Electrophilic aromatic substitution (EAS) represents an important class of reactions taught in the undergraduate organic chemistry curriculum. The EAS reaction of benzene and its substituted derivatives is generally described as proceeding through a carbocation (arenium cation) intermediate, and the regiochemistry of the product is heavily…

Cross-validation is a common statistical procedure applied to problems that are otherwise computationally intractable. It is often employed to assess the effectiveness of prediction procedures. In this report, cross-validation is discussed in terms of "U"-statistics. This approach permits consideration of the statistical properties of…

The COVID-19 crisis has demonstrated the importance of being able to understand complex computational models for everyday life. To make sense of the evolving predictive models of the COVID-19 pandemic, global citizens need to have a firm grasp of both systems thinking (ST) and computational thinking (CT). ST is the ability to understand a problem…

Over the past half century, computational chemistry has evolved from a niche field to a ubiquitous pillar of modern chemical research. Driven by the increased demand for computational chemistry in research settings, the undergraduate curriculum has evolved alongside to ensure that students are well-equipped for modern research. Toward this end,…

A systematic review and meta-analysis is an important step in evidence synthesis. The current paradigm for meta-analyses requires a presentation of the means under a random-effects model; however, a mean with a confidence interval provides an incomplete summary of the underlying heterogeneity in meta-analysis. Prediction intervals show the range…

In the literature related to higher education, the concept of dropout has been approached from several perspectives and, over the years, its definition has been influenced by the use of diversified semantic interpretations. In a general higher education environment dropout can be broadly characterized as the act of a student engaged in a course…

We present a question bank consisting of over 250 multiple-choice and true--false questions covering a broad range of material typically taught in an introductory undergraduate course in numerical analysis or computational science. The questions are ideal for polling students during lectures by means of a student response system that uses…

Much data, both published and anecdotal, have shown that students grasp scientific concepts more easily when they are directly involved in the learning via lab experiments or other hands-on activities. Hands-on or experiential learning also appears to aid in students' ability to retain scientific theory. One way to engage students in a first-year…

Computer science (CS) and computational thinking (a problem-solving process used by computer scientists) teach students design, logical reasoning, and problem solving--skills that are valuable in life and in any career. Computational thinking (CT) concepts such as decomposition teach students how to break down and tackle a large complex problem.…

Intelligent behavior of adaptive educational systems is based on student models. Most research in student modeling focuses on student learning (acquisition of skills). We focus on prior knowledge, which gets much less attention in modeling and yet can be highly varied and have important consequences for the use of educational systems. We describe…

In this paper we have calculated the work of friction force on the arbitrary path. In our method didn't use from energy conservative conceptions any way. The distinction of this procedure is that at least do decrease measurement on the path once. Thus we can forecast the amount of work of friction force without information about speed of…

Like many commodities, the price of gasoline continues to rise, and these price changes are readily observed in gas stations' signage. Moreover, algebraic methods are well suited to model price change and answer the student's question. Over the course of one ninety-minute block or two forty-five-minute classes, students build functions…

Tossing a fair coin 1000 times can have an unexpected result. In the activities presented here, players keep track of the accumulated total for heads and tails after each toss, noting which player is in the lead or whether the players are tied. The winner is the player who was in the lead for the higher number of turns over the course of the game.…

Chess is a game of minds, bodies, and emotions. Most players recognize each of these as essential to playful competition, and all three are embedded in social relations. Thus chess, despite its reputation as a game of the mind, is not only a deeply thoughtful exercise, but also a test of physical endurance and strong emotions in its joys and…

Barth and Paladino (2011) argue that changes in numerical representations are better modeled by a power function whose exponent gradually rises to 1 than as a shift from a logarithmic to a linear representation of numerical magnitude. However, the fit of the power function to number line estimation data may simply stem from fitting noise generated…