The application of mathematics to real-world problems is moving more and more in the focus of attention of mathematics education; however, many learners experience huge difficulties in relating "pure" mathematics to everyday contents. In order to solve "modeling problems", it is first necessary to find a transition from a…

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Kulick and Wright concluded, based on theoretical mathematical simulations of hypothetical student exam scores, that assigning exam grades to students based on the relative position of their exam performance scores within a normal curve may be unfair, given the role that randomness plays in any given student's performance on any given exam.…

The Adequate Yearly Progress (AYP) Model has been used to make many high-stakes decisions concerning schools, though it does not provide a complete assessment of student academic achievement and school effectiveness. To provide a clearer perspective, many states have implemented various Growth and Value Added Models, in addition to AYP. The…

Multivariate matching in Differential Item Functioning (DIF) analyses may contribute to understand the sources of DIF. In this context, detecting appropriate additional matching variables is a crucial issue. This present article argues that the variables which are correlated with communalities in item difficulties can be used as an additional…

There is substantial variability in the degree to which the SAT and high school grade point average (HSGPA) predict first-year college performance at different institutions. This paper demonstrates the usefulness of multilevel modeling as a tool to uncover institutional characteristics that are associated with this variability. In a model that…

Grading on the curve is a common practice in higher education. While there are many critics of the practice it still finds wide spread acceptance particularly in science classes. Advocates believe that in large classes student ability is likely to be normally distributed. If test scores are also normally distributed instructors and students tend…

Most researchers using factor analysis extract factors from a matrix of Pearson product-moment correlation coefficients. A method is presented for extracting factors in a non-parametric way, by extracting factors from a matrix of Spearman rho (rank correlation) coefficients. It is possible to factor analyze a matrix of association such that…

Point-estimate and confidence-interval procedures are proposed for the (1) combined Mann-Whitney U test; (2) combined two-sample normal-scores test; (3) combined matched-pair Wilcoxon signed-ranks test; and (4) combined matched-pair normal-scores test. The four techniques are illustrated with hypothetical examples and are considered either…

A general linear model (GLM) framework is used to suggest that structure coefficients ought to be interpreted in structural equation modeling confirmatory factor analysis (CFA) studies in which factors are correlated. The computation of structure coefficients in explanatory factor analysis and CFA is explained. Two heuristic data sets are used to…

With respect to the often-present covariance between error terms of correlated variables, D. W. Zimmerman and R. H. Williams's (1977) adjusted correction for attenuation estimates the strength of the pairwise correlation between true scores without assuming independence of error scores. This article focuses on the derivation and analysis of…

Three factors that increase score variability yet can be associated with an increase, a decrease, or no change in Pearson's correlation coefficient (r) are discussed (restriction of range, errors of measurement, and linear transformations of data). The connection between changes in variability and r depends on how changes occur. (SLD)

A more generalized error model for time-limit tests is developed. Model estimates are derived for right-attempted and wrong-attempted correlations both within the same test and between different tests. A comparison is made between observed correlations and their model counterparts and a fair agreement is found between observed and expected…

Effects of overextracting factors and components within and between maximum likelihood factor analysis and principal components analysis were examined through computer simulation of a range of factor and component patterns. Results demonstrate similarity of component and factor scores during overextraction. Overall, results indicate that…

A modified "F" test is derived that includes a correction for nonindependence of between-groups and within-groups sample values in analysis of variance (ANOVA) designs. Computer simulations based on normal and nonnormal distributions illustrate the usefulness of the approach, which was more powerful than conventional within-subjects…