This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

A simple method based on the moment of forces and Archimedes' principle is described for finding density without measuring the mass and volume of an object. The method involves balancing two unknown objects of masses M[subscript 1] and M[subscript 2] on each side of a pivot on a metre rule and measuring their corresponding moment arms. The object…

In 3 experiments, the authors compared duration judgments of filled stimuli (tones) with unfilled ones (intervals defined by clicks or gaps in tones). Temporal generalization procedures (Experiment 1) and verbal estimation procedures (Experiments 2 and 3) all showed that subjective durations of the tones were considerably longer than those of…

Converting between degrees Celsius and degrees Fahrenheit isn't difficult. Remembering when to multiply by 5/9 or 9/5 and whether you have to add 32 or subtract 32 makes it fairly easy. Sometimes, though, fairly easy isn't easy enough. Students have trouble remembering the order of operations: "Do I add or subtract 32, and is that before or after…

The estimation of nonlinear structural models is not trivial. One reason for this is that a closed form solution of the likelihood may not be feasible or does not exist. We propose to estimate nonlinear structural models using the efficient method of moments, as generating data according to the models is often very easy. A simulation study of the…

This paper further explores the analytic connections between three commonly used statistical measures of agreement for 2 x 2 contingency tables: sensitivity, specificity, and the kappa coefficient, which are often employed in evaluating diagnostic tests. In particular, for a given fixed kappa the corresponding locus of minimum values of…

This paper is one of a collection of papers written by the Academic Senate for California Community Colleges (ASCCC) to support the use of content review as the basis for establishing communication and computation prerequisites. "Student Success: The Case for Establishing Prerequisites Through Content Review" was adopted at the Fall 2010…

This author became intrigued by the idea that her generation, who had grown up reaping the benefits of second-wave feminism, might differ from previous generations in their attitudes toward women. What was unclear was how this period of progress might have combined with feminist backlash in affecting subsequent generations' responses to typical…

A simple, straightforward and efficient method is proposed for the calculation of the period of anharmonic oscillators as an energy series. The approach is based on perturbation theory and the method of Lindstedt-Poincare.

The purpose of this research is to describe and understand the ways in which deaf middle school students understood and solved compare word problems, and to examine their overall strategy use in learning mathematics. The participants in the study were deaf middle school students, attending a residential state school for the deaf. Most of them used…

The 2001 No Child Left Behind Act required states to report graduation rates as a condition of high school accountability for receipt and use of federal Title I funds, and to set growth targets that would ensure all students graduate from high school. It also reaffirmed the long-standing national policy that graduation rates be used as the…

It is estimated that 50% of beginning teachers leave the profession within the first five years on the job (Murnane, Singer, Willett, Kemple, & Olsen, 1991; Colbert & Wolff, 1992; Ingersoll, 2003b; Schlechty & Vance, 1981). When teachers depart, they take with them their knowledge of instructional techniques, students' learning styles, and…

This publication presents experimental estimates of completion and attrition rates for the latest commencing apprentice and trainee cohorts. Such up-to-date estimates are possible by applying a "life tables" methodology to simple cross tabulations of commencements, completions and cancellations/withdrawals. The resultant cross-sectional…

The accuracy of item parameter estimates in the multidimensional item response theory (MIRT) model context is one that has not been researched in great detail. This study examines the ability of two confirmatory factor analysis models specifically for dichotomous data to properly estimate item parameters using common formulae for converting factor…

At the request of Pittsburgh Public Schools (PPS) and the Pittsburgh Federation of Teachers (PFT), Mathematica has developed value-added models (VAMs) that aim to estimate the contributions of individual teachers, teams of teachers, and schools to the achievement growth of their students. The authors' work in estimating value-added in Pittsburgh…