Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

Studies using tests scores as the dependent variable often report point estimates in student standard deviation units. We note that a standard deviation is not a standard unit of measurement since the distribution of test scores can vary across contexts. As such, researchers should be cautious when interpreting differences in the numerical size of…

Student graduation from high school with a regular high school diploma is an important indicator of school success and one of the most significant indicators of student college and career readiness. In addition, there are substantial economic benefits to high school completion. For example, according to the U.S. Department of Education's National…

We describe an important elaboration of our multiscale/multiresolution model for solving the Traveling Salesman Problem (TSP). Our previous model emulated the non-uniform distribution of receptors on the human retina and the shifts of visual attention. This model produced near-optimal solutions of TSP in linear time by performing hierarchical…

A procedure for examining essential unidimensionality in multicomponent measuring instruments is discussed. The method is based on an application of latent variable modeling and is concerned with the extent to which a common factor for all components of a given scale accounts for their correlations. The approach provides point and interval…

A critical aspect of mathematics study is developing both understanding of quantities and fluency in manipulating them. These abilities are essential for students who intend to enter technical or scientific professions. All students, however, should be exposed to methods of quantitative reasoning in order to function effectively in today's…

"Media Clips" appears in every issue of "Mathematics Teacher," offering readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. The theme of this issue's "Media Clip" revolves around four items relating to lumber. These items include: A Q&A published in the…

Previous confirmatory factor analytic research that has examined the factor structure of the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV) has endorsed either higher order models or oblique factor models that tend to amalgamate both general factor and index factor sources of systematic variance. An alternative model that has not yet…

Today, almost all introductory physics textbooks include standardized "rules" on how to find the number of significant figures in a calculated value. And yet, 30 years ago these rules were almost nonexistent. Why have we increased the role of significant figures in introductory classes, and should we continue this trend? A look back at…

In operational equating situations, frequency estimation equipercentile equating is considered only when the old and new groups have similar abilities. The frequency estimation assumptions are investigated in this study under various situations from both the levels of theoretical interest and practical use. It shows that frequency estimation…

Assuming a constant mass decrease per unit surface and unit time we provide a very simplistic model for the dissolution process of spherical candies. The aim is to investigate the quantitative behaviour of the dissolution process throughout the act of eating the candy. In our model we do not take any microscopic mechanism of the dissolution…

Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

A program is described and presented to readily plot the molecular orbitals from a Huckel calculation. The main features of the program and the scope of its applicability are discussed through some example organic molecules. (Contains 2 figures.)

Word frequencies in natural language follow a highly skewed Zipfian distribution, but the consequences of this distribution for language acquisition are only beginning to be understood. Typically, learning experiments that are meant to simulate language acquisition use uniform word frequency distributions. We examine the effects of Zipfian…

The problem-size effect in simple additions, that is the increase in response times (RTs) and error rates with the size of the operands, is one of the most robust effects in cognitive arithmetic. Current accounts focus on factors that could affect speed of retrieval of the answers from long-term memory such as the occurrence of interference in a…