Abstract:

The work presents a methodology for teaching mathematical modelling skills to students. Mathematical modelling is a skill that needs to be taught in an appropriate context and the choice of context in schools can be problematic. Students need both conceptual understanding in mathematics and experience of real-world situations in the chosen context before they can model given situations confidently. Contexts extracted from the world of industry and commerce are often too far removed from personal experience for students to understand. Simple alternative contexts are required where personal experience can help to promote confidence and provide motivation. A simple mathematical model for how individual vehicles follow each other along a stretch of road is discussed. The ability to predict to response a vehicle in a stream of traffic to the behaviour of its predecessor is important in estimating what effect changes to the driving environment with have on traffic flow. Various models proposed to explain this behaviour have different strengths and weakness. In this paper we discuss a car following model and its results in a second-order or first-order ordinary differential equation. The consequent analysis of the model can be used as an application of techniques taught at first year undergraduate level, and as a motivator to encourage students to think critically about the physical interpretation of the results which the model produces.

Keywords:

Mathematical model, second-order ordinary differential equation, characteristic equation, solution, quick thinking.