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

Mathematics and statistics
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• demonstrate skill in abstracting the essentials of problems, formulating them
mathematically and obtaining solutions by appropriate methods;
• present arguments and conclusions effectively and accurately;
• demonstrate appropriate transferable skills and the ability to work with relatively
little guidance or support.
The authors of this statement go to some lengths to qualify and set the context for this list.
In particular it is stressed that ‘students should meet this standard in an overall sense, not
necessarily in respect of each and every one of the statements listed’. Clearly there has been
no attempt to set a ‘national curriculum’; rather we are presented with generic descriptions
of the type of skills and qualities we should look to be fostering in our programmes.
We cannot, though, expect to find any ‘official’ answers to how we should teach or
support student learning in mathematics and statistics. Mathematicians and statisticians,
indeed, often find themselves challenging approaches to teaching that are advocated
widely across higher education. Learning outcomes, personal development planning,
reflective practice, key skills, and the ‘value’ of replacing blackboards with whiteboards,
smartboards, overhead projectors, Powerpoint or whatever: we are well known for
contesting such notions.
While we will address this debate in what follows, our underlying aim is to concentrate
on discipline-specific issues facing those engaged in facilitating learning and teaching
in mathematics and statistics at higher education level, drawing upon contributions
that are firmly grounded in the discipline. The chapter considers these issues from the
perspectives of pure mathematics, applied mathematics, statistics and the impact of
technology. It is acknowledged that there has been major growth in service teaching for
disciplines, but this is not dealt with in what follows. Nor do we provide a catalogue of
immediately ‘consumable’ classroom resources. Up-to-date materials of this nature are
available, in abundance, at the website of the Mathematics, Statistics and Operational
Research (MSOR) Network that is part of the Higher Education Academy, located at
www.mathstore.ac.uk.
Instead, this contribution to the book seeks to give examples of good practice from
experienced facilitators in the field and to explain the challenges that are presented by
mathematics and statistics education. However, we also offer avenues for exploration
wherein readers may develop their own pedagogic principles. In this it is important to
be aware of ways in which the nature of our discipline grounds approaches to teaching
and learning, while also taking account of key challenges we face, such as the transition
to university. It is to these issues that we thus first of all turn, before moving on to look at
more specialist areas.
THE NATURE OF MATHEMATICS AND ITS APPLICATIONS
What we might term the standard approach to teaching mathematics and its applications
is one that is relatively conservative. In the UK at least, ‘most teaching comprises formal