I provide a visual proof for the "Convergence of a Hyper power sequence," which generalises a beautiful result; also proved visually by Azarpanah in 2004.

Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

We describe best practices in reporting reliability estimates in counseling research with consideration to precision, generalization, and diverse populations. We provide a historical context to reporting reliability estimates, the limitations of past practices, and new methods to address reliability generalization. We highlight best practices…

In this article, we pursue two points of discussion. First, a new illustration is presented of the person-oriented tenet according to which it can be hazardous to generalize to the individual results that are based on the analysis of aggregated data. Second, it is illustrated that taking into account serial dependence information can result in not…

The purpose of this paper is to propose a revision of the well-known Campbellian system for causal research. The revised system, termed the COPS model, applies to both applied and basic research. Five validities are included, where two validities are adopted from the Campbellian system, and the validities are partly hierarchically ordered.…

In educational research, there is the general trade-off that empirical evidence should be generalizable to be applicable across contexts; at the same time, empirical evidence should be as specific as possible to be localizable in subject-specific educational interventions to successfully transfer the empirical evidence to educational practice.…

Much of the literature exploring Chinese international student engagement with critical thinking in Western universities draws on reductive essentialisations of 'Confucianism' in efforts to explain cross-cultural differences. In this paper I review literature problematising these tendencies. I then shift focus from inferences about how philosophy…

This article presents the consensus of an National Council on Measurement in Education Presidential Task Force on Foundational Competencies in Educational Measurement. Foundational competencies are those that support future development of additional professional and disciplinary competencies. The authors develop a framework for foundational…

This paper walks the reader through a simple mathematical characterization of the popular children's game, "Chutes and Ladders," focusing primarily on Monte Carlo simulation. The focus is then shifted to the board game "No Te Enojes" in order to analyze the implications of the introduction of strategy. The presence of strategy…

Performing newly acquired skills over time (i.e., maintenance) and across settings and stimuli (i.e., generalization) is central to what students need to accomplish in preparation for life beyond the classroom. Students, including those with emotional and behavioral disorders (EBD), need opportunities to practice for the purposes of maintaining…

A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need to also split the prior for…

What is 'African dance'? Is the label 'African dance' representative enough of the diverse dance traditions in African communities, or is it just another form of tokenism? How is the term 'African dance' rooted in the histories of colonial racism against the African people? What are the dangers of using the same label as an attempt at instituting…

Efforts to implement high-quality communication instruction for students with autism spectrum disorder (ASD) and complex communication needs (CCN) may be difficult for some educators with limited time and resources. In this article, we offer guidance on implementing several economic strategies that can be easily embedded into existing classroom…

In mixed methods approaches, statistical models are used to identify "nested" cases for intensive, small-n investigation for a range of purposes, including notably the examination of causal mechanisms. This article shows that under a commonsense interpretation of causal effects, large-n models allow no reliable conclusions about effect…