized testing worlds.
Zhi Li 0078, Cheng Ren, Xianyou Li, Zachary A. Pardos
LAK4
2020 Lexical Relation Mining in Neural Word Embeddings
abstract
Work with neural word embeddings and lexical relations has largely focused on confirmatory experiments which use human-curated examples of semantic and syntactic relations to validate against.In this paper, we explore the degree to which lexical relations, such as those found in popular validation sets, can be derived and extended from a variety of neural embeddings using classical clustering methods.We show that the Word2Vec space of word-pairs (i.e., offset vectors) significantly outperforms other more contemporary methods, even in the presence of a large number of noisy offsets.Moreover, we show that via a simple nearest neighbor approach in the offset space, new examples of known relations can be discovered.Our results speak to the amenability of offset vectors from non-contextual neural embeddings to find semantically coherent clusters.This simple approach has implications for the exploration of emergent regularities and their examples, such as emerging trends on social media and their related posts.
Aishwarya Jadhav, Yifat Amir, Zachary A. Pardos
COLING3
2020 Understanding the Source of Semantic Regularities in Word Embeddings
abstract
Semantic relations are core to how humans understand and express concepts in the real world using language.Recently, there has been a thread of research aimed at modeling these relations by learning vector representations from text corpora.Most of these approaches focus strictly on leveraging the co-occurrences of relationship word pairs within sentences.In this paper, we investigate the hypothesis that examples of a lexical relation in a corpus are fundamental to a neural word embedding's ability to complete analogies involving the relation.Our experiments, in which we remove all known examples of a relation from training corpora, show only marginal degradation in analogy completion performance involving the removed relation.This finding enhances our understanding of neural word embeddings, showing that co-occurrence information of a particular semantic relation is the not the main source of their structural regularity.
Hsiao-Yu Chiang, José Camacho-Collados, Zachary A. Pardos
CoNLL3
2020 Applying Recent Innovations from NLP to MOOC Student Course Trajectory Modeling
Clarence Chen, Zachary A. Pardos
EDM2
2020 Evaluating sources of course information and models of representation on a variety of institutional prediction tasks
Weijie Jiang 0007, Zachary A. Pardos
EDM2
2020 Designing for serendipity in a university course recommendation system
abstract
Collaborative filtering based algorithms, including Recurrent Neural Networks (RNN), tend towards predicting a perpetuation of past observed behavior. In a recommendation context, this can lead to an overly narrow set of suggestions lacking in serendipity and inadvertently placing the user in what is known as a "filter bubble." In this paper, we grapple with the issue of the filter bubble in the context of a course recommendation system in production at a public university. Our approach is to present course results that are novel or unexpected to the student but still relevant to their interests. We build one set of models based on course catalog descriptions (BOW) and another set informed by enrollment histories (course2vec). We compare the performance of these models on off-line validation sets and against the system's existing RNN-based recommendation engine in an online user study of undergraduates (N = 70) who rated their course recommendations along six characteristics related to serendipity. Results of the user study show a dramatic lack of novelty in RNN recommendations and depict the characteristic trade-offs that make serendipity difficult to achieve. While the machine learned course2vec models performed best on off-line validation tasks, it was the simple bag-of-words based recommendations that students rated as more serendipitous. We discuss the role of the kind of information presented by the system in a student's decision to accept a recommendation from either algorithm.
