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.,…

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…

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…

The standard model of particle physics is the most successful theory describing the behavior of matter and energy in the subatomic realm. However, success doesn't mean it is perfect, and a recent measurement of the mass of a particle called the W boson is puzzling, as it disagrees with theoretical predictions and earlier precise measurements. If…

The author of this article demonstrates how the unified approach to answering economic questions employed in modern quantitative macroeconomics research can be taught to undergraduate students using the Solow model. Through an application to post-WWII Japan, students get hands-on experience with (1) documenting empirical facts, (2) developing a…

Colleges are increasingly turning to predictive analytics to identify "at-risk" students in order to target additional supports. While recent research demonstrates that the types of prediction models in use are reasonably accurate at identifying students who will eventually succeed or not, there are several other considerations for the…

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…

The article describes a methodology for studying Fresnel diffraction with the active involvement of students in discussing the results of a demonstration experiment. To create a clearly visible model of Fresnel zones, a centimeter radio wave range was chosen, in which the first zone is about 10 cm in size. This makes visible the created…

We propose a cognitive-psychological model of linguistic intuitions about copredication statements. In copredication statements, like "The book is heavy and informative," the nominal denotes two ontologically distinct entities at the same time. This has been considered a problem for standard truth-conditional semantics. In this paper, we…

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…

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…

Planning course study is critical to facilitate strategic intervention in education. As a significant basis of planning course study, student performance prediction aims to utilize students existing relevant information to predict their future learning performance including course grades, course failure, grade point average, etc. We target course…

How might fourth graders address the problem of measuring the size of a leaf? And why might their classroom teachers choose such a shape to measure? One group of fourth-grade students in an urban Australian school were interested in knowing the sizes of leaves on a passionfruit vine growing at their school. The children were excited after a visit…