domains of knowledge, and between the experts in those domains3. (This idea is
discussed more fully in the Nominated Output.)
We have tried to characterise what kind of knowledge is necessary to make sense of a
‘hidden’ calculation through an interface. We do not claim that a visualisation of the
inside workings of a mathematical calculation is always required to make an informed
judgement about it: the judgement can come directly from engineering understanding.
One instance of this is in finite element calculations for structures, where the automatic
element-generation algorithms can easily produce solutions that are spurious. This is an
instance of the ‘reasonableness of output’ knowledge that we referred to above.
On the other hand, even in a multi-disciplinary design team with its own mathematical
specialists, mathematical analysis cannot be a totally black box for any engineer who has
to use a mathematical result and take responsibility for its use:
Engineers have to some sort of intellectual visualisation of what is happening inside the black
box, in order to decide which is the appropriate method [for a problem]. If they didn’t have
that, we could only teach them rules, ‘use this method for that type of thing’. I would be very
scared about that, the engineers have to understand what’s happening inside the black box,
even though they’re not explicitly doing the calculations.
The issue was encapsulated in the words of one engineer who described how, after asking
an analyst to work out some “quite complicated” maths, “once this guy had worked it out
then it was within the range of us to understand what he had done at some level, to be
able to use the results of it.”
Finding 3: The team of design engineers is comprised of many specialisms,
and only a minority of them are mathematics-based. Wherever there is a
division of labour there is a need to communicate information across those
divisions. Each division entails its own 'interface ’: that is, the forms and
language of communication between individuals across that division.
Characterising the embedding of mathematics in expert knowledge
One question that arises is where this understanding of hidden calculation “at some level”
comes from? The scope of this project does not allow a definitive answer. However, we
have indicative data such as the following:
When you’ve done a few of these kind of structures, you begin to understand them. So it’s not
like there is a big equation in my head, but in the past to develop the knowledge and
understanding of how these things work, then there were big equations in my head.
This changing nature of symbols and equations provides a pointer to the role that formal
mathematical knowledge continues to play in shaping the ways engineers think about and
analyse the objects of their practice, even when its ostensible role has diminished, and its
character has transformed.
We observed that experienced structural engineers use an expert repertoire of qualitative
and quantitative ways of thinking about structures.
3 We have had the opportunity to study interactions across mathematical interfaces in several ‘breakdowns’
in the process of design, that is disruptions to the smooth routine of practice which can expose normally
hidden mathematical elements.
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