Zachary A. Pardos, Weijie Jiang 0007
LAK1
2019 Degree Curriculum Contraction: A Vector Space Approach
Mohamed Alkaoud, Zachary A. Pardos
AIED (2)2
2019 Design and Deployment of a Better Course Search Tool: Inferring Latent Keywords from Enrollment Networks
Matthew Dong, Run Yu 0002, Zachary A. Pardos
EC-TEL3
2019 Design and Deployment of a Better University Course Search: Inferring Latent Keywords from Enrollments
Matthew Dong, Run Yu 0002, Zachary A. Pardos
EDM3
2019 Binary Q-matrix Learning with dAFM
Zachary A. Pardos
EDM2
2019 Generalizing Expert Misconception Diagnoses Through Common Wrong Answer Embedding
John Kolb, Scott Farrar, Zachary A. Pardos
EDM3
2019 Beyond Autoscoring: Extracting Conceptual Connections from Essays for Classroom Instruction
Korah J. Wiley, Allison Bradford, Zachary A. Pardos, Marcia C. Linn
EDM3
2019 Beyond Autoscoring: Extracting Conceptual Connections from Essays for Classroom Instruction
Korah J. Wiley, Allison Bradford, Zachary A. Pardos, Marcia C. Linn
EDM3
2019 Goal-based Course Recommendation
abstract
With cross-disciplinary academic interests increasing and academic advising resources over capacity, the importance of exploring data-assisted methods to support student decision making has never been higher. We build on the findings and methodologies of a quickly developing literature around prediction and recommendation in higher education and develop a novel recurrent neural network-based recommendation system for suggesting courses to help students prepare for target courses of interest, personalized to their estimated prior knowledge background and zone of proximal development. We validate the model using tests of grade prediction and the ability to recover prerequisite relationships articulated by the university. In the third validation, we run the fully personalized recommendation for students the semester before taking a historically difficult course and observe differential overlap with our would-be suggestions. While not proof of causal effectiveness, these three evaluation perspectives on the performance of the goal-based model build confidence and bring us one step closer to deployment of this personalized course preparation affordance in the wild.
Weijie Jiang 0007, Zachary A. Pardos, Qiang Wei 0001
LAK2
2019 Data-Assistive Course-to-Course Articulation Using Machine Translation
abstract
Higher education at scale, such as in the California public post-secondary system, has promoted upward socioeconomic mobility by supporting student transfer from 2-year community colleges to 4-year degree granting universities. Among the barriers to transfer is earning enough credit at 2-year institutions that qualify for the transfer credit required by 4-year degree programs. Defining which course at one institution will count as credit for an equivalent course at another institution is called course articulation, and it is an intractable task when attempting to manually articulate every set of courses at every institution with one another. In this paper, we present a methodology towards making tractable this process of defining and maintaining articulations by leveraging the information contained within historic enrollment patterns and course catalog descriptions. We provide a proof-of-concept analysis using data from a 4-year and 2-year institution to predict articulation pairs between them, produced from machine translation models and validated by a set of 65 institutionally pre-established course-to-course articulations. Finally, we create a report of proposed articulations for consumption by the institutions and close with a discussion of limitations and the challenges to adoption.
Zachary A. Pardos, Hung Chau, Haocheng Zhao
L@S1
2019 Time slice imputation for personalized goal-based recommendation in higher education
abstract
Learners are often faced with the following scenario: given a goal for the future, and what they have learned in the past, what should they do now to best achieve their goal? We build on work utilizing deep learning to make inferences about how past actions correspond to future outcomes and enhance this work with a novel application of backpropagation to learn per-user optimized next actions. We apply this technique to two datasets, one from a university setting in which courses can be recommended towards preparation for a target course, and one from a massive open online course (MOOC) in which course pages can be recommended towards quiz preparation. In both cases, our algorithm is applied to recommend actions the learner can take to maximize a desired future achievement objective, given their past actions and performance.
Weijie Jiang 0007, Zachary A. Pardos
RecSys2
2019 Connectionist recommendation in the wild: on the utility and scrutability of neural networks for personalized course guidance
Zachary A. Pardos, Weijie Jiang 0007
User Model. User Adapt. Interact.1
2018 Diagnosing University Student Subject Proficiency and Predicting Degree Completion in Vector Space
abstract
We investigate the issues of undergraduate on-time graduation with respect to subject proficiencies through the lens of representation learning, training a student vector embeddings from a dataset of 8 years of course enrollments. We compare the per-semester student representations of a cohort of undergraduate Integrative Biology majors to those of graduated students in subject areas involved in their degree requirements. The result is an embedding rich in information about the relationships between majors and pathways taken by students which encoded enough information to improve prediction accuracy of on-time graduation to 95%, up from a baseline of 87.3%. Challenges to preparation of the data for student vectorization and sourcing of validation sets for optimization are discussed.
