Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area,…

This study investigated the sources of difficulties experienced by prospective teachers in mathematical modelling in the context of a semester-long course on mathematical modelling for teachers. The data reported in this study were collected from six prospective teachers through in-depth semi-structured interviews supported by audio and videotaped…

Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate…

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…

Decomposition of organic matter controls the flow of carbon and nutrients in terrestrial and aquatic ecosystems. Several kinetic laws have been proposed to describe decomposition rates, but they neglect adaptation of the microbial decomposer to environmental conditions. Here we formalise decomposition as an optimal control problem by assuming that…

Using the sawtooth map as the basis of a coupled map lattice enables simple analytic results to be obtained for the global Lyapunov spectra of a number of standard lattice networks. The results presented can be used to enrich a course on chaos or dynamical systems by providing tractable examples of higher dimensional maps and links to a number of…

This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for…

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…

We present a model for roleplaying (RP) for university students that is aimed at fostering the interactions of each learner with the teacher and coursemates, self- and peer-assessment, as well as an awareness and meaningful learning of mathematics. Specific features of our model are its focus on metacognition and individualized learning, based on…

Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…

Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using "change" concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM…

The SIR model is a differential equations based model of the spread of an infectious disease that compartmentalises individuals in a population into one of three states: those who are susceptible to a disease (S), those who are infected and can transmit the disease to others (I), and those who have recovered from the disease and are now immune…

Since the introduction by Kermack and McKendrick in 1927, the Susceptible-Infected-Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious…