Students and professionals from a variety of domains have demonstrated different approaches to problem solving. These two populations have displayed differences when using and perceiving multiple representations of problem-solving tools. In the domain of transportation engineering, this difference has yet to be evaluated in detail. This study…

This paper was inspired by the work of a previous contributor on the subject of modelling plague epidemiology by comparing it to the physics of series radioactive decay, RC transients, and fluid dynamics. An Arduino-based experiment to illustrate the fluid-dynamical case is described. Attention is drawn to important differences between systems…

We report on a study investigating the influence of context, direction of translation, and function type on undergraduate students' ability to translate between graphical and symbolic representations of mathematical relations. Students from an algebra-based and a calculus-based physics course were asked to solve multiple-choice items in which they…

This study investigates representational code-switching (RCS) by considering three high school students' communications in the process of comparing and contrasting pairs of representations (e.g., equation and graph) in the context of rational functions. Supporting this study is research in the realms of students interacting with mathematical…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

To succeed within scientific disciplines, using representations, including those based on words, graphs, equations, and diagrams, is important. Research indicates that the use of discipline specific representations (sometimes referred to as expert generated representations), as well as multi-representational use, is critical for problem solving…

This paper compares lessons on linear equations from the same curriculum materials taught by two teachers of different levels of mathematical knowledge for teaching (MKT). The analysis indicates that the mathematical quality of instruction in these two classrooms appears to be a function of differences in MKT. Although the two teachers were…

Estimation/smoothing methods that are flexible enough to fit a wide variety of test score distributions are reviewed: kernel method, strong true-score model-based method, and method that uses polynomial log-linear models. Applications of these methods include describing/comparing test score distributions, estimating norms, and estimating…

This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results…

The stochastic interactive activation and competition (SIAC) model of perception is presented and tested using several data sets from previous research. The asymptotic predictions of the SIAC model are compared with those of the fuzzy logical model of perception (FLMP). Evidence favoring the FLMP is reviewed. (SLD)

Ignorance of the characteristics of a mixed population may lead to bias in a summary measure of a phenomenon. A test based on sample kurtosis is demonstrated by a simulation study to be more powerful than six other known tests in detecting a class of mixed normal distributions. (SLD)

Forming the matching variable for the Mantel-Haenszel differential item functioning (DIF) procedure through use of the total score as the matching variable (thin) and forming the matching variable by pooling total score levels (thick) were compared in a Monte Carlo study. Reasons thick matching is superior are discussed. (SLD)

"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and…