This paper describes how a simple application of de Moivre's theorem may be used to not only find the roots of a quadratic equation with real or generally complex coefficients but also to pinpoint their location in the Argand plane. This approach is much simpler than the comprehensive analysis presented by Bardell (2012, 2014), but it does not…

Handedness for acquiring objects was assessed monthly from 6 to 14 months in 328 infants (182 males). A group based trajectory model identified 3 latent groups with different developmental trajectories: those with an identifiable right preference (38%) or left preference (14%) and those without an identifiable preference (48%) but with a…

The analysis of variance (ANOVA) is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study…

An inexpensive procedure for introducing the Suzuki-Miyaura coupling reaction into a high-enrollment undergraduate organic chemistry laboratory course is described. The procedure employs an aqueous palladium solution as the catalyst and a range of para-substituted aryl bromides and arylboronic acids as substrates. The coupling reactions proceed…

The Long-Term Trend (LTT) mathematics assessment of the National Assessment of Educational Progress (NAEP) used the same set of items from 1982 through 2004, including 20 items that were administered to 9-and 13-year-olds, 29 items that were administered to 13-and 17-year-olds, and 4 items that were administered at all three ages. This study used…

Accurate equating results are essential when comparing examinee scores across exam forms. Previous research indicates that equating results may not be accurate when group differences are large. This study compared the equating results of frequency estimation, chained equipercentile, item response theory (IRT) true-score, and IRT observed-score…

The process of prime factor splicing to generate home primes raises opportunity for conjecture and exploration. The notion of "home primes" is relatively new in the chronicle of mathematics. Heleen (1996-97) first described a procedure called "prime factor splicing" (PFS). The exploration of home primes is interesting and…

Given the long history of discussion of issues surrounding statistical testing and effect size indices and various attempts by the American Psychological Association and by the American Educational Research Association to encourage the reporting of effect size, most journals in education and psychology have witnessed an increase in effect size…

A central goal of the education literature is to demonstrate that specific educational interventions--instructional interventions at the student or classroom level, structural interventions at the school level, or funding interventions at the school district level, for example--have a "treatment effect" on student achievement. This paper…

Loglinear smoothing (LLS) estimates the latent trait distribution while making fewer assumptions about its form and maintaining parsimony, thus leading to more precise item response theory (IRT) item parameter estimates than standard marginal maximum likelihood (MML). This article provides the expectation-maximization algorithm for MML estimation…

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under certain circumstances, meet legal criteria of causation.…

This article presents a simple approach to making quick sample size estimates for basic hypothesis tests. Although there are many sources available for estimating sample sizes, methods are not often integrated across statistical tests, levels of measurement of variables, or effect sizes. A few parameters are required to estimate sample sizes and…

Kyle, a kindergartner from a low-income family, is shown a set of three black dots on a white mat. His teacher then hides the dots with a small box lid and lays down an additional set of two dots. She pushes the two dots under the cover, one at a time. Kyle must now choose the number of dots "hiding" under the box from a set of four…

Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap…