Random item effects item response theory (IRT) models, which treat both person and item effects as random, have received much attention for more than a decade. The random item effects approach has several advantages in many practical settings. The present study introduced an explanatory multidimensional random item effects rating scale model. The…

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…

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…

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…

A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need to also split the prior for…

In the context of a rapid digital transformation, digital competence is now regarded as a fourth cultural skill complementing reading, writing, and arithmetic. We argue that a well-structured and sound competence model is needed as a shared foundation for learning, teaching, pedagogical diagnostics and evaluative schemes in the school system.…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

The article presents an open educational resource (OER) to introduce humanities students to data analysis with Python. The article beings with positioning the OER within wider pedagogical debates in the digital humanities. The OER is built from our research encounters and committed to computational thinking rather than technicalities. Furthermore,…

Discusses intelligent tutoring systems and the application of Bayesian networks to student modeling. Considers reasons for not using Bayesian networks, including the computational complexity of the algorithms and the difficulty of knowledge acquisition, and proposes an approach to simplify knowledge acquisition that applies causal independence to…

Provides several algorithms that use extended precision methods to compute large factorials exactly. The programs are written in BASIC and PASCAL. The approach used for computing N considers how large N is, how the built-in limitation on exact integer representation can be bypassed, and how long it takes to compute N. (JN)

Suggests and illustrates ways in which systematic consideration of selected unary operations can be facilitated by using electronic calculators. Emphasis is placed upon unary operations suitable for exploration and investigation at the pre-algebra level, using calculation algorithms as a basis for generating examples and non-examples to develop…

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

Adapts Stanic and McKillip's ideas for the use of developmental algorithms to propose that the present emphasis on symbolic manipulation should be tempered with an emphasis on the conceptual understanding of the mathematics underlying the algorithm. Uses examples from the areas of numeric computation, algebraic manipulation, and equation solving…

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

Describes examples of rational representation as a guide for translating terminology and information encountered in manuals for computers. Discusses four limitations of the representation. (YP)