Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…

Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this article is the origins and nature of those fundamental mechanisms that promoted the emergence of the…

The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

We address the challenging task of "computational natural language inference," by which we mean bridging two or more natural language texts while also providing an explanation of how they are connected. In the context of question answering (i.e., finding short answers to natural language questions), this inference connects the question…

Wollack, Cohen, and Eckerly (2015) suggested the "erasure detection index" (EDI) to detect fraudulent erasures for individual examinees. Wollack and Eckerly (2017) extended the EDI to detect fraudulent erasures at the group level. The EDI at the group level was found to be slightly conservative. This paper suggests two modifications of…

Patient safety is a priority in healthcare today. Good clinician numeracy in doctors contributes to patient safety, since it is essential for accuracy in prescribing, and in data interpretation. Evidence, however, suggests that although doctors are assumed to be highly numerate, they often make errors in drug dose calculation and struggle to…

Obtaining predictions from regression models fit to multiply imputed data can be challenging because treatments of multiple imputation seldom give clear guidance on how predictions can be calculated, and because available software often does not have built-in routines for performing the necessary calculations. This research note reviews how…

This Research Note shows that classic composers created their best works when they were at a similar age when creators in other domains did their best work, namely when they were at an age that represented around 60% of their life span. This finding is very similar to earlier results for painters and authors.

This article takes a close look at Lagrange and Newton interpolation by graphically examining the component functions of each of these formulas. Although interpolation methods are often considered simply to be computational procedures, we demonstrate how the components of the polynomial terms in these formulas provide insight into where these…

To determine the appropriate level of product availability, most operations management textbooks introduce and define service level measures in a Business-to-Customer context. In other words, a retailer that wants to measure product availability in their store calculates the fill rate (FR) or cycle service level over an infinite review horizon.…

Although counting problems are easy to state and provide rich, accessible problem-solving situations, there is much evidence that students struggle with solving counting problems correctly. With combinatorics (and the study of counting problems) becoming increasingly prevalent in K-12 and undergraduate curricula, there is a need for researchers to…

The manuscript presents a Visual Basic[superscript R] for Applications function that operates within Microsoft Office Excel[superscript R] to return the area below the curve for a given F within a specified non-central F distribution. The function will be of use to Excel users without programming experience wherever a non-central F distribution is…

The article illustrates a theoretical approach to scenario modeling of economic indicators of regional waste management system. The method includes a three-iterative algorithm that allows the executive authorities and investors to take a decision on logistics, bulk, technological and economic parameters of the formation of the regional long-term…

The concept of condition-based gas turbine-powered aircraft operation is realized all over the world, which implementation requires knowledge of the end-of-life information related to components of aircraft engines in service. This research proposes an algorithm for estimating the equivalent cyclical running hours. This article provides analysis…