Yuetian Luo, Zachary A. Pardos
AAAI2
2018 Communication at Scale in a MOOC Using Predictive Engagement Analytics
Christopher Vu Le, Zachary A. Pardos, Samuel D. Meyer, Rachel Thorp
AIED (1)2
2018 Deep Knowledge Tracing for Free-Form Student Code Progression
Vinitra Swamy, Allen Guo, Sam Lau, Wilton Wu, Madeline Wu, Zachary A. Pardos, David E. Culler
AIED (2)6
2018 AutoQuiz: A Personalized, Adaptive, Test Practice System (Abstract Only)
abstract
No abstract available.
Zhiping Xiao 0001, Zachary A. Pardos
SIGCSE3
2017 Enabling Real-Time Adaptivity in MOOCs with a Personalized Next-Step Recommendation Framework
abstract
In this paper, we demonstrate a first-of-its-kind adaptive intervention in a MOOC utilizing real-time clickstream data and a novel machine learned model of behavior. We detail how we augmented the edX platform with the capabilities necessary to support this type of intervention which required both tracking learners' behaviors in real-time and dynamically adapting content based on each learner's individual clickstream history. Our chosen pilot intervention was in the category of adaptive pathways and courseware and took the form of a navigational suggestion appearing at the bottom of every non-forum content page in the course. We designed our pilot intervention to help students more efficiently navigate their way through a MOOC by predicting the next page they were likely to spend significant time on and allowing them to jump directly to that page. While interventions which attempt to optimize for learner achievement are candidates for this adaptive framework, behavior prediction has the benefit of not requiring causal assumptions to be made in its suggestions. We present a novel extension of a behavioral model that takes into account students' time spent on pages and forecasts the same. Several approaches to representing time using Recurrent Neural Networks are evaluated and compared to baselines without time, including a basic n-gram model. Finally, we discuss design considerations and handling of edge cases for real-time deployment, including considerations for training a machine learned model on a previous offering of a course for use in a subsequent offering where courseware may have changed. This work opens the door to broad experimentation with adaptivity and serves as a first example of delivering a data-driven personalized learning experience in a MOOC.
Zachary A. Pardos, Daniel Davis, Christopher Vu Le
L@S1
2017 Imputing KCs with Representations of Problem Content and Context
abstract
Cognitive task analysis is a laborious process made more onerous in educational platforms where many problems are user created and mostly left without identified knowledge components. Past approaches to this issue of untagged problems have centered around text mining to impute knowledge components (KC). In this work, we advance KC imputation research by modeling both the content (text) of a problem as well as the context (problems around it) using a novel application of skip-gram based representation learning applied to tens of thousands of student response sequences from the ASSISTments 2012 public dataset. We find that there is as much information in the contextual representation as the content representation, with the combination of sources of information leading to a 90% accuracy in predicting the missing skill from a KC model of 198. This work underscores the value of considering problems in context for the KC prediction task and has broad implications for its use with other modeling objectives such as KC model improvement.
Zachary A. Pardos, Anant Dadu
UMAP1
2016 Adding eye-tracking AOI data to models of representation skills does not improve prediction accuracy
Martina A. Rau, Zachary A. Pardos
EDM2
2016 Improving efficacy attribution in a self-directed learning environment using prior knowledge individualization
abstract
Models of learning in EDM and LAK are pushing the boundaries of what can be measured from large quantities of historical data. When controlled randomization is present in the learning platform, such as randomized ordering of problems within a problem set, natural quasi-randomized controlled studies can be conducted, post-hoc. Difficulty and learning gain attribution are among factors of interest that can be studied with secondary analyses under these conditions. However, much of the content that we might like to evaluate for learning value is not administered as a random stimulus to students but instead is being self-selected, such as a student choosing to seek help in the discussion forums, wiki pages, or other pedagogically relevant material in online courseware. Help seekers, by virtue of their motivation to seek help, tend to be the ones who have the least knowledge. When presented with a cohort of students with a bi-modal or uniform knowledge distribution, this can present problems with model interpretability when a single point estimation is used to represent cohort prior knowledge. Since resource access is indicative of a low knowledge student, a model can tend towards attributing the resources with low or negative learning gain in order to better explain performance given the higher average prior point estimate. In this paper we present several individualized prior strategies and demonstrate how learning efficacy attribution validity and prediction accuracy improve as a result. Level of education attained, relative past assessment performance, and the prior per student cold start heuristic were employed and compared as prior knowledge individualization strategies.
