In this paper, the statistical significance of the contribution of variables to the principal components in principal components analysis (PCA) is assessed nonparametrically by the use of permutation tests. We compare a new strategy to a strategy used in previous research consisting of permuting the columns (variables) of a data matrix…

Previous research has suggested that the use of the fingers may play a functional role in the development of a mature counting system. However, the role of developmental vision in the elaboration of a finger numeral representation remains unexplored. In the current study, 14 congenitally blind children and 14 matched sighted controls undertook…

Barth and Paladino (2011) argue that changes in numerical representations are better modeled by a power function whose exponent gradually rises to 1 than as a shift from a logarithmic to a linear representation of numerical magnitude. However, the fit of the power function to number line estimation data may simply stem from fitting noise generated…

The generalized graded unfolding model (GGUM) is an ideal point model of responding that is consistent with the Thurstonian theory of respondent behavior. Ideal point models have recently generated interest in the realms of attitude and personality assessment. One unclear aspect of applying ideal point models is the influence of…

Researchers must make numerous choices when conducting factor analyses, each of which can have significant ramifications on the model results. They must decide on an appropriate sample size to achieve accurate parameter estimates and adequate power, a factor model and estimation method, a method for determining the number of factors and evaluating…

The use of propensity scores in psychological and educational research has been steadily increasing in the last 2 to 3 years. However, there are some common misconceptions about the use of different estimation techniques and conditioning choices in the context of propensity score analysis. In addition, reporting practices for propensity score…

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

The story is often told of the calculation by G.I. Taylor of the yield of the first ever atomic bomb exploded in New Mexico in 1945. It has indeed become a staple of the classroom whenever dimensional analysis is taught. However, while it is true that Taylor succeeded in calculating this figure at a time when it was still classified, most versions…

Background: This article reports on an analysis of errors that were displayed by students who studied mathematics in Chemical Engineering in derivatives of mostly trigonometric functions. The poor performance of these students triggered this study. The researcher (lecturer) works in a mathematics support programme to enhance students'…

It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…

Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…

This study tested the hypothesis that subitizing ability may cause achievement differences in mathematics especially for students with mathematics learning disabilities. Students from 1st through 4th grade were applied to curriculum based math achievement tests (MAT). Based on MAT scores, they were divided into four groups as Mathematics Learning…

The School Composition and the Black-White Achievement Gap study was undertaken by the National Center for Education Statistics to present both descriptive and associative information on the relationships among the percentage of students in a school who were Black (referred to as "Black student density" or "density"), the…

Background: Primary school math skills form a basis for academic success down the road. Different math skills have different antecedents and there is a reason to believe that more complex math tasks require better self-regulation. Aims: The study aimed to investigate longitudinal interrelations of calculation and problem-solving skills, and…

Three cohorts of third-grade students (N = 813) were evaluated on achievement, cognitive abilities, and behavioral attention according to contrasting research traditions in defining math learning disability (LD) status: low achievement versus extremely low achievement and IQ-achievement discrepant versus strictly low-achieving LD. We use methods…