A latent variable modeling procedure that can be used to evaluate intraclass correlation coefficients in two-level settings with discrete response variables is discussed. The approach is readily applied when the purpose is to furnish confidence intervals at prespecified confidence levels for these coefficients in setups with binary or ordinal…

Applied researchers have employed chi-square tests for more than one hundred years. This paper addresses the question of how one should follow a statistically significant chi-square test result in order to determine the source of that result. Four approaches were evaluated: calculating residuals, comparing cells, ransacking, and partitioning. Data…

The general formulation of a linear combination of population means permits a wide range of research questions to be tested within the context of ANOVA. However, it has been stressed in many research areas that the homogeneous variances assumption is frequently violated. To accommodate the heterogeneity of variance structure, the…

Research Findings: Teachers and parents often use trade books to introduce or reinforce mathematics concepts. To date, an analysis of the early numeracy content of trade books has not been conducted. Consequently, this study evaluated the properties of numbers and counting within trade books. We coded 160 trade books targeted at establishing early…

This two-period undergraduate laboratory experiment involves the synthesis of a mixture of isomeric unknowns, isolation of the mixture by means of distillation, and characterization of the two products primarily by NMR spectroscopy (1D and 2D) supported with IR spectroscopy and GC-MS techniques. Subsequent calculation and examination of the…

Computational tools and methods have permeated multiple science and engineering disciplines, because they enable scientists and engineers to process large amounts of data, represent abstract phenomena, and to model and simulate complex concepts. In order to prepare future engineers with the ability to use computational tools in the context of…

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…

The "Yet Another extended Hu¨ckel Molecular Orbital Package" (YAeHMOP) has been merged with the Avogadro open-source molecular editor and visualizer. It is now possible to perform YAeHMOP calculations directly from the Avogadro graphical user interface for materials that are periodic in one, two, or three dimensions, and to visualize…

Collection and analysis of longitudinal data is an important tool in understanding growth and development over time in a whole range of human endeavors. Ideally, researchers working in the longitudinal framework are able to collect data at more than two points in time, as this will provide them with the potential for a deeper understanding of the…

In many elementary classrooms nationwide, less and less time is spent on social studies. Lack of attention to social studies is evident in states like New York where teacher evaluations are contingent on students' performance on two subjects: English Language Arts (ELA) and mathematics. In this article, the authors describe their experience…

The sudden perception of a connection between ideas is exhilarating. We might call these moments 'Aha!' moments. The purpose of this paper is to demonstrate how several different ideas can come together in Year 12 mathematics. The subject Further Mathematics in the Victorian Certificate of Education (VCE) is the Victorian adaptation of General…

Algebraic reasoning is foundational to all mathematical thinking. This is no less the case in the early years of school, where the capacity to recognise the structure of mathematical processes enables students to acquire deep conceptual understanding. It is through algebra, therefore, that students are able to explore and express mathematical…

Multiple imputation (MI) can be used to address missing data at Level 2 in multilevel research. In this article, we compare joint modeling (JM) and the fully conditional specification (FCS) of MI as well as different strategies for including auxiliary variables at Level 1 using either their manifest or their latent cluster means. We show with…

Researchers are often interested in testing the effectiveness of an intervention on multiple outcomes, for multiple subgroups, at multiple points in time, or across multiple treatment groups. The resulting multiplicity of statistical hypothesis tests can lead to spurious findings of effects. Multiple testing procedures (MTPs) are statistical…

Purpose: This study aimed to create a mobile serious game that incorporates a learning framework, particularly collaborative learning theory, to develop students' computational thinking skills. Methodology: Based on the framework of Brennan and Resnick, an adaptation was made within the context of a mobile serious game mapping the different…