More often than one might at first imagine, a simple trick involving integration by parts can be used to compute indefinite integrals in unexpected and amusing ways. A systematic look at the trick illuminates the question of whether the trick is useful enough to be called an actual technique of integration.

In "The Theory of Almost Everything", Robert Oerter asserts the following: "Take a beam of electrons that are all spinning in the same direction and fire it at, say, a brick. If you could keep this up for long enough, and if there were no other forces acting on the brick, the electrons would transfer their rotation to the brick, and it would begin…

We find the correlation of two jointly distributed random variables connected with a coin tossing experiment. The marginal distributions are binomial and negative binomial.

For a test that consists of dichotomously scored items, several approaches have been reported in the literature for estimating classification consistency and accuracy indices based on a single administration of a test. Classification consistency and accuracy have not been studied much, however, for "complex" assessments--for example,…

Time perception has long been known to be affected by numerical representations. Recent studies further demonstrate that when participants estimate the duration of Arabic numbers, number magnitude, though task-irrelevant, biases duration judgment to produce underestimation for smaller numbers and overestimation for larger numbers. Such effects…

Rayleigh's criterion states that a pair of point sources are barely resolved by an optical instrument when the central maximum of the diffraction pattern due to one source coincides with the first minimum of the pattern of the other source. As derived in standard introductory physics textbooks, the first minimum for a rectangular slit of width "a"…

We examined preschool children's use of count information in making quantity judgments. Study 1 involved 35 children 3-5 years old using a balance-scale task to judge relative quantity with or without count information provided. Study 2 replicated and extended the exploration as 54 children 3-4 years old judged relative quantity in multiple…

Derivation of the second- and higher-order virial coefficients for models of the gaseous state is demonstrated by employing a direct differential method and subsequent term-by-term comparison to power series expansions. This communication demonstrates the application of this technique to van der Waals representations of virial coefficients.…

Incorrect handling of item parameter drift during the equating process can result in equating error. If the item parameter drift is due to construct-irrelevant factors, then inclusion of these items in the estimation of the equating constants can be expected to result in equating error. On the other hand, if the item parameter drift is related to…

In this article, we examine the use of electronic textiles (e-textiles) for introducing key computational concepts and practices while broadening perceptions about computing. The starting point of our work was the design and implementation of a curriculum module using the LilyPad Arduino in a pre-AP high school computer science class. To…

This article provides a statistical analysis of the reading gains observed at one American school in the Caribbean that was using Accelerated Reader. It provides an estimate of the number of hours students needed to read to advance their reading performance an additional year. The authors estimate how much Accelerated Reader contributed to the…

The purpose of this study was to assess the relative contribution of teacher and tutor ratings of inattentive behavior in two different instructional settings in predicting students' performance on fraction concepts and whole-number calculations. Classroom teachers rated each student's attentive behavior in a whole-class setting and tutors rated…

One-in-five of Arizona's youth did not complete high school and a similarly large proportion of the state's youth is disconnected from either work or education. These youth face higher risks of unemployment and economic insecurity and are more reliant on government supports. This situation, which fails to ensure that the state's youth are…

This "What Works Clearinghouse Procedures and Standards Handbook (Version 3.0)" provides a detailed description of the standards and procedures of the What Works Clearinghouse (WWC). The remaining chapters of this Handbook are organized to take the reader through the basic steps that the WWC uses to develop a review protocol, identify…

"Two and Two Make Zero" considers children's acquisition of numerical concepts from a wide range of perspectives including topics that are often overlooked, most notably: the principal properties of the counting numbers in and of themselves; the role that numerical symbols play in number acquisition; the underlying conceptual structure of number…