Mathematical models have become an important tool for understanding the control of eye movements during reading. Main goals of the development of the SWIFT model (R. Engbert, A. Longtin, & R. Kliegl, 2002) were to investigate the possibility of spatially distributed processing and to implement a general mechanism for all types of eye movements…

Biological phenomena can be investigated at multiple levels, from the molecular to the cellular to the organismic to the ecological. In typical biology instruction, these levels have been segregated. Yet, it is by examining the connections between such levels that many phenomena in biology, and complex systems in general, are best explained. We…

Offering mathematics majors the opportunity to engage in current, real-world applications can be an important enhancement to their undergraduate course curriculum. Instead of focusing on the traditional topic areas in pure and/or applied mathematics, one may structure a seminar course for senior mathematics majors by concentrating on a specific…

The focus is on the metacognitive awareness of ten high-achieving high school pupils in mathematics in Denmark and England and their understanding of their cognitive learning processes and strategies. Mainly unstructured focus group interviews investigate how they explain that they learn a mathematical concept that is new to them. I develop the…

This note, which is based on a final year project for a BSC degree, presents an investigation on the Olympic decathlon. It shows that the existing non-linear transformation which is used to assign points to athletes' performance gives practically identical results to that of a simpler linear one. In addition, the paper presents evidence to support…

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

Using Ehrenberg's application of mathematical models to the analysis and prediction of repeated buying patterns of consumers, this study focuses on the concept of library use as a form of consumer behavior. The following hypotheses were tested: designated library user groups will tend to exhibit stable behavioral patterns with respect to the…

The interest in the application of large-scale computerized adaptive testing has served to focus attention on issues that arise when theoretical advances are made operational. Some of these issues stem less from changes in testing conditions and more from changes in testing paradigms. One such issue is that of the order in which questions are…

Centering is a problem in multilevel analysis that needs to be addressed. Multilevel analysis gives researchers a choice between centering within context and grand mean centering, both statistically sound ways to improve estimation of the parameters in the model. Researchers of the most widely used software package for the analysis of…

This paper documents how eight high school students in a precalculus class enhanced with graphing calculators think about functions. Three models of thinking about functions emerged from students' function images observed over a period of 9 months. In the graph model, students believed that functions are essentially graphs; in the equation model,…

An analysis of covariance (ANCOVA) is done to correct for chance differences that occur when subjects are assigned randomly to treatment groups. When properly used, this correction results in adjustment of the group means for pre-existing differences caused by sampling error and reduction of the size of the error variance of the analysis. The…

The application of mathematical programming techniques is extended to the construction of measurement instruments in generalizability theory. Key concepts in generalizability theory are explained and a description is given of: (1) the one-facet crossed design; (2) the two-facet crossed design; and (3) a two-facet nested design. The optimization of…

While functions and relations are important concepts in the teaching of mathematics, research suggests that many students lack an understanding and appreciation of these concepts. The present paper discusses an approach for teaching functions and relations that draws on the use of illustrations from database management. This approach has the…

This Monte Carlo study examined strategies for forming the matching variable for the Mantel-Haenszel (MH) differential item functioning (DIF) procedure. Data were generated using a three-parameter logistic item response theory model, with common guessing parameters. The number of subjects and test length were manipulated, as were the difficulty,…

Some item response theory (IRT) techniques work in applications even though the usual structural IRT assumptions, and local independence (LI) in particular, do not hold. When the departure from LI is too great, traditional procedures will break down. Although violations of strictly unidimensional, monotone, locally independent latent structure can…