Bell's theorem is a topic of perennial fascination. Publishers and the general public have a steady appetite for approachable books about its implications. The scholarly literature includes many analogies to Bell's theorem and simple derivations of Bell inequalities, and some of these simplified discussions are the basis of interactive web pages.…

We propose an algorithm that allows calculating the remainder and the quotient of division between polynomials over commutative coefficient rings, without polynomial long division. We use the previous results to determine the quadratic factors of polynomials over commutative coefficient rings and, in particular, to completely factorize in Z[x] any…

Calculating analytical uncertainties as a part of method validation is a relevant aspect of field and laboratory practices in instrumental analytical chemistry subjects, which usually require complex algorithms. This work describes the development and didactic use of an automatic and straightforward informatics tool, implemented in an Excel macro,…

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…

Cross-validation is a common statistical procedure applied to problems that are otherwise computationally intractable. It is often employed to assess the effectiveness of prediction procedures. In this report, cross-validation is discussed in terms of "U"-statistics. This approach permits consideration of the statistical properties of…

American Educational Research Association (AERA) standards stipulate that researchers show evidence of the internal structure of instruments. Confirmatory factor analysis (CFA) is one structural equation modeling procedure designed to assess construct validity of assessments that has broad applicability for counselors interested in instrument…

The article serves as a guide for researchers in developing evidence of validity using bivariate correlations, specifically construct validity. The authors outline the steps for calculating and interpreting bivariate correlations. Additionally, they provide an illustrative example and discuss the implications.

Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.

The content validity ratio (Lawshe) is one of the earliest and most widely used methods for quantifying content validity. To correct and expand the table, critical values in unit steps and at multiple alpha levels were computed. Implications for content validation are discussed. (Contains 2 tables and 1 figure.)

Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas…

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

We walk through a module intended for undergraduates in mathematics, with the focus of finding the best strategies for competing in the Showcase Showdown on the game show "The Price Is Right." Students should have completed one semester of calculus, as well as some probability. We also give numerous suggestions for further questions that…

This paper presents an extended project that offers, through American football, an application of concepts from enumerative combinatorics and an introduction to proofs course. The questions in this paper and subsequent details concerning equivalence relations and counting techniques can be used to reinforce these new topics to students in such a…

Engineers often need to predict how a part, mechanism or machine will perform in service, and this insight is typically achieved thorough computer simulations. Therefore, instruction in the creation and application of simulation models is essential for aspiring engineers. The purpose of this project was to develop a unified approach to teaching…

Steinley (2007) provided a lower bound for the sum-of-squares error criterion function used in K-means clustering. In this article, on the basis of the lower bound, the authors propose a method to distinguish between 1 cluster (i.e., a single distribution) versus more than 1 cluster. Additionally, conditional on indicating there are multiple…