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.

Knowledge tracing (KT) models aim to predict students' future performance based on their historical interactions. Most existing KT models rely exclusively on human-defined knowledge concepts (KCs) associated with exercises. As a result, the effectiveness of these models is highly dependent on the quality and completeness of the predefined KCs. Human errors in labeling and the cost of covering all potential underlying KCs can limit model performance. In this paper, we propose a KT model, Sparse Binary Representation KT (SBRKT), that generates new KC labels, referred to as auxiliary KCs, which can augment the predefined KCs to address the limitations of relying solely on human-defined KCs. These are learned through a binary vector representation, where each bit indicates the presence (one) or absence (zero) of an auxiliary KC. The resulting discrete representation allows these auxiliary KCs to be utilized in training any KT model that incorporates KCs. Unlike pre-trained dense embeddings, which are limited to models designed to accept such vectors, our discrete representations are compatible with both classical models, such as Bayesian Knowledge Tracing (BKT), and modern deep learning approaches. To generate this discrete representation, SBRKT employs a binarization method that learns a sparse representation, fully trainable via stochastic gradient descent. Additionally, SBRKT incorporates a recurrent neural network (RNN) to capture temporal dynamics and predict future student responses by effectively combining the auxiliary and predefined KCs. Experimental results demonstrate that SBRKT outperforms the tested baselines on several datasets and achieves competitive performance on others. Furthermore, incorporating the learned auxiliary KCs consistently enhances the performance of BKT across all tested datasets.

Bayesian Knowledge Tracing (BKT) is a probabilistic model of a learner's state of mastery corresponding to a knowledge component. It considers the learner's state of mastery as a "hidden" or latent binary variable and updates this state based on the observed correctness of the learner's response using parameters that represent transition probabilities between states. BKT is often represented as a Hidden Markov Model and the Expectation-Maximization (EM) algorithm is used to infer these parameters. However, this algorithm can suffer from several issues including producing multiple viable sets of parameters, settling into a local minima, producing degenerate parameter values, and a high computational cost during fitting. This paper takes a "from first principles" approach to deriving constraints that can be imposed on the BKT parameter space. Starting from the basic mathematical truths of probability and building up to the behaviors expected of the BKT parameters in real systems, this paper presents a mathematical derivation that results in succinct constraints that can be imposed on the BKT parameter space. Since these constraints are necessary conditions, they can be applied prior to fitting in order to reduce computational cost and the likelihood of issues that can emerge from the EM procedure. In order to see that promise through, the paper further introduces a novel algorithm for estimating BKT parameters subject to the newly defined constraints. While the issue of degenerate parameter values has been reported previously, this paper is the first, to our best knowledge, to derive the constrains from first principles while also presenting an algorithm that respects those constraints.

Computer Science researchers have long sought ways to apply the fruits of their labors to education. From the Logo turtles to the latest Cognitive Tutors, the allure of computers that will understand and help humans learn and grow has been a constant thread in Artificial Intelligence research. Now, advances in robotics and our understanding of Human-Robot Interaction make it feasible to develop physically-present robots that are capable of presenting educational material in an engaging manner, adapting online to sensory information from individual students, and building sophisticated, personalized models of a student’s mastery over complex educational domains. In this paper, we discuss how using physical robots as platforms for artificially intelligent tutors enables an expanded space of possible educational interactions. We also describe a work-in-progress to (1) extend previous work in personalized user models for robotic tutoring and (2) further explore the differences between interaction with physical robots and onscreen agents. Specifically, we are examining how embedding an tutoring interaction inside a story, game, or activity with an agent may differentially affect learning gains and engagement in interactions with physical robots and screen-based agents.