Collaboration between Mathematicians and Mathematics Educators is crucial in advancing knowledge on the teaching and learning of Mathematics, particularly in advanced Mathematics pedagogy. However, there is a need for the type of collaborations where Mathematicians and Mathematics Educators can find common ground, and the synergy of their…

An introductory guide to deducing the mechanism of chemical reactions is presented. Following a typical workflow for probing reaction mechanism, the guide introduces a wide range of kinetic and mechanistic tools. In addition to serving as a broad introduction to mechanistic analysis for students and researchers, the guide has also been used by…

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model…

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

The problem of obtaining the apparent equation of motion and shape of a moving body from its arbitrary given equation of motion in special relativity is considered. Also the inverse problem of obtaining the body's equation of motion from a known equation of motion of its image is discussed. Some examples of this problem solution are considered. As…

Meta-analytic reliability generalizations (RGs) are limited by the scarcity of reliability reporting in primary articles, and currently, RG investigators lack a method to quantify the impact of such nonreporting. This article introduces a stepwise procedure to address this challenge. First, the authors introduce a formula that allows researchers…

American students continue to struggle on measures of student achievement. This study employed Hierarchical Linear Modeling to estimate a two-level model and examine the influences of calculator use and teachers' instructional practices on student achievement in mathematics amongst first-grade students. The outcome variable was mathematics test…

An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

Reviews what information and software sciences have thus far accomplished in search for empirical regularities and laws and examines what theories have been developed to explain and account for regularities and laws. Specific laws and theories of information highlighted are those of Zipf, Bradford, Lotka, Mandelbrot, and Simon. (Forty references)…

Four empirical laws of bibliometrics--anomalous number, Lotka's, Zipf's, and Bradford's--together with Laplace's "law of succession" and de Solla Price's cumulative advantage distribution are shown to be almost identical. A simple model shows that the frequency forms conform with inverse square law over appropriate interval. (Fifteen…

This essay distinguishes several different kinds of measures of information from each other, noting that differences between them show that our pretheoretical concept of information is multiply ambiguous. Incremental information, conditional information, transmitted information, expected information, and deductive information are discussed. Ten…

It is shown that there is no ambiguity in Bradford's theory of distribution. Starting with two basic postulates laid down by Bradford, a mathematical expression is derived such that its curve agrees with the experimentally plotted data for periodicals in fields of applied geophysics and lubrication. Five references are listed. (Author/EJS)

Describes the recall precision trade-off in information retrieval as the deceleration in the proportion of relevant documents retrieved over time. Several mathematical functions sharing this property are examined and it is concluded that the equation that best models recall as a function of time is the logarithm of a quadratic equation. (21…

After discussion of the equivalency of the information laws of Bradford, Leimkuhler, Lotka, and Mandelbrot, aberrations from Leimkuhler's law (including "Groos droop" as encountered in practice) are studied. Other aberrations of Leimkuhler's law are explained, starting from generalization of verbal formulation of Bradford's Law. (18…

Use of "special" orthonormal mean contrasts and mean contrast variances can help educational researchers interpret a wide variety of repeated measures data. Most statistical packages allow educational researchers to test for differences across repeated measures using both the univariate mixed model F test and a multivariate test.…