This study investigated the performance of 790 fourth graders from Taiwan for judging the reasonableness of a computational result by using corresponding methods pertaining to whole numbers. A number-sense web-based two-tier diagnostic test was used to assess the number-sense performance of the fourth graders who participated in this study. The…

Identifying mediators in variable chains as part of a causal mediation analysis can shed light on issues of causation, assessment, and intervention. However, coefficients and effect sizes in a causal mediation analysis are nearly always small. This can lead those less familiar with the approach to reject the results of causal mediation analysis.…

Contemporary research has explored educational robotics, but it has not examined the development of computational thinking in the context of programming embodied interactions. Apart from the goal of the robot and how the robot will interact with its environment, another important aspect that should be taken into consideration is whether and how…

Growth mixture models (GMMs) are prevalent for modeling unknown population heterogeneity via distinct latent classes. However, GMMs are riddled with convergence issues, often requiring researchers to atheoretically alter the model with cross-class constraints to obtain convergence. We discuss how within-class random effects in GMMs exacerbate…

"Sensor-free" detectors of student affect that use only student activity data and no physical or physiological sensors are cost-effective and have potential to be applied at large scale in real classrooms. These detectors are trained using student affect labels collected from human observers as they observe students learn within…

There is a quantum computing race among the tech giants Google, IBM, and Microsoft, including to a lesser extent Amazon and China's Alibaba. Governments, particularly America and China, are funding work in the area with the concern that quantum computers may soon crack current encryption methods, giving the country that gets there first a major…

This article provides a detailed description of three factors (specification of the ability distribution, numerical integration, and frame of reference for the item parameter estimates) that might affect the item parameter estimation of the three-parameter logistic model, and compares five item calibration methods, which are combinations of the…

A number of probabilistic experiments are described to estimate e, p and v2, with results from computer simulations being used to investigate convergence. A number of possible classroom exercises and extensions are presented.

Because of the continuing debates about statistics, many researchers may feel confused about how to analyze and interpret data. Current guidelines in psychology advocate the use of effect sizes and confidence intervals (CIs). However, researchers may be unsure about how to extract effect sizes from factorial designs. Contrast analysis is helpful…

This article describes how Charles Lovitt found a classroom activity in a resource book and by peering through a pedagogy lens, enhanced, tweaked, adapted, and extended the idea into a richer, healthier, well balanced classroom lesson. The task described in the article is often presented to students as a flash card for a limited time with the…

This article critically explores the ways by which the Web could become a more learning-oriented medium in the age of, but also in spite of, the newly bred algorithmic cultures. The social dimension of algorithms is reported in literature as being a socio-technological entanglement that has a powerful influence on users' practices and their lived…

Free fall is commonly discussed as an example of the equivalence principle, in the context of a homogeneous gravitational field, which is a reasonable approximation for small test masses falling moderate distances. Newton's law of gravity provides a generalisation to larger distances, and also brings in an inhomogeneity in the gravitational field.…

A vote with two candidates is simple -- the majority is clear. When there are more candidates, the vote is still clear if one receives more votes than all the others put together. Problems can occur if no candidate has that overall majority. Here are illustrated several voting methods that attempt to achieve fairness in a single election without…

To indicate that atomic weights of many elements are not constants of nature, in 2009 and 2011 the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International Union of Pure and Applied Chemistry (IUPAC) replaced single-value standard atomic weight values with atomic weight intervals for 12 elements (hydrogen, lithium, boron,…

Districts across the nation are seeking ways to increase efficiency by maintaining, if not improving, educational outcomes using fewer resources. One measure that is sometimes used as a proxy for school district efficiency is an expenditure-to-performance ratio, for example a ratio of per pupil expenditures to student academic performance. This…