Partially automated assessment is implemented via the 'Printable worksheet' mode in the Numbas e-assessment system to create a mathematical modelling worksheet which is individualised with random parameters but completed and marked as if it were a non-automated piece of coursework, preserving validity while reducing the risk of academic misconduct…

The purpose of this note is to describe a classroom activity that can be used in introductory Operations Research courses. It consists of modelling a one-dimensional puzzle using mathematical programming to produce glider models. The exercise is designed to motivate the students in solving a problem with the opportunity of producing by themselves…

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…

On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

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 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.bibliotheek.ehb.be/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…

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…

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 complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

This article is about utilizing the process of building and exploiting models as a framework for inquiry in mathematics education research. We introduce and discuss a model of such a process and compare this model with key methodological features of design research in mathematics education. We argue that despite several communalities, educational…

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.…

Synthesis and diffusion of a pigment molecule can be simulated using deterministic equations in computer software. These lesson materials describe how tiger stripes emerge from manipulations in this code, and how students can engage in mathematical inquiry by exploring these reaction-diffusion equations.

In differential equations textbooks, the motion of a simple pendulum for small-amplitude oscillations is analyzed. This is due to the impossibility of expressing, in terms of simple elementary functions, the solutions of the nonlinear differential equation (NLDE) that models the pendulum, which is why the authors usually choose the linearized…