Zachary A. Pardos, Yanbo Xu
LAK1
2016 Predicting Student Learning using Log Data from Interactive Simulations on Climate Change
abstract
Interactive simulations are commonly used tools in technology enhanced education. Simulations can be a powerful tool for allowing students to engage in inquiry, especially in science disciplines. They can help students develop an understanding of complex science phenomena in which multiple variables are at play. Developing models for complex domains, like climate science, is important for learning. Equally important, though, is understanding how students use these simulations. Finding use patterns that lead to learning will allow us to develop better guidance for students who struggle to extract the useful information from the simulation. In this study, we generate features from action log data collected while students interacted with simulations on climate change. We seek to understand what types of features are important for student learning by using regression models to map features onto learning outcomes.
Elizabeth A. McBride, Jonathan M. Vitale, Hannah Gogel, Mario M. Martinez, Zachary A. Pardos, Marcia C. Linn
L@S5
2016 Deep Neural Networks and How They Apply to Sequential Education Data
abstract
Modern deep neural networks have achieved impressive results in a variety of automated tasks, such as text generation, grammar learning, and speech recognition. This paper discusses how education research might leverage recurrent neural network architectures in two small case studies. Specifically, we train a two-layer Long Short-Term Memory (LSTM) network on two distinct forms of education data: (1) essays written by students in a summative environment, and (2) MOOC clickstream data. Without any features specified beforehand, the network attempts to learn the underlying structure of the input sequences. After training, the model can be used generatively to produce new sequences with the same underlying patterns exhibited by the input distribution. These early explorations demonstrate the potential for applying deep learning techniques to large education data sets.
Joshua C. Peterson, Zachary A. Pardos
L@S3
2015 Understanding Student Success in Chemistry Using Gaze Tracking and Pupillometry
Joshua C. Peterson, Zachary A. Pardos, Martina A. Rau, Anna Swigart, Colin Gerber, Jon McKinsey
AIED2
2015 Ethics and Privacy in EDM
Dragan Gasevic, Taylor Martin, Zachary A. Pardos, Mykola Pechenizkiy, John C. Stamper, Osmar R. Zaïane
EDM3
2015 Evaluating Educational Videos using Bayesian Knowledge Tracing and Big Data
Zachary MacHardy, Zachary A. Pardos
EDM2
2015 Desirable Difficulty and Other Predictors of Effective Item Orderings
Hannah Gogel, Elizabeth A. McBride, Zachary A. Pardos
EDM4
2015 Toward the Evaluation of Educational Videos using Bayesian Knowledge Tracing and Big Data
abstract
Along with the advent of MOOCs and other online learning platforms such as Khan Academy, the role of online education has continued to grow in relation to that of traditional on-campus instruction. Rather than tackle the problem of evaluating large educational units such as entire online courses, this paper approaches a smaller problem: exploring a framework for evaluating more granular educational units, in this case, short educational videos. We have chosen to leverage an adaptation of traditional Bayesian Knowledge Tracing (BKT), intended to incorporate the usage of video content in addition to assessment activity. By exploring the change in predictive error when alternately including or omitting video activity, we suggest a metric for determining the relevance of videos to associated assessments. To validate our hypothesis and demonstrate the application of our proposed methods we use data obtained from the popular Khan Academy website.
Zachary MacHardy, Zachary A. Pardos
L@S2
2015 moocRP: An Open-source Analytics Platform
abstract
In this paper, we address issues of transparency, modularity, and privacy with the introduction of an open source, web-based data repository and analysis tool tailored to the Massive Open Online Course community. The tool integrates data request/authorization and distribution workflows as well as a simple analytics module upload format to enable reuse and replication of analytics results among instructors and researchers. We survey the evolving landscape of competing data models, all of which can be accommodated in the platform. Data model descriptions are provided to analytics authors who choose, much like with smartphone app stores, to write for any number of data models depending on their needs and the proliferation of the particular data model. Two case study examples of analytics and interactive visualizations are described in the paper. The result is a simple but effective approach to learning analytics immediately applicable to X consortium institutions and beyond.
