Studied the order-statistics models, extending the usual normal order-statistics model into one in which the underlying random variables followed a multivariate normal distribution. Used a Bayesian approach and the Gibbs sampling technique. Applied the proposed method to analyze presidential election data from the American Psychological…

Discusses , in the context of confirmatory latent class analysis, model selection using Bayes factors and (pseudo) likelihood ratio statistics. Uses a small simulation study to show that in this context, Bayes factors and the pseudo likelihood ratio statistics have the best properties. (SLD)

Assessed the extent to which results in exploratory factor analysis (EFA) studies can be replicated by confirmatory factor analysis in the same sample. Used 10 factor structures drawn from the literature. Results show that confirmatory factor models in which all low EFA pattern coefficients were fixed to zero fitted especially poorly. (SLD)

Many institutions regularly conduct surveys of students. In some cases these provide descriptive statistics about students' actual use of course components and the descriptive statistics are discussed using ordinary language. A number of refinements to these surveys are proposed. It is argued that mathematical modeling as used in the discipline of…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

The teaching of mathematical modeling to undergraduate students requires that students are given ample opportunity to develop their own models and experience first-hand the process of model building. Finding an appropriate context within which modeling can be undertaken is not a simple task as it needs to be readily understandable and seen as…

The goal of this study was to determine how the fear relevancy of outcomes during probabilistic classification learning affects behavior and strategy use. Novel variants of the "weather prediction" task were created, in which cue cards predicted either looming fearful or neutral outcomes in a between-groups design. Strategy use was…

This article describes how sixth-grade students developed concrete models to solve division of fractions story problems. Students developed separate two-step procedures to solve measurement and partitive problems, drawing on invented procedures for division of whole numbers. Errors also tended to be specific to the type of division problem…

At least 3 different types of computational model have been shown to account for various facets of both normal and impaired single word reading: (a) the connectionist triangle model, (b) the dual-route cascaded model, and (c) the connectionist dual process model. Major strengths and weaknesses of these models are identified. In the spirit of…

This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve…

The oxygen dissociation curve (ODC) of hemoglobin (Hb) has been widely studied and mathematically described for nearly a century. Numerous mathematical models have been designed to predict with ever-increasing accuracy the behavior of oxygen transport by Hb in differing conditions of pH, carbon dioxide, temperature, Hb levels, and…

People tend to perceive ongoing continuous activity as series of discrete events. This partitioning of continuous activity may occur, in part, because events correspond to dynamic patterns that have recurred across different contexts. Recurring patterns may lead to reliable sequential dependencies in observers' experiences, which then can be used…

This paper reports on the implementation of a self-directed learning process in a circuit theory course, incorporating dynamic training elements which were designed on the basis of a cybernetic model of cognitive process management. These elements are centrally linked in a dynamic learning frame, created on the monitor screen, which displays the…

AN INQUIRY INTO RECRUITMENT OF APPRENTICES TO SKILLED TRADES IN WESTERN AUSTRALIA INDICATED LITTLE CORRELATION BETWEEN THE NUMBER OF NEW APPRENTICES AND THE LEVEL OF INDUSTRIAL EMPLOYMENT OR THE TOTAL NUMBER OF APPRENTICES. THIS ARTICLE ATTEMPTS TO OUTLINE A MATHEMATICAL MODEL OF AN APPRENTICESHIP SYSTEM AND DISCUSS ITS IMPLICATIONS. THE MODEL, A…