initially being given relatively routine tasks, and gradually being given more
responsibility for DESIGN.
This finding, which emerged primarily from phase 1, throws light on the first project
objective (see Section 2). It suggests that over time, the mathematical profile of activities
with which an individual engages becomes less explicit (and performed), and more tacit
(and performed by other people) as the focus of the engineer’s work shifts from analysis
to DESIGN.
Finding 1: There is a division of mathematical labour which separates
‘analysis ’ from ‘design ’ in structural design work. As engineers become more
experienced, their work roles shift from analysing (calculating) to designing.
Design and Analysis: Where is the mathematics?
Design involves using the results of analysis, so it is not — in the way most engineers
think about it — a quantitative, mathematical activity at all, beyond the most basic kind
of numerical manipulation. Indeed, when this issue was probed in interview, some
engineers stressed the ‘art’ of design, its qualitative, creative characteristics. The
relationship between the qualitative and quantitative components of practice is a point of
great current concern among professional engineers, not least since the sheer power of
modern computer calculation means that nearly anything can be built, but calculation by
itself does not lead to an understanding of what to build, in terms of quality or efficiency.
In phase 2, we encountered a ubiquitous view from senior engineers that the majority of
structural engineers did not do mathematics of any sophistication in their professional
careers. So, whilst it was important for graduate engineers to have an appreciation for
advanced mathematics, it is something they would rarely be expected to use:
Once you’ve left university you don’t use the maths you learnt there, ‘squared’ or ‘cubed’ is
the most complex thing you do. For the vast majority of the engineers in this firm, an awful lot
of the mathematics they were taught, I won’t say learnt, doesn’t surface again.
However, this statement needs to be elaborated, as we encountered various slants and
degrees of sophistication of mathematical expertise when we probed further into the
engineers’ use and thinking about mathematics. Engineers (in common with other non-
specialist users of mathematics, such as the nurses studied in a previous project), might
not consciously think that some of the concepts that they regularly use are mathematical
in character, because they have become so intimately bound up with engineering practice.
For example, for most structural engineers, it seems that geometry and trigonometry
become embedded in practice, whereas much of calculus is ‘not used’ and is therefore
consciously thought of as being ‘mathematics’. However, this would not be true for those
structural engineers, and engineers in other disciplines, who do use calculus regularly.
The transformation in the character of mathematics appears to be not simply a
quantitative one, nor merely a replacement of mathematical activity by professional
expertise and experience. To further explore this phenomenon of transformation, our
study progressively focused on attempting to characterise what mathematical knowledge
‘remained’ in design work, and how it was embedded within it. A crucial aspect, which
we turn to in the next section, is the ‘remainder’ of mathematical knowledge which
allows design engineers to understand, and make use of, mathematical work that is done
by others.
Finding 2: What is consciously thought of as mathematics by engineers
appears to be only the visible component of a larger body of mathematics in
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