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…

A straightforward experimental set-up, requiring a two-liter bottle, a ruler and a stopwatch, is used to provide data appropriate for modelling with Torricelli's Law in the simplest case, and a more sophisticated differential equation when losses are taken into account and a pipe extension is considered. With only an exit hole included in the…

Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the…

The emergence of COVID-19 favoured the development at Université de Montréal of an educational initiative aimed at promoting modelling and simulation in teaching and learning postsecondary mathematics. In our learning activities, modelling is not reduced to curve fitting; software is used and questions are asked to get a deeper understanding of…

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 study examined the effects of the concrete-representational-abstract integrated sequence (CRA-I) on teaching place value concepts and their application. The research questions addressed the extent to which CRA-I changed student performance in (a) completing equations that required subtraction with regrouping in the tens place, (b) completing…

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…

In this article, the authors introduce and illustrate a new activity that involves "follow-up equations," which are equations that follow up on ideas children have already expressed when solving fraction story problems. Specifically, teachers pose story problems and purposely attend to fraction ideas that arise in children's strategies…

The Nernst equation is key to understanding the electrophysiology of the cell membrane and the pathophysiology of K[superscript +] imbalances (i.e., hyperkalemia and hypokalemia). However, in our experience teaching medical students over the years, many students struggle to make connections between a brief introduction of the Nernst equation and…

It is well known that Newton's work on mechanics depended in a crucial way on the previous observations of Galileo. The key insight of Galileo was that one can analyze the motion of bodies using experiments and mathematical equations. One experimental observation that roughly emerges from this work in modern terms is that two objects of different…

Bridges are a popular topic in this journal, because they are a very visual display of static and dynamic physical principles. In this paper, we provide an intuitive derivation of the equations associated with suspension bridge cables and load-bearing arches, which is of pedagogical interest in illustrating the consequences of Newton's laws for…

Slamecka and McElree (1983) and Rivera-Lares et al. (2022), like others before them, factorially manipulated the number of learning trials and the retention interval. The results revealed two unsurprising main effects: (a) the more study trials, the higher the initial degree of learning, and (b) the longer the retention interval, the more items…

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.

In diffraction experiments, natural gratings often create uncommon diffraction patterns compared with those resulting from manufactured gratings. This study analyzed a unique diffraction pattern obtained by a grating from a flying termite wing. A ring-like diffraction pattern was formed because of the grating morphology from a flying termite wing,…