This report provides an overview of the process used to derive a school's growth level and summarizes 2015 math and reading/ELA growth levels for all AISD elementary, middle and high schools. Additionally, longitudinal data are provided for each school level.

The paper shows how to find the min and max extreme interval values for the exponential and triangular distributions from the min and max uniform extreme interval values. Tables are provided to show the min and max extreme interval values for the uniform, exponential, and triangular distributions for different probabilities and observation sizes.

Apprentice and trainee data are reported by the State and Territory Training Authorities to NCVER (National Centre for Vocational Education Research) on a quarterly basis, starting at the September quarter of 1994. The set of data submitted that quarter is referred to as Collection 1. The sets of data submitted in subsequent quarters are referred…

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…

This paper investigates a general identity which expresses an apparently complicated and intriguing sum of fractions as an elegant and straightforward sum of simple terms.

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

This Technical Report is designed to provide technical detail to support the analysis and findings presented in the "Head Start Impact Study Final Report" (U.S. Department of Health and Human Services, January 2010). Chapter 1 provides an overview of the Head Start Impact Study and its findings. Chapter 2 provides technical information on the…

Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.

The purpose of this study was to develop general outcome measures (GOM) in mathematics so that teachers could focus their instruction on needed prerequisite skills. We describe in detail, the manner in which content-related evidence was established and then present a number of statistical analyses conducted to evaluate the technical adequacy of…

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.

Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.

The mean and variance of the number of turning points in random permutations of two kinds of distinct elements are evaluated. These results are applied to a Wald-Wolfowitz run test.

This article describes the most compact 100c% interval for a probability density for 0

Descriptors: Probability, Computation, Mathematical Concepts, Statistics