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

248 ❘
Teaching in the disciplines
lectures’, more innovative methods are used only ‘occasionally’ and most assessment
strategies rely on formal examinations rather than a wider range of assessment methods
(QAA, 2001). But there remains a significant basis for this standard approach in
considering the nature of the discipline. If we view mathematics as a system of ideas
that is underpinned by logic and applied to modelling the real world, then it makes
sense to offer coherent explanations of this system to students. If, in addition, we
include opportunities for students to work through a set of problems or examples
so that they can themselves own this body of knowledge, then we have the natural
defaults of lectures and tutorials based around the solution of problems. Mathematics
is the science of strict logical deduction and reasoning, a severe taskmaster for both
learner and teacher.
Challenges for the discipline
We also find that mathematics and statistics are often taught in schools as a collection of
rules, procedures, theorems, definitions, formulae or applications that need to be
unthinkingly memorised, and then used to solve problems. Of course, as the level of
complexity increases such an approach becomes difficult to sustain; and universities find
themselves coping with the legacy. If we simply present mathematics, though, as a logical
system of thought, might we not fail to shift ingrained perceptions of mathematics as a
collection of facts to be memorised?
What about the challenges we face in a system of mass higher education? The range
and diversity of those engaged in learning the subject is considerable and is destined to
become wider still in the near future. This will range from foundation-level material,
preparing students for entry to other numerate disciplines, to advanced-level specialist
mathematical study at or near the contemporary frontiers of the subject. And to what
extent does the standard approach to teaching mathematics rely on the students
themselves being able to pick up the essential strategies mathematicians employ in
making sense of a proof or solving a problem? Will they even be motivated to tackle a
problem for themselves?
We have the exploding breadth in the applicability of mathematics. Mathematics is
fundamental not only to much of science and technology but also to almost all situations
that require an analytical model-building approach, whatever the discipline. In recent
decades there has been a huge growth of the use of mathematics in areas outside the
traditional base of science, technology and engineering. How do we help to ensure that
our students will be able to shape this new body of mathematically related knowledge,
as well as be able to make sense of existing knowledge?
Whether it is changing policies affecting school mathematics, the need to recruit more
students to our disciplines or the impact of rapidly developing technology, mathematicians
and statisticians face many new challenges. There are clear signs that the wider
world too is becoming aware of the issues that currently surround the discipline, many
of them international; but we too need to respond as educators.