High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…

The federal government's student loan programs for higher education convey substantial financial benefits to borrowers because of their broad availability and favorable terms. Of the various provisions included in a federal student loan contract, the option to consolidate individual loans contributes greatly to a borrower's benefits and the cost…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

Statistical methodology for handling omitted variables is presented in a multilevel modeling framework. In many nonexperimental studies, the analyst may not have access to all requisite variables, and this omission may lead to biased estimates of model parameters. By exploiting the hierarchical nature of multilevel data, a battery of statistical…

Hoping to develop in her students an understanding of mathematics as a way of thinking more than a way of doing, the author of this article describes how her students worked on a spatial reasoning problem stemming from an iteratively constructed sequence of cylinders. She presents an activity of making cylinders out of paper models, and for every…

This paper uses data from the National Education Longitudinal Study to estimate the association between high school alcohol use and educational attainment measured around age 26. Initially, the effect of alcohol use on educational attainment is estimated using baseline probit models, which ignore the possibility that unmeasured determinants of…

To complement recent articles in this journal on structural equation modeling (SEM) practice and principles by Martens and by Quintana and Maxwell, respectively, the authors offer a consumer's guide to SEM. Using an example derived from theory and research on vocational psychology, the authors outline six steps in SEM: model specification,…

The effects of five ability estimators, that is, maximum likelihood estimator, weighted likelihood estimator, maximum a posteriori, expected a posteriori, and Owen's sequential estimator, on the performances of the item response theory-based adaptive classification procedure on multiple categories were studied via simulations. The following…

This study contributes to understanding sources of gender differential item functioning (DIF) on mathematics tests. This study focused on identifying sources of DIF and differential bundle functioning for boys and girls on the British Columbia Principles of Mathematics Exam (Grade 12) using a confirmatory SIBTEST approach based on a…

We examine whether abortion removes from the population those infants most at risk of homicide. As part of our identification strategy, we find that abortion reduces the number of unwanted births, estimating that 1 percent increase in the abortion ratio reduces unwanted births by approximately 0.35 percent. Using cross-sectional time-series data…

The objectives of this study were to generate precise estimates of suicide rates in the military while controlling for factors contributing to rate variability such as demographic differences and classification bias, and to develop a simple methodology for the determination of statistically derived thresholds for detecting significant rate…

This article reports on the ability of observers who are sighted and those with low vision to make time-to-collision (TTC) estimations using video. The TTC estimations made by the observers with low vision were comparable to those made by the sighted observers, and both groups made underestimation errors that were similar to those that were…

The study of federal education initiatives that takes place over multiple years in multiple settings often calls for aggregating and comparing data-in particular, student achievement data-across a broad set of schools, districts, and states. The need to track the trends over time is complicated by the fact that the data from the different schools,…

For those instructors lacking artistic skills, teaching 3-dimensional calculus can be a challenge. Although some instructors spend a great deal of time working on their illustrations, trying to get them just right, students nevertheless often have a difficult time understanding some of them. To address this problem, the author has written a series…

The Law of Sines and The Law of Cosines are of paramount importance in the field of trigonometry because these two theorems establish relationships satisfied by the three sides and the three angles of any triangle. In this article, the authors use these two laws to discover a host of other trigonometric relationships that exist within any…