This paper discusses a new form of specifying and normalizing a Linear Logistic Test Model (LLTM) as suggested by Bechger, Verstralen, and Verhelst ("Psychometrika," 2002). It is shown that there are infinitely many ways to specify the same normalization. Moreover, the relationship between some of their results and equivalent previous…

In this paper, the author introduces a simple problem relating to a pair of ladders. A mathematical model of the problem produces an equation which can be solved in a number of ways using mathematics appropriate to "A" level students or first year undergraduates. The author concludes that the ladder problem can be used in class to develop and…

This article presents an overview of the Supervisory Working Alliance Model (E. S. Bordin, 1983) and related research. The author proposes an extension of the model by applying it to evaluation and multicultural competency. The following major advantages of the model for supervision in college counseling centers are discussed: (a) model's…

The purpose of this study was to examine the use of socially relevant mathematics applications in high school mathematics classrooms and students' views of mathematics in light of their experiences with these applications. Also, the study sought to determine whether inquiries afforded by these applications incorporated features that promoted…

Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…

Although it is well known that vaccines against many infectious diseases confer positive economic externalities via indirect protection, analysts have typically ignored possible herd protection effects in policy analyses of vaccination programs. Despite a growing literature on the economic theory of vaccine externalities and several innovative…

Mathematical software packages such as Polymath, MATLAB, and Mathcad are currently widely used for engineering problem solving. Applications of several of these packages to typical chemical engineering problems have been demonstrated by Cutlip, et al. The main characteristic of these packages is that they provide a "problem-solving environment…

This article allows students to apply their knowledge and experience of area and volume to find the volume of Norris Lake, a large reservoir lake in Tennessee. Students have the opportunity to demonstrate their skills in using maps and scales as well as to incorporate the use of technology in developing the solution. This project satisfied the…

This article details the application of an economic theory to the fiscal operation of a small engineering consulting firm. Nobel Prize-winning economist Wassily Leontief developed his general input-output economic theory in the mid-twentieth century to describe the flow of goods and services in the U.S. economy. We use one mathematical model that…

This study aimed to evaluate the impact of individual differences in working memory capacity on number transcoding. A recently proposed model, ADAPT (a developmental asemantic procedural transcoding model), accounts for the development of number transcoding from verbal form to Arabic form by two mechanisms: the learning of new production rules…

Studies of group differences in intelligence often invite conclusions about groups in general from studies of group differences in selected populations. The same design is used in the study of group differences in other traits as well. Investigators observe samples from two groups (e.g. men and women) in some accessible population, but seek to…

P. J. Kellman, P. Garrigan, & T. F. Shipley presented a theory of 3-D interpolation in object perception. Along with results from many researchers, this work supports an emerging picture of how the visual system connects separate visible fragments to form objects. In his commentary, B. L. Anderson challenges parts of that view, especially the idea…

This article presents a project for a differential equations class using an inverse problem based on the second order differential equation that models an electrical circuit. (Contains 2 footnotes.)

Each ellipse and hyperbola has a circle associated with it called the director circle. In this article, the author derives the equations of the circle for the ellipse and hyperbola through a different approach. Then the author concentrates on the director circle of the central conic given by the general quadratic equation. The content of this…

Hypotheses that do not have the standard bilinear form theta=CBM=0 occur naturally in the analysis of repeated measurement designs. An expanded class of the tests of the form psi=Tr(G theta)=0, called extended linear hypotheses, provides a richer class of parametric functions. A method to analyze double multivariate and mixed multivariate models…