Gravitational lensing is an interesting phenomenon in astronomy and is most typically given rise to by galaxies. The majority of the matter in a galaxy is thought to be dark matter, and the galactic gravitational lensing effect is mainly caused by dark matter halos. In gravitational lensing-related demonstrations in physics education, the feet of…

The purpose of this analysis was to assess whether effects of first-grade mathematics intervention apply across the range of at-risk learners' initial skill levels. Students were randomly assigned to control (n = 213) and two variants of intervention (n = 385) designed to improve arithmetic. Of each 30-minute intervention session (48 over 16…

This study explored the mental constructions displayed by pre-service mathematics teachers (PMTs) when applying Cramer's rule. The aim was to reveal the character of mental constructions made around the nature of the solution set of equations and the role of parameters in the solution of equations with parametric coefficients. These mental…

In experimental evaluations of policy interventions, the so-called Bloom adjustment is commonly used to estimate the impact of the treatment on the treated. It does so by rescaling the estimated impact of the intention to treat--that is, the overall treatment-control group difference in outcomes for the entire experimental sample--by the…

In computer science education at school, computational thinking has been an emerging topic over the last decade. Even though, computational thinking is interpreted and integrated in classrooms in different ways, an identification process about what computational thinking is about has been in progress among computer science school-teachers and…

Many countries include mental calculation within their curriculum, as the literature shows benefits related to it. However, evidence mainly focuses on the effects of teaching mental calculation on computational fluency. Therefore, the authors aimed to assess the effects of teaching mental calculation on double-digit computation, number line…

Although teachers need to assess computational thinking (CT) for computer science education in K-12, it is not easy for them to evaluate students' programs based on the perspective. The purpose of this study was to investigate students' CT skills reflected in their Scratch programs. The context of the study was a middle school coding club where…

In psychological and survey research, the prevalence and serious consequences of careless responses from unmotivated participants are well known. In this study, we propose to iteratively detect careless responders and cleanse the data by removing their responses. The careless responders are detected using person-fit statistics. In two simulation…

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…

Panel or grouped data are often used to allow for unobserved individual heterogeneity in econometric models via fixed effects. In this paper, we discuss identification of a panel data model in which the unobserved heterogeneity both enters additively and interacts with treatment variables. We present identification and estimation methods for…