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

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Teaching in the disciplines
Case study 1: Mathematical modelling
A typical goal in implementing a modelling element is to stimulate student
motivation in mathematical studies through ‘applying mathematics’ and to
demonstrate the associated problem-solving capabilities. It also offers the chance
to provide a synoptic element that brings together mathematical ideas and
techniques from differing areas of undergraduate studies that students often meet
only within individual modules. This in itself can lead students into a more active
approach to learning mathematics and an appreciation and acquisition of
associated key skills.
The underlying premise in this type of course can be accommodated through
activities loosely grouped as ‘mathematical modelling’. Associated assessments
and feedback designed around project-based work, whether as more extensive
coursework assignments or as substantial reports, can allow students to
demonstrate their understanding and problem-solving abilities and enhance both
mathematical and key skills. Often quoted attributes gained by graduates are the
subject-specific, personal and transferable skills gained through a mathematicsrich
degree.
Increasingly, students are selecting their choice of degree to meet the flexible
demands of a changing workplace, and well-designed MSOR programmes have
the potential to develop a profile of the knowledge, skills, abilities and personal
attributes integrated alongside the more traditional subject-specific education.
A mathematical model is typically defined as a formulation of a real-world
problem phrased in mathematical terms. Application is often embedded in a
typical mathematics course through well-defined mathematical models that can
enhance learning and understanding within individual theory-based modules
through adding reality and interest. A common example is in analysing predator–
prey scenarios as motivation for studying the complex nonlinear nature of
solutions to coupled equations within a course on ordinary-differential equations;
this may also extend to obtaining numerical solutions as the basis of coursework
assignments. Such a model is useful in demonstrating and investigating the
nature of real-world problems by giving quantitative insight, evaluation and
predictive capabilities.
Other embedded applications of mathematical modelling, particularly within
applied mathematics, are based around the formal development of continuum
models such as those found, for instance, in fluid mechanics, electromagnetism,
plasma dynamics or relativity. A marked success in MSOR within recent years has
been the integration of mathematics into other less traditional discipline areas of
application, particularly in research, and this has naturally led to an integration
of such work into the modern mathematics curriculum through the development