Defines a mathematical model of uniform response bias (URB) and proposes ipsative measures to minimize the effect of URB in multigroup confirmatory factor analysis. Illustrates the method using real data from the Chinese Personality Assessment Inventory for 2 groups of sample sizes 793 and 792 adults. (SLD)

Reports on a study comparing the use of Multi-base arithmetic blocks (MAB) and an alternative, LAB (linear arithmetic blocks) on the basis of epistemic fidelity and accessibility for students. Use of LAB was associated with more active engagement by students and deeper discussion. (Author/MM)

Dimension analysis is promoted as a technique that promotes better understanding of the role of units and dimensions in mathematical modeling problems. Dimensional analysis is shown to lead to interesting systems of linear equations to solve, and can point the way to more quantitative analysis. Two student problems are discussed. (Author/MM)

Evaluated the performance of several alternative cluster analytic approaches to initial model specification using population parameter analyses and a Monte Carlo simulation. Of the six cluster approaches evaluated, the one using the correlations of item correlations as a proximity metric and average linking as a clustering algorithm performed the…

This article proposes an extension to Kintsch's Construction-Integration (CI) model of text comprehension, which changes its mathematical implementation and emphasizes the connectionist features of the model. Specifically, the extension proposed here (a) simulates the learning process in a connectionist manner by making explicit changes in the…

A core assumption of the standard multiple regression model is independence of residuals, the violation of which results in biased standard errors and test statistics. The structural equation model (SEM) generalizes the regression model in several key ways, but the SEM also assumes independence of residuals. The multilevel model (MLM) was…

A simplified mathematical model for the calculation of imprecision associated with the construction of a calibration line is presented. The model also aims at a discussion on variables that really affect it and to integrate the resulting imprecision with that caused by the other steps in the analytical method in order to calculate a real…

This paper deals with an empirical study, which aims at showing the effects of the integration of modelling tasks into daily school routine in a comprehensive manner. At first the theoretical and methodological approach is explained. The main part of the paper deals with the results of the study. On the one hand the results show obstacles to the…

We discuss application of the Thomas-Reiche-Kuhn sum rule to simple quantum-mechanical models and its apparent violation by the rigid rotator.

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for…

The time of flight, range and the angle which maximizes the range of a projectile in a linear resisting medium are expressed in analytic form in terms of the recently defined Lambert W function. From the closed-form solutions a number of results characteristic to the motion of the projectile in a linear resisting medium are analytically confirmed,…

A model for car following on a closed loop is defined. The stability of the solutions of the model is investigated by considering the evolution of the roots of the corresponding characteristic equation in the complex plane. The solution provides a motivation for investigating the behaviour of the roots of a simple class of algebraic equation.…

When the character Yoda first appeared on the silver screen, his movements were due to the efforts of famed muppeteer Frank Oz. In "Star Wars Episode II: Attack of the Clones," Yoda returned to the movies but this time the character was not a puppet but a digital image within a computer. This paper discusses the role, or, more aptly, the force, of…

An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful…