The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

This paper promotes the use of adapted primary literature as a curriculum and instruction innovation for use in high school. Adapted primary literature is useful for promoting an understanding of scientific and mathematical reasoning and argument and for introducing modern science into the schools. We describe a prototype adapted from a published…

In longitudinal studies data is collected in a series of waves. Each wave after the first suffers from attrition. Therefore it can be difficult to discriminate between changes in sample parameters due to a longitudinal process (e.g. ageing) and changes due to attrition. The problem is particularly vexing if one of the purposes is to compare…

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for…

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

Electricity is regarded as one of the most challenging topics for students of all ages. Several researchers have suggested that naive misconceptions about electricity stem from a deep incommensurability (Slotta and Chi 2006; Chi 2005) or incompatibility (Chi et al. 1994) between naive and expert knowledge structures. In this paper we argue that…

The mathematical model used to describe independence between two events in probability has a non-intuitive consequence called dependent spaces. The paper begins with a very brief history of the development of probability, then defines dependent spaces, and reviews what is known about finite spaces with uniform probability. The study of finite…

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…

With the current economic slump possibly the deepest since the Great Depression, interest in the subject of macroeconomics has reignited, and the number of students majoring in economics has increased during the last two years. While this would appear to be good news for educators in the economics field, the profession is nervous about more than…

The author offers innovative approaches to 3 topics that are typically only briefly mentioned (if at all) in money and banking courses. The first topic is a Treasury bill auction experiment in which students have an opportunity to participate directly. The results from a class of 14 money and banking students are used to explain how an instructor…

In recent years, there has been some dispute over the appropriate way to model decision making in professional sports leagues. In particular, Szymanski and Kesenne (2004) argue that formulating the decision-making problem in a noncooperative game leads to radically different conclusions about the nature of competition in sports leagues. The author…

This project was developed as an interdisciplinary application of the optimization of a single-variable function. It was used in a freshman-level single-variable calculus course. After the first month of the course, students had been exposed to the concepts of the derivative as a rate of change, average and instantaneous velocities, derivatives of…

The butterfly curve was introduced by Temple H. Fay in 1989 and defined by the polar curve r = e[superscript cos theta] minus 2 cos 4 theta plus sin[superscript 5] (theta divided by 12). In this article, we develop the mathematical model of the butterfly curve and analyse its geometric properties. In addition, we draw the butterfly curve and…

Visual backward masking is a versatile tool for understanding principles and limitations of visual information processing in the human brain. However, the mechanisms underlying masking are still poorly understood. In the current contribution, the authors show that a structurally simple mathematical model can explain many spatial and temporal…

The primary application of dimensional analysis (DA) is in problem solving. Typically, the problem description indicates that a physical quantity Y(the unknown) is a function f of other physical quantities A[subscript 1], ..., A[subscript n] (the data). We propose a qualitative problem-solving procedure which consists of a parallel decomposition…