Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

Akaike's information criterion is suggested as a tool for evaluating fit and dimensionality in metric multidimensional scaling that uses least squares methods of estimation. This criterion combines the least squares loss function with the number of estimated parameters. Numerical examples are presented. The results from analyses of both simulation…

Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup…

The present study presents the formulation of graded response models in the multilevel framework (as nonlinear mixed models) and demonstrates their use in estimating item parameters and investigating the group-level effects for specific covariates using Bayesian estimation. The graded response multilevel model (GRMM) combines the formulation of…

States require a measure of poverty that captures all family resources net of taxes and nondiscretionary expenses and uses thresholds reflecting current needs in the state to assess the well-being of families under current and alternative policies. This paper describes the implementation of a poverty measure for the State of Connecticut based on…

The world is filled with information delivered through graphical representations--everything from voting trends to economic projections to health statistics. Whether comparing incomes of individuals by their level of education, tracking the rise and fall of state populations, or researching home ownership in different geographical areas, basic…

Much evidence suggests that common posterior parietal mechanisms underlie the orientation of attention in physical space and along the "mental number line." For example, the small leftward bias ("pseudoneglect") found in paper-and-pencil line bisection is also found when participants "bisect" number pairs, estimating (without calculating) the…

We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…

We examined developmental and individual differences in 6th and 8th graders' fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross-sectional design. Results indicated that the…

In this study, the researcher sought to determine whether Nebraska teachers and administrators agreed about what constitutes sound grading practice. The results of this study indicated that Nebraska teachers and administrators working in public schools in 7th-12th grade settings did not always agree about what constituted sound grading practice.…

The low number of college graduates with science degrees--particularly among underrepresented minorities--is of growing concern. We examine differences across universities in graduating students in different fields. Using student-level data on the University of California system during a period in which racial preferences were in place, we show…

A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for…

Gaps in achievement test scores continue to exist in students depending upon race, gender, income, and ethnicity according to the Center on Education Policy (CEP), an advocate for public schools. School districts and schools are struggling to close the achievement gap that exists. In the 2010-2011 school years, 34.4% of African American students…

This brief shows how middle and high school teachers in a Time-Technology Swap school model, with or without Multi-Classroom Leaders, may earn more while reaching more students, sustainably. In this model, students alternate between learning with teachers and working in a digital learning lab, where they learn online and engage in offline skill…

In education randomized control trials (RCTs), the misreporting of student outcome data could lead to biased estimates of average treatment effects (ATEs) and their standard errors. This article discusses a statistical model that adjusts for misreported binary outcomes for two-level, school-based RCTs, where it is assumed that misreporting could…