Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem…

Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…

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…

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.

Coefficient alpha, the most commonly used estimate of internal consistency, is often considered a lower bound estimate of reliability, though the extent of its underestimation is not typically known. Many researchers are unaware that coefficient alpha is based on the essentially tau-equivalent measurement model. It is the violation of the…

This cross-sectional study identifies key conceptual difficulties experienced by upper secondary school and pre-service chemistry teachers (N = 191) in the area of reaction rates. Students' ideas about reaction rates were elicited through a series of written tasks and individual interviews. In this paper, students' ideas related to reaction rate…

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…