We demonstrate the Stirling formula, approximating the factorial, utilising accessible and elementary methods in an engaging manner.

Missing data are common with large scale assessments (LSAs). A typical approach to handling missing data with LSAs is the use of listwise deletion, despite decades of research showing that approach can be a suboptimal strategy resulting in biased estimates. In order to help researchers account for missing data, we provide a tutorial using R and…

We present a method to compute the power series expansions of e[superscript x] ln (1 + x), sin x, and cos x without relying on mathematical analysis. Using the properties of elementary functions, we determine the coefficients of each series through the method of undetermined coefficients. We have validated our formulae through the use of…

Educational researchers often report effect sizes in standard deviation units (SD), but SD effects are hard to interpret. Effects are easier to interpret in percentile points, but converting SDs to percentile points involves a calculation that is not transparent to educational stakeholders. We show that if the outcome variable is normally…

Binary logistic regression is one of the most widely used statistical tools. The method uses odds, log odds, and odds ratios, which are difficult to understand and interpret. Understanding of logistic regression tends to fall down in one of three ways: (1) Many students and researchers come to believe that an odds ratio translates directly into…

Although there is an extensive methodological literature on the measurement of intergenerational income mobility, there has been limited research on the conceptual interpretation of mobility measures and the methodological implications of those interpretations. In this article, I focus on the three measures of mobility most frequently used in the…

This computational exercise gives students an in-depth look at the reactants, transition state, and product of the crystal violet alkaline hydrolysis reaction. The exercise, which is aimed at second semester general chemistry students, involves DFT energy calculations on five structures: crystal violet cation, crystal violet alcohol, and 4-water…

The Nolan Index (NI) is a normed, quantitative measure for comparing the degree of resemblance (similarity or dissimilarity) between free listings with an Excel program for calculating it. This article enhances that effort with the addition of an R program and additional applications. Free-list resemblance measures have been used to investigate…

Learning environments for programming education need a comprehensive task set that guides students from basic programming concepts to complex challenges. For creating such a task set, it is beneficial to utilize the concept of a design space--a systematic mapping of design dimensions and choices along these dimensions. We propose an iterative…

The advancement of large language model-based generative artificial intelligence (LLM-based GenAI) has sparked significant interest in its potential to address challenges in computational thinking (CT) education. CT, a critical problem-solving approach in the digital age, encompasses elements such as abstraction, iteration, and generalisation.…

Ion transport, involving the diffusion and migration of ions within the electrolyte, stands as a fundamental concept in electrochemistry and serves as the driving force for electrochemical reactions. Electric double layers are critical in the fields of electrochemical energy storage and chemical conversion, constituting a central focus of…

In the realm of K-12 Education, the growing significance of Computational Thinking has sparked extensive inquiry into its nature and instructional methodologies. Despite a wealth of literature on the subject, ongoing debates persist regarding its fundamental components. Across global educational landscapes, Computational Thinking is being…

Computer adaptive testing (CAT) is an increasingly common mode of test administration offering improved test security, better measurement precision, and the potential for shorter testing experiences. This article presents a new item selection algorithm based on a generalized objective function to support multiple types of testing conditions and…

The same and different routine offers an opportunity to build a strong foundation for future grades while also deepening the experiences of prekindergarten and transitional kindergarten students. Students have opportunities to make sense, share ideas, and engage in the ideas of others. We conjecture this type of experience supports students and…

There is a longstanding debate on whether the analysis of covariance (ANCOVA) or the change score approach is more appropriate when analyzing non-experimental longitudinal data. In this article, we use a structural modeling perspective to clarify that the ANCOVA approach is based on the assumption that all relevant covariates are measured (i.e.,…