In this note, we give a method for finding the inverse of a three by three magic square matrix without using the usual methods for finding the inverse of a matrix. Also we give a method for finding the inverse of a three by three magic square matrix whose entries are also matrices. By using these ideas, we can construct large matrices whose…

Force platforms (FPs) are regularly used in the biomechanical analysis of sport and exercise techniques, often in combination with image-based motion analysis. Force time data, particularly when combined with joint positions and segmental inertia parameters, can be used to evaluate the effectiveness of a wide range of movement patterns in sport…

The DA-T Gibbs sampler is proposed by Maris and Maris (2002) as a Bayesian estimation method for a wide variety of "Item Response Theory (IRT) models". The present paper provides an expository account of the DA-T Gibbs sampler for the 2PL model. However, the scope is not limited to the 2PL model. It is demonstrated how the DA-T Gibbs…

Methods for calculating confidence intervals for the mean are reviewed for the case where the data come from a log-normal distribution. In a simulation study it is found that a variation of the method suggested by Cox works well in practice. An approach based on Generalized confidence intervals also works well. A comparison of our results with…

The data illustrate outliers that are not mistakes and not observations that are unusually high or low. The reasons for them are all interesting historically. They illustrate that "outliers" need not be errors but may instead be particularly interesting cases. The data also illustrate that different data displays may differ in their ability to…

Hadamard's two integral inequalities are generalized and the quadrature formulae associated with them are demonstrated.

This note considers continuous functions f on an interval [a, b] and develops sufficient conditions to answer the question, for what points c in the interval is there a rectangle with height f(c) and some width beta-alpha that has a signed area equal to [integral of] beta over alpha f(x)dx?

In this note, we recall the convex (or barycentric) coordinates of the points of a closed triangular region. We relate the convex and trilinear coordinates of the interior points of the triangular region. We use the relationship between convex and trilinear coordinates to calculate the convex coordinates of the symmedian point of the triangular…

In this article the authors demonstrate two instances where the jackknife can be used to enhance hierarchical linear model (HLM) analyses. The jackknife was used to improve the HLM estimates of composite measures by jackknifing over items. The first study examined fixed-effects and variance component estimation. The jackknife appeared to reduce…

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph.

The game presented in this article provides for students' development of the use of models, benchmarks, and equivalent forms to judge the size of fractions in a motivational and flexible way.

The isotopic distribution in mass spectroscopy is described for identifying pure compounds, being able to distinguish molecular fragments by masses. Punnett squares are familiar, easy to compute, and often graphical which makes helpful to students and the relative distribution of isotopic combination is easily generated for even isotopic…

The rapid changes in information technology in recent years have rendered current high school curricula unable to cope with student needs. In consequence, students do not possess the proper skills required in today's information era. Specifically, many students lack the skills to search efficiently for information. Moreover, even when abundant…

This Technical Report is designed to provide technical detail to support the analysis and findings presented in the "Head Start Impact Study Final Report" (U.S. Department of Health and Human Services, January 2010). Chapter 1 provides an overview of the Head Start Impact Study and its findings. Chapter 2 provides technical information on the…

This study implemented a three-stage problem-based estimation instruction scenario and combined it with mobile technology to provide elementary teachers with an effective e-tool for observing student estimation and leading effective class or group discussions on the selection and assessment of appropriate strategies for solving daily estimation…