This paper examines the context for developing computational thinking (CT), computational participation (CP), and spatial reasoning among predominantly Black elementary students in grades 5 and 6, who attended a public school in the urban fringe of a large city in the Eastern United States. A case study is presented as the method to examine two…

The Mathematics, 3D Printing, and Computational Thinking Through Work-Based Learning (MPACT) program relies on teacher professional development, specialized curriculum and materials, and STEM industry mentors to provide grades 4-7 students with project-based experiences implemented across three learning modules. This technical report presents…

The Mathematics, 3D Printing, and Computational Thinking Through Work-Based Learning (MPACT) program combines teacher professional development, specialized curriculum and materials and STEM industry mentors to provide grade 4-7 students with project-based experiences implemented across three learning modules. This technical report presents…

When a multisite randomized trial reveals between-site variation in program impact, methods are needed for further investigating heterogeneous mediation mechanisms across the sites. We conceptualize and identify a joint distribution of site-specific direct and indirect effects under the potential outcomes framework. A method-of-moments procedure…

Journal impact factors are a metric often used to evaluate journals; they are calculated by considering a journal's citation and publication rates during a specified time period. In some cases, impact factors can be misleading because they do not take into account the publication of different types of papers. In the "Journal of Chemical…

The article provides perspectives on p values, null hypothesis testing, and alternative techniques in light of modern robust statistical methods. Null hypothesis testing and "p" values can provide useful information provided they are interpreted in a sound manner, which includes taking into account insights and advances that have…

The variance formula derived for a two-stage sampling design without replacement employs the joint inclusion probabilities in the first-stage selection of clusters. One of the difficulties encountered in data analysis is the lack of information about such joint inclusion probabilities. One way to solve this issue is by applying Hájek's…

Dropping out of university is regularly discussed as a negative indicator. However, research on actual career trajectories of dropouts is virtually non-existent. This study estimates the association between tertiary dropouts and career chances in 15 European countries. Using data from the 2011 Programme for the International Assessment of Adult…

Researchers addressing posttreatment complications in randomized trials often turn to principal stratification to define relevant assumptions and quantities of interest. One approach for the subsequent estimation of causal effects in this framework is to use methods based on the "principal score," the conditional probability of belonging…

The article serves as a guide for researchers in developing evidence of validity using bivariate correlations, specifically construct validity. The authors outline the steps for calculating and interpreting bivariate correlations. Additionally, they provide an illustrative example and discuss the implications.

The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or "magnitudes" may be especially important for building robust…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…

Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this article is the origins and nature of those fundamental mechanisms that promoted the emergence of the…

The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…