The issue of the area of irregular shapes is absent from the modern mathematical textbooks in elementary education in Greece. However, there exists a collection of books written for educational purposes by famous Greek scholars dating from the eighteenth century, which propose certain techniques concerning the estimation of the area of such…

The purpose of this article is to discuss specific techniques for the computation of the volume of a tetrahedron. A few of them are taught in the undergraduate multivariable calculus courses. Few of them are found in text books on coordinate geometry and synthetic solid geometry. This article gathers many of these techniques so as to constitute a…

A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…

Monte Carlo simulations are a classical tool to analyse physical systems. When unlikely events are to be simulated, the importance sampling technique is often used instead of Monte Carlo. Importance sampling has some drawbacks when the problem dimensionality is high or when the optimal importance sampling density is complex to obtain. In this…

This article compares Donald Campbell's and Donald Rubin's work on causal inference in field settings on issues of epistemology, theories of cause and effect, methodology, statistics, generalization, and terminology. The two approaches are quite different but compatible, differing mostly in matters of bandwidth versus fidelity. Campbell's work…

A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these…

Background: Researchers have noted difficulties in attracting adequate numbers of participants with intellectual disabilities (ID) to their studies. Methods: This study was a review of participation by adults with ID in research conducted in South Eastern Ontario over a 20-year period (1987-2006). Original research studies were identified by local…

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical…

The author shows how a quick approximation of the Lorenz curve's Gini coefficient can be calculated empirically using numerical data presented in cumulative income quintiles. When the technique here was used to estimate 621 income quintile/Gini coefficient observations from the Deninger and Squire/World Bank data set, this approach performed…

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of…

The 2012 National Household Education Surveys Program (NHES:2012) Data File User's Manual provides documentation and guidance for users of the NHES:2012 data files. The manual provides information about the purpose of the study, the sample design, data collection procedures, data processing procedures, response rates, imputation, weighting and…

Introduction: The objectives of the study reported here were to describe the physical and psychological health of persons with Usher syndrome Type II (USH2) and to explore any differences in terms of gender. Methods: The participants were recruited from the Swedish Usher database. In the first step, 122 persons received the questionnaire by mail,…

Advances in technology have caused high schools to update their computer science curricula; however there has been little analogous attention to technology-related education in middle schools. With respect to computer-related knowledge and skills, middle school students are at a critical phase in life, exploring individualized education options…

This research examined the impact of teacher licensure routes, particularly those identified as either traditional or alternative on student achievement by comparing Virginia Standards of Learning (SOL) end of year scores in math and reading for minority students in grades six through eight during the period from 2005 through 2009. To compare the…

In randomized control trials (RCTs) of educational interventions, there is a growing literature on impact estimation methods to adjust for missing student outcome data using such methods as multiple imputation, the construction of nonresponse weights, casewise deletion, and maximum likelihood methods (see, for example, Allison, 2002; Graham, 2009;…