For various reasons there has been a recent trend in college and high school calculus courses to de-emphasize teaching the Partial Fraction Decomposition (PFD) as an integration technique. This is regrettable because the Partial Fraction Decomposition is considerably more than an integration technique. It is, in fact, a general purpose tool which…

The Onsager reciprocal relations are essential to multicomponent transport theory. A discussion of the principles that should be used to derive flux laws for coupled diffusion is presented here. Fluctuation theory is employed to determine the reciprocal relation for transport coefficients that characterize coupled mass and heat transfer in binary…

Ask a graduating chemical engineering student the following question: What makes one reactor different from the next? The answers received will often be unsatisfactory and will vary widely in scope. Some may cite the difference between the basic design equations, others may point out a PFR is "longer," and still others may state that it…

Univariate latent growth modeling (LGM) of composites of multiple items (e.g., item means or sums) has been frequently used to analyze the growth of latent constructs. This study evaluated whether LGM of composites yields unbiased parameter estimates, standard errors, chi-square statistics, and adequate fit indexes. Furthermore, LGM was compared…

Multisite research designs involving cluster randomization are becoming increasingly important in educational and behavioral research. Researchers would like to compute effect size indexes based on the standardized mean difference to compare the results of cluster-randomized studies (and corresponding quasi-experiments) with other studies and to…

The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all…

Due to the difficulty in achieving a random assignment, a quasi-experimental or observational study design is frequently used in the behavioral and social sciences. If a nonrandom assignment depends on the covariates, multiple group structural equation modeling, that includes the regression function of the dependent variables on the covariates…

At present, although the percentages of students with disabilities (SDs) and/or students who are English language learners (ELL) excluded from a NAEP administration are reported, no statistical adjustment is made for these excluded students in the calculation of NAEP results. However, the exclusion rates for both SD and ELL students vary…

Six of California's largest urban school districts have joined together in the Partnership for Urban Education Research (PUER), to address the most pressing issues in urban education. The six PUER districts have agreed to work together to increase data availability, enhance internal research capacity, and promote collaboration and information…

The purpose of this study was to examine the reliability, validity, and predictive utility of 3 measures for screening kindergarten students for risk for math difficulty (MD). The screening measures assessed number sense and computational fluency, constructs central to typical early mathematical development. Conceptual and operational outcomes…

Background: Developmental dyscalculia is a heterogeneous disorder with largely dissociable performance profiles. Though our current understanding of the neurofunctional foundations of (adult) numerical cognition has increased considerably during the past two decades, there are still many unanswered questions regarding the developmental pathways of…

This article presents a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials. The purpose of the study was to test the opportunity of extending the conventional curriculum by optional applied problem-solving activities and get initial evidence on the possible…

Learning to question is essential for determining pathways of conservation and development in southwestern Amazonia during a time of rapid global environmental change. Teaching such an approach in graduate science programs in regional universities can be done using play-acting and simulation exercises. Multiple working hypotheses help students…

When serial neurocognitive assessments are performed, 2 main factors are of importance: test-retest reliability and practice effects. With children, however, there is a third, developmental factor, which occurs as a result of maturation. Child tests recognize this factor through the provision of age-corrected scaled scores. Thus, a ready-made…

Children's number sense in kindergarten was used to predict their calculation fluency in second grade (N = 198). Using block entry regression, usual predictors of age, reading, memory, and verbal and spatial cognition were entered in the first block and number sense measures were added in the second block. Number sense measures contributed a…