A Handbook for Teaching and Learning in Higher Education Enhancing academic and Practice

Mathematics and statistics
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of mathematics models. Applied mathematics has always been a strong part of
engineering and physical sciences but now extends to modelling processes in
biology, medicine, economics, financial services and many more.
The difficulty often inherent in practical ‘real-world’ problems requires some
preselection or guidance on initial problems to enable students to gain a threshold
level of expertise. Once some expertise is gained, exposure to a wider range
of difficulties provides students with a greater and more realistic challenge.
In general, modelling is best viewed as an open-ended, iterative exercise. This can
be guided by a framework for developing the skills and expertise required,
together with the general principle ‘solve the simple problems first’, which
requires some reflection on the student’s own mathematical skills and
competencies to identify a ‘simple problem’.
As with most learning and teaching activities, the implementation of modelling
can be at a variety of levels and ideally as an integrated activity through a degree
programme. The learning outcomes that can be associated with an extensive
modelling provision include:
• knowledge and understanding;
• analysis;
• problem-solving;
• creativity/originality;
• communication and presentation;
• evaluation;
• planning and organisation;
• interactive and group skills.
In practice most will only be achieved through a planned programme of activities.
(The Authors)
According to Hibberd (2002), mathematical modelling is the process of:
• translating a real-world problem into a mathematically formulated representation;
• solving this mathematical formulation; and then
• interpreting the mathematical solution in a real-world context.
The principal processes are about how to apply mathematics and how to communicate
the findings. There are, however, many difficulties that can arise. For those with an interest
in exploring the ideas offered in Case study 1, the article by Hibberd (2002) contains
further case studies illustrating the application of these principles; while Townend et al.
(1995) and Haines and Dunthorne (1996) offer further practical materials.