A structure for learning the connections among standard deviations, z-scores, and normal distributions is presented. The components of this structure are classified into intuitive or previously learned conceptual knowledge, computational knowledge, and formalized conceptual knowledge. (Contains 1 figure.)

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…

In textbook treatments of enzyme inhibition kinetics, adjustment of the initial inhibitor concentration for inhibitor bound to enzyme is often neglected. For example, in graphical plots such as the Dixon plot for estimation of an inhibition constant, the initial concentration of inhibitor is usually plotted instead of the true inhibitor…

In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…

An objective method is presented to group discrete self-injurious behavior (SIB) events into bouts. Survival analysis was used to determine how long after an SIB the probability of observing a subsequent SIB remained elevated. This estimated bout length criterion time point was determined individually for 19 subjects with developmental disorders…

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a "transposition" of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic…

The purpose of this study was to document the instrument development of maze measures for grades 3-8. Each maze passage contained twelve omitted words that students filled in by choosing the best-fit word from among the provided options. In this technical report, we describe the process of creating, reviewing, and pilot testing the maze measures.…

A multitude of methods has been proposed to estimate the sampling variance of ratio estimates in complex samples (Wolter, 1985). Hansen and Tepping (1985) studied some of those variance estimators and found that a high coefficient of variation (CV) of the denominator of a ratio estimate is indicative of a biased estimate of the standard error of a…

Traditionally, the Doppler effect for sound is introduced in high school and college physics courses. Students calculate the perceived frequency for several scenarios relating a stationary or moving observer and a stationary or moving sound source. These calculations assume a constant velocity of the observer and/or source. Although seldom…

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…