This article considers starting with an existing SIMIODE modeling scenario [Winkel, B. (2015). 1-031-CoolIt-ModelingScenario. SIMIODE (Version 2.0). "QUBES Educational Resources." https://doi.org/10.25334/3WG8-EC31] that develops Newton's law of cooling by considering data on the cooling of a beaker of water in a room, and expanding upon…

Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in…

It is well-known that the Lotka-Volterra predator-prey model has a family of periodic orbits, but does not possess limit cycles and therefore the model is said to be structurally unstable. The Lotka-Volterra model is a special case of a much larger group namely the quadratic population models and it can be shown that none of them can produce limit…

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of…

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course.

This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual…

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…

In this article, the author reports results in their efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in their model. They have offered the reader two sets of data and several approaches to determine the rate of sublimation of a piece of solid dry ice. They presented several models…

Growing awareness of the importance of modelling activities in mathematics education has raised the question of whether teachers are prepared to facilitate the engagement of students in such activities. The current study investigates the effects of how teachers cope with modelling activities in developing their abilities to identify modelling…

The mathematical language and its tools are complementary to the formalism in chemistry, in particular at an advanced level. It is thus crucial, for its understanding, that students acquire a solid knowledge in Calculus and that they know how to apply it. The frequent occurrence of indeterminate forms in multiple areas, particularly in Physical…

The story is often told of the calculation by G.I. Taylor of the yield of the first ever atomic bomb exploded in New Mexico in 1945. It has indeed become a staple of the classroom whenever dimensional analysis is taught. However, while it is true that Taylor succeeded in calculating this figure at a time when it was still classified, most versions…

In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…

In this article we examine 2 x 2 first-order systems of ordinary differential equations and show how to identify separatrices for phase plane portraits when the system has a saddle point critical value. We describe how to use a computer algebra system to generate trajectories from contour plots, when possible, and determine the equation of the…

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…