Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Students often enter biology programs deficient in the math and computational skills that would enhance their attainment of a deeper understanding of the discipline. To address some of these concerns, I developed a series of spreadsheet simulation exercises that focus on some of the mathematical foundations of scientific inquiry and the benefits…

When speaking, how do we convert our thoughts into the sounds that come out of our mouths? Though seemingly effortless, the process of word production is realized by a complex system working over different levels of representation. By focusing on the sublexical factors, this work investigates the representations and dynamics of the word production…

Smaller universities may produce research which is on a par with larger, elite establishments. This is confirmed by a recently developed mathematical model, supported by data from British and French higher education research-evaluation exercises. The detailed nature of the UK system, in particular, allows quantification of the notion of critical…

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves…

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying…

This paper identifies several serious problems with the widespread use of ANOVAs for the analysis of categorical outcome variables such as forced-choice variables, question-answer accuracy, choice in production (e.g. in syntactic priming research), et cetera. I show that even after applying the arcsine-square-root transformation to proportional…

In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaputa's belief in a Science of Need to motivate and direct the development of tasks and tools for engaging students in…

A PUBMED search for "mathematical models in medicine" shows more than 15,000 articles covering almost every field of medicine. We designed a course with the goal of developing the students' skills in computerized data analysis and mathematical modelling, as well as enhancing their ability to read and interpret mathematical data analysis. The study…

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…

The multivariate stochastic processes associated with the Marshall-Olkin multivariate exponential distribution are shown to be able to generate several models of similarity or preference data in the literature. (JKS)

Various types of finite mixtures of confirmatory factor analysis models are proposed for handling data heterogeneity. Proposed classes of mixture models differ in their unique representations of data heterogeneity, and three sampling schemes for these mixtures are distinguished. Advantages of the Approximate Scoring method are outlined. (SLD)

Data are often a continuous function of a variable such as time observed over some interval. One or more such functions might be observed for each subject. The extension of classical data analytic techniques to such functions is discussed. (Author/JKS)

Some mathematical aspects of minimum trace factor analysis (MTFA) are discussed. The uniqueness of an optimal point of MTFA is proved, and necessary and sufficient conditions for any particular point to be optimal are given. The connection between MTFA and classical minimum rank factor analysis is discussed. (Author/JKS)

A model for four-mode component analysis is developed and presented. The developed model, which is an extension of Tucker's three-mode factor analytic model, allows for the simultaneous analysis of all modes of a four-mode data matrix and the consideration of relationships among the modes. (Author/JKS)