Trading cards for various sports and a range of other subjects such as architecture, animals, hobbies, and war have been in existence since the late nineteenth century and still enjoy great popularity. Two of the most prominent examples are baseball cards in the U.S. and football cards in Europe. Three strategies for collecting European football…

Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions…

This article considers potential problems that can arise in estimating a unidimensional item response theory (IRT) model when some test items are multidimensional (i.e., show a complex factorial structure). More specifically, this study examines (1) the consequences of model misfit on IRT item parameter estimates due to unintended minor item-level…

Rubin and Thayer ("Psychometrika," 47:69-76, 1982) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one,…

Meta-analyses often include studies that report multiple effect sizes based on a common pool of subjects or that report effect sizes from several samples that were treated with very similar research protocols. The inclusion of such studies introduces dependence among the effect size estimates. When the number of studies is large, robust variance…

This task asks readers to figure out why when you stir a cup of hot liquid and tap on the side of the cup with a spoon, the pitch of sound starts low and ends up high. The solution to last month's tasks relating to the circumference of the Earth and how many stars are in the (visible) sky is also presented.

In our previous article on CCl[subscript 4] in this "Journal," we presented an investigation of the fine structure of the symmetric stretch of carbon tetrachloride (CCl[subscript 4]) due to isotopic variations of chlorine in C[superscript 35]Cl[subscript x][superscript 37]Cl[subscript 4-x]. In this paper, we present an investigation of…

Given that the root mean square error of approximation (RMSEA) is currently one of the most popular measures of goodness-of-model fit within structural equation modeling (SEM), it is important to know how well the RMSEA performs in models with small degrees of freedom ("df"). Unfortunately, most previous work on the RMSEA and its…

Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…

Lorraine Day and Derek Hurrell provide a convincing argument for using arrays to promote students' understandings of mental computation strategies for multiplication. They also provide a range of different examples that illustrate the benefits of arrays in the primary classroom.

This paper uses a multilevel analysis of mathematical reasoning rooted in Cultural Historical Activity Theory to examine how mathematical discourse and student reasoning about linear functions developed across 3 weeks in a ninth grade bilingual algebra class. Despite the teacher's expertise teaching with a conceptual focus, and her stated…

Several studies have stressed the importance of simultaneously estimating interaction and quadratic effects in multiple regression analyses, even if theory only suggests an interaction effect should be present. Specifically, past studies suggested that failing to simultaneously include quadratic effects when testing for interaction effects could…

Counting all and counting on are distinct counting strategies that can be used to compute such quantities as the total number of objects in two sets (Wright, Martland, and Stafford 2010). Given five objects and three more objects, for example, children who use counting all to determine quantity will count both collections; that is, they count…

A computational laboratory experiment is described, which involves the advanced study of an atomic system. The students use concepts and techniques typically covered in a physical chemistry course but extend those concepts and techniques to more complex situations. The students get a chance to explore the study of atomic states and perform…

Purpose: In this study, a new algorithm for automated determination of speech rate (SR) in dysarthric speech is evaluated. We investigated how reliably the algorithm calculates the SR of dysarthric speech samples when compared with calculation performed by speech-language pathologists. Method: The new algorithm was trained and tested using Dutch…