Different indices for the internal consistency, reproducibility, or homogeneity of a test are based upon highly similar conceptual frameworks. Illustrations are presented to demonstrate how the maximum and minimum values of KR20 are influenced by test difficulty and the shape of the distribution of test scores. (Author/CTM)

Reliability coefficients of linear combinations of observed scores have anomalous properties which have led to difficulties in the investigation of difference scores and gain scores in test theory. Discrepancies between classical results and correct results obtained from more general formulas, which allow for correlated errors, are examined…

Five approaches to grading student tests are described and their advantages and limitations are examined. It is suggested that the fifth approach, which takes into account the general ability level of the class and applies predetermined percentages to determine the number of students receiving each grade, is the most rational approach. (JMD)

Introducing a four-vector strain and a four-force stress, Hooke's law is written as a four-vector equation. This formulation is shown to clarify seemingly paradoxical results in connection with uniformly accelerated motion, and rotational motion with angular acceleration. (Author/JN)

Demonstrates that the observed path of a particle in quantum mechanics is a fractal curve with Hausdorff dimension two. (Author/JN)

As time spent in academic research becomes more controversial, it is proposed that a quantitative measure of research productivity be applied to faculty efforts. The formula takes into account single- and multiple-author publication rates and appropriate types of publication. The validity of a publication rate index is discussed. (MSE)

Simple and efficient methods for adding angular momenta and for finding angular momentum eigenstates for systems of equivalent electrons are developed. Several different common representations are used in specific examples. The material is suitable for a graduate course in quantum mechanics. (SK)

By algebraically defining a school finance structure as a total budget system, partial derivatives can be used to find the kinds of rewards, incentives, and distributions the structure defines for individual districts and among districts. Equity concerns can also be answered. (Author/IRT)

An example is presented that can be used to introduce the study of limits of sequences through recursive formulas yielding square roots. (MP)

In an article from the July 1995 issue of Educational Studies in Mathematics, Even and Tirosh claim that the quantity (-8)1/3 is undefined. This article presents arguments as to why the reasoning of Tirosh and Even is flawed. Attempts to convince educators of the importance of applying a mathematical definition precisely. (AIM)

Discussion of ranking systems used in various settings, including college football and academic admissions, focuses on the Google search engine. Explains the PageRank mathematical formula that scores Web pages by connecting the number of links; limitations, including authenticity and accuracy of ranked Web pages; relevancy; adjusting algorithms;…

Discussion of relevance feedback in information retrieval focuses on a proposal for the Bayesian Network Retrieval Model. Bases the proposal on the propagation of partial evidences in the Bayesian network, representing new information obtained from the user's relevance judgments to compute the posterior relevance probabilities of the documents…

Describes how the cubic formula can be presented easily at the precalculus level, shows how to verify that the formula is correct, and identifies when it is profitable to use. (KHR)

Examines the writing of two groups of students in a college-level calculus class to identify criteria that discriminate successful versus unsuccessful writers in mathematics. Discusses results from the mathematics writers' checklist and methods for its use as an instructional and assessment tool in the classroom. (Author/KHR)

Presents two methods for replacing a series by one converging more rapidly: regrouping the terms of a series and manipulations of power series. Describes a general algorithm for approximating the natural logarithm of any number. (YP)