This work gathers in one place what is pertinent about the connections between metric coefficients, basis- and unit vectors in a four-dimensional relativistic manifold. Some of this material can be found scattered elsewhere; its collection into one place reveals connections that either are not known or are obscure, for example that the metric…

Most textbooks and lecturers present Michaelis-Menten kinetics using the equation v = V[subscript max][S]/(K[subscript m] + [S]). There are advantages to presenting this relationship in a slightly different form, namely v = V[subscript max]/{1 + (K[subscript m]/[S])}. We articulate advantages for single-substrate reactions and extend the formalism…

Transfer of structural math knowledge to physics is difficult for students. While research suggests various improvement techniques, enhancing parallelism of algebraic structures used in physics to those studied in mathematics courses seems underrepresented. This paper proposes an alternative way of introducing wave functions as a set of parametric…

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…

Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

Calculations are presented showing that the usual 'faster than g' demonstration has a surprising property. That is, a rod hinged at its bottom end rotates at an exponentially increasing rate until it falls with maximum vertical acceleration, unlike an object that falls freely by gravity alone. If the rod is hinged at its top end and released from…

Redox reaction is a core concept in teaching and learning chemistry. This article explores a new method for balancing organic redox reactions that requires the balancing of both atoms and charges. The H+, O, H[subscript 2]O, and e- are used as balanced vehicles in two half reactions. A non-oxidation number approach can be applied to both molecular…

Contribution: Although a limited number of studies have compared textbooks used in introductory science courses (ISCs) and technical engineering courses (TECs), such a study has not been conducted regarding the Laplace transform (LT). The LT is one of the important topics that electrical engineering students learn as part of their undergraduate…

Despite its crucial importance in physics, there are not many studies focusing on student difficulties and teaching strategies related to the (1D) wave equation in the PER literature. In order to contribute to fill this gap, we conducted a study with university students which focused on specific aspects that are crucial for understanding this…

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a…

It is commonly accepted that repeatedly using mental procedures results in a transition to memory retrieval, but the determinant of this process is still unclear. In a 3-week experiment, we compared two different learning situations involving basic additions, one based on counting and the other based on arithmetic fact memorization. Two groups of…

Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…

This article introduces an innovative teaching and learning tool called "Edelman Gamblegrams" that aims to help medical learners better understand disorders related to water/plasma tonicity homeostasis, i.e., hyponatremia and hypernatremia. Gamblegrams, named after physician James L. Gamble, are bar diagrams displaying the relative…

The udu is a traditional Nigerian percussion instrument that can be thought of as a Helmholtz resonator with two apertures. We use a simple two-particle mechanical analogue to study the behaviour of such a resonator and find that the model describes quite well the main features of udu acoustics.