In the context of introductory courses in physical geography and meteorology, it is common around February 2 for curiosity to arise among students regarding the veracity of "Groundhog Day" predictions. Historically, most instructors' immediate response to such inquiries has been a definitive "NO," emphasizing the impossibility…

In the last years special "ovals" appear increasingly often in diagrams and applets for discussing crucial items of statistical inference (when dealing with confidence intervals for an unknown probability p; approximation of the binomial distribution by the normal distribution; especially in German literature, see e.g. [Meyer,…

As an excellent means of improving students' effective learning, knowledge tracking can assess the level of knowledge mastery and discover latent learning patterns based on students' historical learning evaluation of related questions. The advantage of knowledge tracking is that it can better organize and adjust students' learning plans, provide…

Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate…

In any meta-analysis, it is critically important to report the dispersion in effects as well as the mean effect. If an intervention has a moderate clinical impact "on average" we also need to know if the impact is moderate for all relevant populations, or if it varies from trivial in some to major in others. Or indeed, if the…

On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

Since 2018, institutions of higher education have been aware of the "enrollment cliff" which refers to expected declines in future enrollment. This paper attempts to describe how prepared institutions in Ohio are for this future by looking at trends leading up to the anticipated decline. Using IPEDS data from 2012-2022, we analyze trends…

Massive open online courses (MOOCs) have become one of the most popular ways of learning in recent years due to their flexibility and convenience. However, high dropout rate has become a prominent problem that hinders the further development of MOOCs. Therefore, the prediction of student dropouts is the key to further enhance the MOOCs platform.…

Most existing solutions to the current replication crisis in science address only the factors stemming from specific poor research practices. We introduce a novel mechanism that leverages the experts' predictive abilities to analyze the root causes of replication failures. It is backed by the principle that the most accurate predictor is the most…

Currently, dynamic structural equation modeling (DSEM) and residual DSEM (RDSEM) are commonly used in testing intensive longitudinal data (ILD). Researchers are interested in ILD mediation models, but their analyses are challenging. The present paper mathematically derived, empirically compared, and step-by-step demonstrated three types (i.e.,…

This report provides advice to policymakers and school leaders on the use of assessment centres as part of a teacher selection approach. It discusses the relationship between assessment centre scores prior to joining teaching, and teacher effectiveness over a six-year period. It draws from various stages of a wider research project, the overall…

Research in early childhood settings requires careful consideration of the impact on all children in the setting, whether participants or non-participants, and evolving ethical approaches in response to children's needs. However, flexible approaches and, 'in the moment', ethical adaptations are not routinely reported as part of early childhood…

Some patients benefit from a treatment while others may do so less or do not benefit at all. We have previously developed a two-stage network meta-regression prediction model that synthesized randomized trials and evaluates how treatment effects vary across patient characteristics. In this article, we extended this model to combine different…

To prevent students from learning risks and improve teachers' teaching quality, it is of great significance to provide accurate early warning of learning performance to students by analyzing their interactions through an e-learning system. In existing research, the correlations between learning risks and students' changing cognitive abilities or…

There have been substantial advances in the development of states' education data systems over the past 20 years, supported by large investments from the federal government. However, the availability of modern data systems has not translated into meaningful improvements in how consequential state policies, such as funding and accountability…