Computer adaptive testing (CAT) is an increasingly common mode of test administration offering improved test security, better measurement precision, and the potential for shorter testing experiences. This article presents a new item selection algorithm based on a generalized objective function to support multiple types of testing conditions and…

The design of algorithms is one of the hardest topics of high school computer science. This is mainly due to the universality of algorithms as solution methods that guarantee the calculation of a correct solution for all potentially infinitely many instances of an algorithmic problem. The goal of this paper is to present a comprehensible and…

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

With the rapid development of information technology, the internet has emerged as a pivotal driving force in reshaping higher education paradigms. This paper delves into clustering algorithms and proposes an enhanced version, exploring how this enhanced clustering algorithm can be applied to blended teaching of digital electronic technology…

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

The emergence of artificial intelligence (AI) in academia has prompted various debates on the uses, threats, and limitations of tools that can create text for numerous academic purposes. Critics argue that these advancements may provide opportunities for cheating and plagiarism and even replace the art of writing entirely. To reclaim the…

This paper develops a spreadsheet simulation methodology for teaching simulation and performance analysis of priority queues with multiple servers, without resorting to macros, add-ins, or array formula. The approach is made possible by a "single overtaking" simplifying assumption under which any lower-priority customer may be passed in…

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…

This volume is largely about nontraditional data; this paper is about a nontraditional visualization: classification trees. Using trees with data will be new to many students, so rather than beginning with a computer algorithm that produces optimal trees, we suggest that students first construct their own trees, one node at a time, to explore how…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on…

In this paper, we describe an educational activity involving the use of a digital artifact, implemented in a visual programming environment, for mediating the learning of axial symmetry in primary school through algorithmics and computer programming. The educational activity was designed with the aim of bringing out increasingly…

Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of…

Much has been written about how to improve the fairness of AI tools for decision-making but less has been said about how to approach this new field from the perspective of philosophy of education. My goal in this paper is to bring together criteria from the general algorithmic fairness literature with prominent values of justice defended by…

The global pandemic has brought about significant changes in education, which have led to concerns regarding fairness and accessibility in a technology-driven learning environment. This article focuses on the use of Artificial Intelligence (AI) in education and examines the potential for bias in AI-powered tools. By using the example of a…

Educational assessment is inherently uncertain, where physiological, psychological and social factors play an important role in establishing judgements which are assumed to be "absolute". AI and other algorithmic approaches to grading of student work strip-out uncertainty, leading to a lack of inspectability in machine judgement and…