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

Mathematics and statistics
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How much room for movement is there in our teaching?
In this response, we may well rely on the standard approach to teaching mathematics,
recognising the robustness of mathematical knowledge in contrast to bodies of knowledge
that are seemingly more relative. Put most starkly, young colleagues embarking upon a
university career feel that they are obliged to embrace an ideology of learning that is
completely foreign to the core values of the discipline. For example, faced with the
assertion that Hamlet is a lousy play, it may be reasonable and effective to adopt a strategy
which respects this as a valid personal view that should be respected and debated
alongside other views – all deserving of equal respect. Consider, on the other hand, a new
lecturer faced with the claim that the recurring decimal 0.99999 . . . is less than 1. One
may sympathise with a student who might think this is true and adopt an understanding
approach, but no one can, in all honesty, pretend that it has equal validity with the view
that 0.99999 . . . is equal to 1.
Of course things need not be as extreme as may be implied here. All of us in the
knowledge economy should treat students with sympathy and respect, whatever our
subject. But at the same time, those charged with ‘training’ our new young colleagues
must be aware that there is, within mathematics, restricted room for movement when
attempting to allow students ‘ownership’ of the subject. Perhaps it is for reasons such
as this that there has been the emergence of an interest in ‘discipline-based’ staff
development, whether this is for new or experienced colleagues (see e.g. Durkin and
Main, 2002).
But we will find that alternative approaches are still of value, and these may equally
well be rooted in our understanding of mathematics and its applications. We can, for
instance, also conceive of mathematics as a human activity, involving creativity and
imagination, rather than simply seeing it as an abstracted system of thought. Teaching
then takes its place as helping students to enter into this world of mathematical activity
– rather than simply as an opportunity to present to students the finished products
of our rigour. The challenge is to help students enter into the process of doing
mathematics or applying it to the real world. Before looking at teaching and learning
through specialist perspectives, it will thus help to give further consideration to the
changing student body; and to the challenges students face in making the transition to
higher education.
THE TRANSITION TO HIGHER EDUCATION
The transition from one educational stage to another can often be a fraught and uncertain
process. In mathematics there has been ongoing publicity over many years about the
issues around the transition to higher education. Notable among these are the Smith
Report, Making Mathematics Count (Department for Education and Skills, 2004), and the
earlier reports from the London Mathematical Society (1992) and the Engineering Council