Effect size use has been increasing in the past decade in many research areas. Confidence intervals associated with effect sizes are encouraged to be reported. Prior work has investigated the performance of confidence interval estimation with Cohen's d. This study extends this line of work to the analysis of variance case with more than two…

All methods presented in textbooks for computing inverse "Z"-transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence "x"("k") whose "Z"-transform is "X"("z"); 2) computation using the inversion integral…

Adjusted Wald intervals for binomial proportions in one-sample and two-sample designs have been shown to perform about as well as the best available methods. The adjusted Wald intervals are easy to compute and have been incorporated into introductory statistics courses. An adjusted Wald interval for paired binomial proportions is proposed here and…

Acquisition of relational knowledge is a core process in cognitive development. Relational knowledge is dynamic and flexible, entails structure-consistent mappings between representations, has properties of compositionality and systematicity, and depends on binding in working memory. We review three types of computational models relevant to…

Does modeling matter? We address this question by providing a broad survey of the computational models of cognitive development that have been proposed and studied over the last three decades. We begin by noting the advantages and limitations of computational models. We then describe four key dimensions across which models of development can be…

In this article, the author shares his comments on statistical analysis for multisite trials, and focuses on the contribution of Stephen Raudenbush, Sean Reardon, and Takako Nomi to future research. Raudenbush, Reardon, and Nomi provide a major contribution to future research on variation in program impacts by showing how to use multisite trials…

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…

A basketball player attempting a free throw has two parameters under his or her control: the angle of elevation and the force with which the ball is thrown. We compute upper and lower bounds for the initial velocity for suitable values of the angle of elevation, generating a subset of the configuration space of all successful free throws. A…

It has been hypothesized that developmental dyscalculia (DD) is either due to a defect of the approximate number system (ANS) or to an impaired access between that system and symbolic numbers. Several studies have tested these two hypotheses in children with DD but none has dealt with adults who had experienced DD as children. This study aimed to…

Viscous damping is commonly discussed in beginning differential equations and physics texts but dry friction or Coulomb friction is not despite dry friction being encountered in many physical applications. One reason for avoiding this topic is that the equations involve a jump discontinuity in the damping term. In this article, we adopt an energy…

The purpose of this study was to examine the potential for using propensity score-based matching methods to estimate teacher contributions to student learning. Value-added models are increasingly used in teacher accountability systems in the United States in spite of ongoing qualms about the validity of teacher quality estimates resulting from…

This study was conducted on year 4 students enrolled in the Bachelor of Education program for Cycle one teacher candidates. The effect of practicing mental calculation strategies in improving students' numeracy proficiency was put under some tests to measure its effect in a scientific way. A Pre-quiz was conducted before with no prior practice…

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new…

This article reports on the main experiences gained from a 2-year study which incorporated A.L.E.X., an educational puzzle game available on iPad or Android tablet devices, within the primary school mathematics curriculum. The study took place in a public primary school, located in a rural area of Cyprus. The majority of its students come from low…

"The Language of Mathematics in Science" is an ASE/Nuffield project aimed at supporting teachers of 11-16 science in the use of mathematical ideas in the science curriculum. Two publications have been produced. This article focuses on the first of these, "The Language of Mathematics in Science: A Guide for Teachers of 11-16…