The principle of inversion--that a + b - b must equal a--requires a sensitivity to the relation between addition and subtraction that is critical for understanding arithmetic. Use of inversion, albeit inconsistent, has been observed in school-age children, but when use of a computational shortcut based on inversion emerges and how awareness of the…

One of the pitfalls of engineering education is to lose the physical insight of the problem while tackling the mathematical part. Forced convection heat transfer (the Graetz-Nusselt problem) certainly falls into this category. The equation of energy together with the equation of motion leads to a partial differential equation subject to various…

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models,…

The analysis of interaction among latent variables has received much attention. This article introduces a Bayesian approach to analyze a general structural equation model that accommodates the general nonlinear terms of latent variables and covariates. This approach produces a Bayesian estimate that has the same statistical optimal properties as a…

Narrow Window theory, suggested by Y. Kareev ten years ago, has so far focused on one central implication of the limited capacity of working memory on intuitive correlation estimation, namely, overestimation of the distal population correlation. This paper points to additional and perhaps more dramatic implications due to the large dispersion of…

The purpose of this activity was to help students understand the percentage of cloud cover and make more accurate cloud cover observations. Students estimated the percentage of cloud cover represented by simulated clouds and assigned a cloud cover classification to those simulations. (Contains 2 notes and 3 tables.)

This experiment, designed for a general chemistry laboratory, illustrates the use of Dalton's law of partial pressures to determine the vapor pressure of a volatile liquid. A predetermined volume of air is injected into a calibrated tube filled with a liquid whose vapor pressure is to be measured. The volume of the liquid displaced is greater than…

This article develops a general thermodynamic treatment to predict the direction of shift in a chemical equilibrium when it is subjected to a stress. This treatment gives an inequality that relates the change in the perturbed variable and the change that the equilibrium shift produces in the conjugated variable. To illustrate the generality of…

Children differ in how much they spontaneously pay attention to quantitative aspects of their natural environment. We studied how this spontaneous tendency to focus on numerosity (SFON) is related to subitizing-based enumeration and verbal and object counting skills. In this exploratory study, children were tested individually at the age of 4-5…

The objective was to determine whether discrepancies between husbands' and wives' past year heavy drinking predicted decreased marital satisfaction over time. Participants (N = 634) were recruited at the time they applied for their marriage licenses. Couples completed questionnaires about their alcohol use and marital satisfaction at the time of…

This reprint from the June 1912 issue of "Mathematics Teacher" gives readers a sense of the timelessness of some of the issues relating to teaching for computational fluency.

Mackintosh and Bennett [Mackintosh, N. J., Bennett, E. S. (2005). What do Raven's Matrices measure? An analysis in terms of sex differences. "Intelligence, 33," 663-674] reported that male students obtained higher scores than females on Raven's items that required for their solution addition/subtraction or distribution of two rules, but…

One of the most important concepts being taught in principles classes is the idea of "thinking on the margin." It can also be one of the most difficult to get across. One of the most telling examples, according to this author, comes in trying to get students to learn the profit maximizing condition for perfectly competitive firms. She…

The aim of this study was to validate an individualised measure of quality of life (WeDQoL-Goals-Thailand). Three hundred and sixty-nine Thai people completed the WeDQoL by interview. Respondents rated (0-2) the perceived necessity for wellbeing of 51 goals (goal necessity), then rated (0-3) their satisfaction with the same goals (goal…

This report examines the fiscal neutrality of three funding formulas that have been proposed to replace the current funding formula for Oklahoma's common schools in an attempt to have greater equity in the distribution of funds to the various districts. Using data from SY-03 to SY-07, calculations of state aid for the 540- districts and fiscal…