Zachary A. Pardos, Kevin Kao
L@S1
2015 Item Ordering Effects with Qualitative Explanations using Online Adaptive Tutoring Data
abstract
Online computer adaptive learning is increasingly being used in classrooms as a way to provide guided learning for students. Such tutors have the potential to provide tailored feedback based on specific student needs and misunderstandings. Bayesian knowledge tracing (BKT) is used to model student knowledge when knowledge is assumed to be changing throughout a single assessment period; in contrast, traditional Item Response Theory (IRT) models assume student knowledge to be constant within an assessment period. The basic BKT model assumes that the chance a student transitions from "not knowing" to "knowing" after each item is the same, and problems are considered learning opportunities. It could be the case, however, that learning is actually context sensitive, where students' learning might be improved when the items and their associated tutoring content are delivered to the student in a particular order. In this paper, we use BKT models to find such context sensitive transition probabilities from real data delivered by an online tutoring system, ASSISTments. After empirically deriving orderings that lead to better learning, we qualitatively analyze the items and their tutoring content to uncover any mechanisms that might explain why such orderings are modeled to have higher learning potential.
Elizabeth A. McBride, Hannah Gogel, Zachary A. Pardos
L@S4
2015 Dynamic Approaches to Modeling Student Affect and its Changing Role in Learning and Performance
Seth Corrigan, Tiffany Barkley, Zachary A. Pardos
UMAP3
2014 Refining Learning Maps with Data Fitting Techniques: Searching for Better Fitting Learning Maps
Seth Adjei, Douglas Selent, Neil T. Heffernan, Zachary A. Pardos, Angela Broaddus, Neal Kingston
EDM4
2013 First Annual Workshop on Massive Open Online Courses
Zachary A. Pardos, Emily Schneider
AIED1
2013 A Spectral Learning Approach to Knowledge Tracing
Mohammad Hassan Falakmasir, Zachary A. Pardos, Geoffrey J. Gordon, Peter Brusilovsky
EDM2
2013 Adapting Bayesian Knowledge Tracing to a Massive Open Online Course in edX
Zachary A. Pardos, Yoav Bergner, Daniel T. Seaton, David E. Pritchard
EDM1
2013 Affective states and state tests: investigating how affect throughout the school year predicts end of year learning outcomes
abstract
In this paper, we investigate the correspondence between student affect in a web-based tutoring platform throughout the school year and learning outcomes at the end of the year, on a high-stakes mathematics exam. The relationships between affect and learning outcomes have been previously studied, but not in a manner that is both longitudinal and finer-grained. Affect detectors are used to estimate student affective states based on post-hoc analysis of tutor log-data. For every student action in the tutor the detectors give us an estimated probability that the student is in a state of boredom, engaged concentration, confusion, and frustration, and estimates of the probability that they are exhibiting off-task or gaming behaviors. We ran the detectors on two years of log-data from 8th grade student use of the ASSISTments math tutoring system and collected corresponding end of year, high stakes, state math test scores for the 1,393 students in our cohort. By correlating these data sources, we find that boredom during problem solving is negatively correlated with performance, as expected; however, boredom is positively correlated with performance when exhibited during scaffolded tutoring. A similar pattern is unexpectedly seen for confusion. Engaged concentration and frustration are both associated with positive learning outcomes, surprisingly in the case of frustration.
