In this note Scott's result is generalized and a method given to factorize separable-variable functions.

This report summarizes research findings and implementation practices for teacher and principal value-added models (VAMs), as a first step in the Team Pennsylvania Foundation's (Team PA) pilot project to inform the development of a full, statewide model evaluation system. We have selected 21 studies that represent key issues and findings in the…

Engaging all students in grade-level mathematics is often a challenge for teachers, especially in diverse urban classrooms. Too often in her role of supporting the development of effective practices with middle school teachers, the author observes traditional classroom instructors presenting information and demonstrating procedures. In this…

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

The purpose of the study was to demonstrate improvements in celerations, performance changes, and fluency of digits written correctly using repeated drill and practice procedures with Precision Teaching measurement approaches during one-minute timings among middle school students who also exhibit identified emotional and/or behavioral disabilities…

Employment of a data-acquisition system for data collection and calculations makes experiments with antennas more convenient and less time consuming. The determined directional patterns of the dipole antennas of different lengths are in reasonable agreement with theory. The enhancement of the signal by using a reflector is demonstrated, and a…

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…

Well-known numerical integration methods are applied to item response theory (IRT) with special emphasis on the estimation of the latent regression model of NAEP [National Assessment of Educational Progress]. An argument is made that the Gauss-Hermite rule enhanced with Cholesky decomposition and normal approximation of the response likelihood is…

A coordinate-free definition of complex-structure multidimensional item response theory (MIRT) for dichotomously scored items is presented. The point of view taken emphasizes the possibilities and subtleties of understanding MIRT as a multidimensional extension of the classical unidimensional item response theory models. The main theorem of the…

Background: Since the 1990s, people with intellectual disability (ID) in the Netherlands have been moving from institutions to supported accommodation in the community. The Government is in need of recent data on the numbers of these people, to ensure adequate care provision and funding. This paper reports on the prevalence of people with ID in…

There has been a growing interest in understanding the computations involved in the processes underlying visual segmentation and interpolation in conditions of occlusion. P. J. Kellman, P. Garrigan, T. F. Shipley, and B. P. Keane and M. K. Albert defended the view that identical contour interpolation mechanisms underlie modal and amodal…

Special ability in computing the day of the week from given dates was observed in a 18 years old male, L.E., suffering from autism. Neuropsychological testing revealed severe deficits in all cognitive domains and poor explicit knowledge of calendar structure. The subject scored well above the chance level on dates of the past and future decades.…

This article presents some identities on the sum of the entries in the first half of a row in Pascal's triangle. The results were discovered while the author was working on a problem involving Laplace transforms, which are used in proving of the identities.

This article considers an old version of the classical pursuit problem as posed by Francis Godwin in 1599, who imagines a wedge of swans flying from the earth to the moon in twelve days, always flying at constant speed toward the moon. The return trip, during which the swans always fly toward the earth at the same speed, takes eight days. A little…

A ball placed on the edge of a horizontal table is hit with a pendulum and thrown over the floor. The fall time is measured by recording the sounds produced by the collisions with the pendulum and the floor. If the height of the ball with respect to the floor is known, one can determine the acceleration of gravity.