Using 1990-91 data for 143 Ph.D. granting institutions, this study applies a simultaneous equation model to determine whether an institution's amount of research grants is a function of its academic ranking. Results show a simultaneous relationship among grants per full-time-equivalent enrollment, institutional ranking, and graduate students as a…

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…

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.

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of…

Cognitive mechanisms underlying repetition priming in picture naming were decomposed in several experiments. Sets of encoding manipulations meant to selectively prime or reduce priming in object identification or word production components of picture naming were combined factorially to dissociate processes underlying priming in picture naming.…

The abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical…

The current mantra in education is "technology, technology, technology." Many teachers and prospective teachers become frustrated with their lack of knowledge regarding the "appropriate" use of technology in the classroom. Prospective teachers need training in their education to understand how technology can be used "appropriately" in the…

Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…