Zachary A. Pardos, Ryan Baker 0001, Maria Ofelia Clarissa Z. San Pedro, Sujith M. Gowda, Supreeth M. Gowda
LAK1
2012 The real world significance of performance prediction
Zachary A. Pardos, Qing Yang Wang, Shubhendu Trivedi
EDM1
2012 Investigating Practice Schedules of Multiple Fraction Representations Using Knowledge Tracing Based Learning Analysis Techniques
Martina A. Rau, Zachary A. Pardos
EDM2
2012 Co-Clustering by Bipartite Spectral Graph Partitioning for Out-of-Tutor Prediction
Shubhendu Trivedi, Zachary A. Pardos, Gábor N. Sárközy, Neil T. Heffernan
EDM2
2012 Content Learning Analysis Using the Moment-by-Moment Learning Detector
Sujith M. Gowda, Zachary A. Pardos, Ryan Baker 0001
ITS2
2012 Knowledge Component Suggestion for Untagged Content in an Intelligent Tutoring System
Mario Karlovcec, Mariheida Cordova-Sanchez, Zachary A. Pardos
ITS3
2012 Clustered Knowledge Tracing
Zachary A. Pardos, Shubhendu Trivedi, Neil T. Heffernan, Gábor N. Sárközy
ITS1
2011 Clustering Students to Generate an Ensemble to Improve Standard Test Score Predictions
Shubhendu Trivedi, Zachary A. Pardos, Neil T. Heffernan
AIED2
2011 Comparing of Traditional Assessment with Dynamic Testing in a Tutoring System
Mingyu Feng, Neil T. Heffernan, Zachary A. Pardos, Cristina Heffernan
EDM3
2011 Less is More: Improving the Speed and Prediction Power of Knowledge Tracing by Using Less Data
Bahador B. Nooraei, Zachary A. Pardos, Neil T. Heffernan, Ryan Baker 0001
EDM2
2011 Ensembling Predictions of Student Post-Test Scores for an Intelligent Tutoring System
Zachary A. Pardos, Sujith M. Gowda, Ryan Baker 0001, Neil T. Heffernan
EDM1
2011 Does Time Matter? Modeling the Effect of Time with Bayesian Knowledge Tracing
Yumeng Qiu, Yingmei Qi, Hanyuan Lu, Zachary A. Pardos, Neil T. Heffernan
EDM4
2011 Spectral Clustering in Educational Data Mining
Shubhendu Trivedi, Zachary A. Pardos, Gábor N. Sárközy, Neil T. Heffernan
EDM2
2011 Ensembling Predictions of Student Knowledge within Intelligent Tutoring Systems
Ryan Baker 0001, Zachary A. Pardos, Sujith M. Gowda, Bahador B. Nooraei, Neil T. Heffernan
UMAP2
2011 KT-IDEM: Introducing Item Difficulty to the Knowledge Tracing Model
Zachary A. Pardos, Neil T. Heffernan
UMAP1
2010 Navigating the parameter space of Bayesian Knowledge Tracing models: Visualizations of the convergence of the Expectation Maximization algorithm
Zachary A. Pardos, Neil T. Heffernan
EDM1
2010 Learning What Works in ITS from Non-traditional Randomized Controlled Trial Data
Zachary A. Pardos, Matthew D. Dailey, Neil T. Heffernan
Intelligent Tutoring Systems (2)1
2010 Modeling Individualization in a Bayesian Networks Implementation of Knowledge Tracing
Zachary A. Pardos, Neil T. Heffernan
UMAP1
2009 Detecting the Learning Value of Items In a Randomized Problem Set
abstract
Researchers that make tutoring systems would like to know which pieces of educational content are most effective at promoting learning among their students. Randomized controlled experiments are often used to determine which content produces more learning in an ITS. While these experiments are powerful they are often very costly to setup and run. The majority of data collected in many ITS systems consist of answers to a finite set of questions of a given skill often presented in a random sequence. We propose a Bayesian method to detect which questions produce the most learning in this random sequence of data. We confine our analysis to random sequences with four questions. A student simulation study was run to investigate the validity of the method and boundaries on what learning probability differences could be reliably detected with various numbers of users. Finally, real tutor data from random sequence problem sets was analyzed. Results of the simulation data analysis showed that the method reported high reliability in its choice of the best learning question in 89 of the 160 simulation experiments with seven experiments where an incorrect conclusion was reported as reliable (p < 0.05). In the analysis of real student data, the method returned statistically reliable choices of best question in three out of seven problem sets.
Zachary A. Pardos, Neil T. Heffernan
AIED1
2009 Determining the Significance of Item Order In Randomized Problem Sets
Zachary A. Pardos, Neil T. Heffernan
EDM1
2008 The Composition Effect: Conjuntive or Compensatory? An Analysis of Multi-Skill Math Questions in ITS
Zachary A. Pardos, Neil T. Heffernan, Carolina Ruiz, Joseph E. Beck
EDM1
2007 Analyzing Fine-Grained Skill Models Using Bayesian and Mixed Effects Methods
Zachary A. Pardos, Mingyu Feng, Neil T. Heffernan, Cristina Heffernan
AIED1