The results of the cognitive research on numbers' representations can provide a sound theoretical framework to develop educational activities on representing numbers. A program of such activities for a nursery school was designed in order to enable the children to externalize and strengthen their internal representations about numerosity and link…

The final report of the Williams committee (DCSF, 2008: 68) argues that the revised mathematics Framework (DfES, 2006) "should be reconsidered to achieve a more suitable, user-friendly form." It might also have added that there is not much help and support in it for early years teachers. A much more useful document is the "Practice guidance for…

This article provides the theory and application of the 2-stage maximum likelihood (ML) procedure for structural equation modeling (SEM) with missing data. The validity of this procedure does not require the assumption of a normally distributed population. When the population is normally distributed and all missing data are missing at random…

Adaptation to right-shifting prisms improves left neglect for mental number line bisection. This study examined whether adaptation affects the mental number line in normal participants. Thirty-six participants completed a mental number line task before and after adaptation to either: left-shifting prisms, right-shifting prisms or control…

A simple algorithm for computing the partial fraction expansions of proper rational functions with multiple poles is presented. The main idea is to use the Heaviside's cover-up technique to determine the numerators of the partial fractions and polynomial divisions to reduce the multiplicities of the poles involved successively, without the use of…

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 develops a series of models for optimal tuition pricing for private colleges and universities. The university is assumed to be a profit maximizing, price discriminating monopolist. The enrollment decision of student's is stochastic in nature. The university offers an effective tuition rate, comprised of stipulated tuition less financial…

The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…

For RCTs of education interventions, it is often of interest to estimate associations between student and mediating teacher practice outcomes, to examine the extent to which the study's conceptual model is supported by the data, and to identify specific mediators that are most associated with student learning. This paper develops statistical power…

This fact sheet highlights the statistics of the current status of high schools in the United States. It provides information on the following variables: (1) demography of high school students; (2) students with disabilities; (3) high school student achievement; (4) the schools; (5) school funding; (6) high school graduation rate; (7) high school…