A 100 years-old formula that was given by J. J. Thomson recently found numerous applications in computational electrostatics and electromagnetics. Thomson himself never gave a proof for the formula; but a proof based on Differential Geometry was suggested by Jackson and later published by Pappas. Unfortunately, Differential Geometry, being a…

Test security has been a concern for computerized adaptive tests (CAT) due to the nature of continuous testing. This concern becomes unprecedentedly severe with increasingly easy access to the World-Wide-Web where some examinees post on the internet their recollections of items they are administered, leaving future examinees with opportunities to…

I have found that students easily understand that a measurement cannot be exact, but they often seem to lack an understanding of why it is important to know "something" about the magnitude of the uncertainty. This tends to promote an attitude that almost any uncertainty value will do. Such indifference may exist because once an uncertainty is…

The function 1 divided by "x"[superscript 2] minus "e"[superscript"-x"] divided by (1 minus "e"[superscript"-x"])[superscript 2] for "x" greater than 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function "t" divided by "e"[superscript "at"] minus "e"[superscript"(a-1)""t"] for "a"…

In this study, we directly contrast two approaches that have been proposed to explain the SNARC effect. The traditional direct mapping account suggests that a direct association exists between the position of a number on the mental number line and the location of the response. On the other hand, accounts are considered that propose an intermediate…

The achievement level is a variable measured with error, that can be estimated by means of the Rasch model. Teacher grades also measure the achievement level but they are expressed on a different scale. This paper proposes a method for combining these two scores to obtain a synthetic measure of the achievement level based on the theory developed…

The purpose of this study was to examine the impact of misspecifying a growth mixture model (GMM) by assuming that Level-1 residual variances are constant across classes, when they do, in fact, vary in each subpopulation. Misspecification produced bias in the within-class growth trajectories and variance components, and estimates were…

According to one theory about how children learn the meaning of the words for the positive integers, they first learn that "one," "two," and "three" stand for appropriately sized sets. They then conclude by inductive inference that the next numeral in the count sequence denotes the size of sets containing one more object than the size denoted by…

In this paper, we examine two aspects of recent increases in marriage preceded by pregnancy (bridal pregnancy) in Japan. Using information on 28,973 respondents to the Japanese National Fertility Surveys, we first demonstrate that increases in bridal pregnancy between 1970 and 2002 were concentrated among women without postsecondary education. We…

Students in many countries face increased costs of education in the form of direct payments and future tax liabilities and, as a consequence, their education decisions have taken on a greater financial dimension. This has refocused attention on obtaining meaningful estimates of the return to education. Routinely these returns are estimated as the…

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…