This study compares two confirmatory factor analysis methods on their ability to verify whether correct assignments of items to subtests are supported by the data. The confirmatory common factor (CCF) method is used most often and defines nonzero loadings so that they correspond to the assignment of items to subtests. Another method is the oblique…

The number [pie] [approximately] 3.14159 is defined to be the ratio C/d of the circumference C to the diameter d of any given circle. In this article, the author looks at some surprising and unexpected places where [pie] occurs, and then thinks about some ways of remembering all those digits in the expansion of [pie].

A derivative is the limit of a quotient. It is an abstraction of division. Since division is harder to understand than multiplication, teachers teach it later, hopefully only after a sound understanding of multiplication has been attained. For the same reason, it may make sense to teach integration first, and move on to differential calculus only…

In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by…

Hurricanes and tropical storms served as natural experiments for investigating whether autism is associated with exposure to stressful events during sensitive periods of gestation. Weather service data identified severe storms in Louisiana from 1980 to 1995 and parishes hit by storm centers during this period. Autism prevalences in different…

Item response theory (IRT) procedures have been used extensively to study normal latent trait distributions and have been shown to perform well; however, less is known concerning the performance of IRT with non-normal latent trait distributions. This study investigated the degree of latent trait estimation error under normal and non-normal…

Spontaneous transfer of learning is often difficult to elicit. This finding may be widespread partly because pretests proactively interfere with transfer. To test this hypothesis, 7-year-olds' transfer was examined across 2 numerical tasks (number line estimation and categorization) in which similar representational changes have been observed. As…

This handbook describes the structure and processes that the What Works Clearinghouse (WWC) uses for its reviews, presenting in one place all the standards the WWC currently uses to assess research. The handbook will be revised as new standards are developed and major new features are finalized. A distinguishing feature of the WWC is that it does…

A rapid serial visual presentation (RSVP) technique was used to investigate the role of the nature of processing carried out on targets in the Lag-1 sparing phenomenon. Lag-1 sparing refers to a higher accuracy in the task associated with the 2nd target when the 2 targets are immediately successive in the RSVP stream relative to when there are 1…

The purpose of this paper is to present the types of measures that may be used to describe intervention effects from single subject designs. A regression approach and several non-regression approaches are described. Non-regression approaches include Standard Mean Difference, Percentage of Non-Overlapping Data, Percent Reduction, and Percentage…

It has been claimed that recursion is one of the properties that distinguishes human language from any other form of animal communication. Contrary to this claim, a recent study purports to demonstrate center-embedded recursion in starlings. I show that the performance of the birds in this study can be explained by a counting strategy, without any…

Although statistical procedures are well-known for comparing hierarchically related (nested) mean and covariance structure models, statistical tests for comparing non-hierarchically related (nonnested) models have proven more elusive. Although isolated attempts at statistical tests of non-hierarchically related models have been made, none exist…

Students served in juvenile correctional school settings often arrive with histories of trauma, aversive educational experiences, low achievement, and other severe risk factors that impeded psychosocial development, educational progress, and occupational outcomes. Schools serving adjudicated youth must address a higher percentage of severe…

Few people realize the impact that high school dropouts have on a community's economic, social, and civic health. Business owners and residents--in particular, those without school-aged children--may not be aware that they have much at stake in the success of their local high schools. Indeed, everyone--from car dealers and realtors to bank…

At the request of Pittsburgh Public Schools (PPS) and the Pittsburgh Federation of Teachers (PFT), Mathematica is developing 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 analyses described in this report are intended as an…