Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further.

Bell's theorem is a topic of perennial fascination. Publishers and the general public have a steady appetite for approachable books about its implications. The scholarly literature includes many analogies to Bell's theorem and simple derivations of Bell inequalities, and some of these simplified discussions are the basis of interactive web pages.…

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

The relativistic addition of velocities is usually introduced early in the study of Einstein's special theory of relativity. The equations are simple enough, but randomly chosen velocities lead to unwieldy calculations that can dishearten the student. This paper presents tables of velocity components in two dimensions, composed of five or fewer…

As a core competence in 21st century, computational thinking (CT) is of great significance for undergraduates. However, there are few researches on the CT evaluation about undergraduates, and nor do a theoretical framework. Additionally, it is not clear what factors may affect their CT development. Therefore, according to Marzano's new taxonomy of…

Education has undergone many changes in teaching and learning, intensified by the significant technological developments that have responded to the fourth industrial revolution and other emergent situations. In this context, developing information and communication technologies has become vital in supporting new ways and learning models in the…

An alternative approach for introducing instrumental variables in econometrics courses is presented in this article. The method is based on the ordinary least squares omitted variable bias formula. The intuition for the approach capitalizes on students' understanding and intuition of omitted variables. Thus, if students understand omitted variable…

Ben Zunica describes a lesson in which computational thinking has been successful in assisting students to understand the process of simplifying surds. The strengths and limitations of this approach are discussed. The author concludes that computational thinking can assist in solidifying understanding of a range of mathematical processes for…

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…

Early mathematics plays an important role in introducing foundational concepts for number sense in children. One of the critical areas of learning is the establishment of a linear view of numbers. It is essential to create opportunities for young children to understand that numbers are equally spaced on the number line and that they increase in…

Computers and computer algorithms have contributed to important scientific advances by allowing scientists and engineers to create and use sophisticated models to explain and predict phenomena. Yet, of the eight "Next Generation Science Standards" ("NGSS") science and engineering practices, computational thinking may be the…

The presence of clustered data is common in the sociobehavioral sciences. One approach that specifically deals with clustered data but has seen little use in education is the generalized estimating equations (GEEs) approach. We provide a background on GEEs, discuss why it is appropriate for the analysis of clustered data, and provide worked…

The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into…

It is difficult for an instructor to just make up valid numbers for B[subscript x], B[subscript y], B[subscript z], E[subscript x], E[subscript y], and E[subscript z] in the creation of homework problems and test questions calculating the Poynting vector. In this paper, 25 examples are given of the electric and magnetic fields of electromagnetic…

An elementary method to calculate the area, centroid and volume of rotation of the Koch curve is presented. Classroom extensions are provided to allow students to investigate the method used.