The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take…

The Nolan Index (NI) is a normed, quantitative measure for comparing the degree of resemblance (similarity or dissimilarity) between free listings with an Excel program for calculating it. This article enhances that effort with the addition of an R program and additional applications. Free-list resemblance measures have been used to investigate…

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…

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 Big Data revolution, the education sector is being reshaped. The current data-driven education system provides many opportunities to utilize the enormous amount of collected data about students' activities and performance for personalized education, adapting teaching methods, and decision making. On the other hand, such benefits come at a…

This article outlines a readily applicable procedure for point and interval estimation of the population discrepancy between reliability and the popular Cronbach's coefficient alpha for unidimensional multi-component measuring instruments with uncorrelated errors, which are widely used in behavioral and social research. The method is developed…

The topic of the seasons is covered in both primary and secondary schools in Australia. It may be difficult for some students to comprehend how the Sun alters its position throughout the year. This article shows how to calculate the changing rising and setting positions of the Sun for one's locality and the extremes of its elevation near noon over…

The acid-catalyzed dehydration of regioisomeric methylcyclohexanols is a classic organic chemistry experiment featured in a variety of laboratory textbooks and literature. The mechanistic details of this reaction have received an inconsistent and occasionally inaccurate treatment, wherein the reaction has been described as a mix of E1, E2-like,…

Enzymes are nature's catalysts, mediating chemical processes in living systems. The study of enzyme function and mechanism includes defining the maximum catalytic rate and affinity for substrate/s (among other factors), referred to as enzyme kinetics. Enzyme kinetics is a staple of biochemistry curricula and other disciplines, from molecular and…

Computational modeling and thinking skill sets were previously relegated to computer scientists and programmers. As a result, computational tools are largely unfamiliar to K-12 science teachers and students. Using Mathematical and Computational Thinking and Developing and Using Models were included in the "Next Generation Science…

This paper outlines the potential gains for Constructionist research and praxis in modelling that might be obtained by recognising the power of the Patch--a humble computational being in the NetLogo modelling environment that has been overshadowed by its more popular fellow agent, the Turtle. To contextualise this opportunity, I describe how…

This article presents the consensus of an National Council on Measurement in Education Presidential Task Force on Foundational Competencies in Educational Measurement. Foundational competencies are those that support future development of additional professional and disciplinary competencies. The authors develop a framework for foundational…

Item Response Theory models with varying thresholds are essential tools to account for unknown types of response tendencies in rating data. However, in order to separate constructs to be measured and response tendencies, specific constraints have to be imposed on varying thresholds and their interrelations. In this article, a multidimensional…

The introduction of Computational Chemistry via "Molecular Modelling and Drug Design" course at undergraduate level has opened wide possibilities for students to expand their knowledge of quantum chemistry, organic reaction mechanisms, protein-ligand interactions, drug design, and probable "in vivo" behavior of drug candidates.…

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.…