Bayesian Knowledge Tracing (BKT) is a probabilistic model of a learner's state of mastery for a knowledge component. The learner's state is a "hidden" binary variable updated based on the correctness of the learner's responses to questions corresponding to that knowledge component. The parameters used for this update are inferred/learned…

Students' reading ability affects their outcomes in learning software even outside of reading education, such as in math education, which can result in unexpected and inequitable outcomes. We analyze an adaptive learning software using Bayesian Knowledge Tracing (BKT) to understand how the fairness of the software is impacted when reading ability…

Although statistical practices to evaluate intervention effects in SCEDs have gained prominence in the recent times, models are yet to incorporate and investigate all their analytic complexities. Most of these statistical models incorporate slopes and autocorrelations both of which contribute to trend in the data. The question that arises is…

Mastery learning -- requiring students to achieve proficiency in a topic before advancing -- is a well-established and effective teaching method. Digital learning systems support this approach by personalizing content sequences, enabling students to focus on practicing topics they have not yet mastered. To achieve this, digital learning systems…

The use of Bayesian Knowledge Tracing (BKT) models in predicting student learning and mastery, especially in mathematics, is a well-established and proven approach in learning analytics. In this work, we report on our analysis examining the generalizability of BKT models across academic years attributed to "detector rot." We compare the…

Diagnostic classification models (DCMs) are psychometric models that can be used to estimate the presence or absence of psychological traits, or proficiency on fine-grained skills. Critical to the use of any psychometric model in practice, including DCMs, is an evaluation of model fit. Traditionally, DCMs have been estimated with maximum…

Location tracking devices are becoming increasingly popular in practice to study movement of customers or track inventory. However, using location tracking devices in education contexts is quite novel. In this paper, we present a robust Bayesian nonparametric mixture model that clusters location data. We successfully apply this model on location…

In this article, the beta-binomial model for count data is proposed and demonstrated in terms of its application in the context of oral reading fluency (ORF) assessment, where the number of words read correctly (WRC) is of interest. Existing studies adopted the binomial model for count data in similar assessment scenarios. The beta-binomial model,…

There has been considerable interest in techniques for modelling student learning across practice problems to drive real-time adaptive learning, with particular focus on variants of the classic Bayesian Knowledge Tracing (BKT) model proposed by Corbett & Anderson, 1995. Over time researches have proposed many variants of BKT with…

One crucial function of a classroom, and a school more generally, is to prepare students for future learning. Students should have the capacity to learn new information and to acquire new skills. This ability to "learn" is a core competency in our rapidly changing world. But how do we measure ability to learn? And how can we measure how…

Knowledge tracing algorithms such as Bayesian Knowledge Tracing (BKT) can provide students and teachers with helpful information about their progress towards learning objectives. Despite the popularity of BKT in the research community, the algorithm is not widely adopted in educational practice. This may be due to skepticism from users and…

The Bayesian information criterion (BIC) can be useful for model selection within multilevel modeling studies. However, the formula for BIC requires a value for N, which is unclear in multilevel models, since N is observed in at least two levels. The present study uses simulated data to evaluate the rate of false positives and power when using a…

Knowledge tracing (KT) models are a popular approach for predicting students' future performance at practice problems using their prior attempts. Though many innovations have been made in KT, most models including the state-of-the-art Deep KT (DKT) mainly leverage each student's response either as correct or incorrect, ignoring its content. In…

Peer-grading is commonly adopted by instructors as an effective assessment method for MOOCs (Massive Open Online Courses) and SPOCs (Small Private online course). For solving the problems brought by varied skill levels and attitudes of online students, statistical models have been proposed to improve the fairness and accuracy of peer-grading.…

Knowledge tracing algorithms are embedded in Intelligent Tutoring Systems (ITS) to keep track of students' learning process. While knowledge tracing models have been extensively studied in offline settings, very little work has explored their use in online settings. This is primarily because conducting experiments to evaluate and select knowledge…