This publication presents experimental estimates of completion and attrition rates for the latest commencing apprentice and trainee cohorts. Such up-to-date estimates are possible by applying a "life tables" methodology to simple cross tabulations of commencements, completions and cancellations/withdrawals. The resultant cross-sectional…

The accuracy of item parameter estimates in the multidimensional item response theory (MIRT) model context is one that has not been researched in great detail. This study examines the ability of two confirmatory factor analysis models specifically for dichotomous data to properly estimate item parameters using common formulae for converting factor…

At the request of Pittsburgh Public Schools (PPS) and the Pittsburgh Federation of Teachers (PFT), Mathematica has developed value-added models (VAMs) that aim to estimate the contributions of individual teachers, teams of teachers, and schools to the achievement growth of their students. The authors' work in estimating value-added in Pittsburgh…

The National Dropout Prevention Center for Students with Disabilities (NDPC-SD) was assigned the task of compiling, analyzing, and summarizing the data for Indicator 2--Dropout--from the FFY 2010 Annual Performance Reports (APRs) and the revised State Performance Plans (SPPs), which were submitted to the Office of Special Education Programs (OSEP)…

Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…

Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the…

The circle of Apollonius is named after the ancient geometrician Apollonius of Perga. This beautiful geometric construct can be helpful when solving some general problems of geometry and mathematical physics, optics, and electricity. Here we discuss two of its applications: localizing an object in space and calculating electric fields. First, we…

Perhaps no topic has as thoroughly vexed officials who oversee the nation's leading test of academic progress as the wide variation among states and cities in the proportion of students with disabilities and limited English proficiency whom they exclude from taking the exam or provide with special accommodations for it. The board that sets policy…

In earlier columns, the celestial coordinate system of hour circles of right ascension and degrees of declination was introduced along with the use of an equatorial star chart (see SFA Star Charts in Resources). This system shows the planets' motion relative to the ecliptic, the apparent path the Sun follows during the year. An alternate system,…

A simplified version of a volumetric apparatus for gas/liquid solubility measurements is proposed. The procedure familiarizes undergraduate students with the experimental study of the solubility of a gas in a liquid and contributes to the understanding of this important phase equilibrium concept. The experimental results report the determination…

The purpose of this article is to propose a new design for the presentation of the periodic system of the elements. It is a system that highlights the fundamental importance of elements as basic substances rather than elements as simple substances, a distinction that is explained in the article. The proposed table is a variant of the Janet or…

Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrodinger equation for a diatomic oscillator. Calculations of the vibration-rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data. (Contains 1 table and 1 figure.)

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…

The SNARC (spatial-numerical association of response codes) effect refers to the finding that small numbers facilitate left responses, whereas larger numbers facilitate right responses. The development of this spatial association was studied in 7-, 8-, and 9-year-olds, as well as in adults, using a task where number magnitude was essential to…

The examination of measurement invariance in polytomous items is complicated by the possibility that the magnitude and sign of lack of invariance may vary across the steps underlying the set of polytomous response options, a concept referred to as differential step functioning (DSF). This article describes three classes of nonparametric DSF effect…