Hi Ken,
Apologies about the delay in responding to your earlier posts.
Some significant developments here are talking up all of my time at the
moment.
I'll reply fully as soon as I've some decent amount of free time.
In the meantime, a quick response.
There are ways of teaching mathematics fast. My experience is pretty well
everyone is capable of doing maths at a high level. Most people's maths
development has been temporarily blocked because of missing elements in
their early maths education. The sequential nature of maths learning means
later study became impossible.
Second, the same concepts (in terms of epistemological structure) relating
to all aspects of a field apply across all disciplines. This makes learning
multiple disciplines in short time possible. Maths is helpful to provide a
shorthand code for universalising concepts.
Together these cut the need for multiple amounts of 10,000 hour blocks
Think of the proposal for maths being increasingly of benefit in design as
being like suggesting in the 1950s that industrial art would in the future
be predominately done by computers and hence design schools will have to
teach industrial artists how to use software. Some at the time would be
arguing about removing elements from the curriculum like sizing and
stretching paper, grinding inks and paints, developing complex curves by
rules, and other conventional art skills on which industrial design of that
time depended (and have since mostly disappeared from graphic design
courses). Some would be arguing there would only a few that would be capable
of it. Some would argue that only a few would be needed.
Best regards,
Terry
-----Original Message-----
From: [log in to unmask]
[mailto:[log in to unmask]] On Behalf Of Ken Friedman
Sent: Saturday, 3 May 2014 3:07 PM
To: PHD-DESIGN PHD-DESIGN
Subject: Ten Thousand Hours for Expertise
Dear All,
My questions to Terry on mathematical expertise for designers have had me
thinking further. Two specific issues rank high.
First, where are we to get design students with a sufficient foundation in
mathematics to move from competence to mastery?
This is not a case of finding students who are preparing for careers in
theoretical or applied mathematics, or in fields that require these skills,
for example, physics, engineering, actuarial science, or some branches of
psychology. These people are developing the foundations they need to move
from competence to mastery in mathematics.
Here, we are talking about design students. These people are developing
foundations in the skills they need to move from competence to mastery in
design. It is from this cohort that we would need to find students who are
ALSO developing the foundations they need to move from competence to mastery
in mathematics. If they do not arrive at university with a high level of
competence, they will not achieve the kinds of mathematical fluency that
Terry (2014) describes, a capacity for "mastering abstraction and
meta-abstraction along with predicting dynamic behaviors in
multi-dimensional spaces, going beyond linear four-dimensional understanding
of the world, understanding and using limits and disjoints, moving between
discrete and continuous, combinatorics and design theory (different from
what is known as design theory in the design industry), understanding the
calculus of change and feedback, and moving between set and metrological
mapping of concepts."
Second, assuming that we can find students with foundations for both sets of
skills, how are we to find time within the design curriculum to bring
students to MASTERY in both?
There is an extensive amount of research on the time that human beings
require to move from competence to mastery in any field. Innate talent and
possible genius aside, the rule of thumb is roughly ten thousand hours or
roughly ten years of deliberate, reflective practice.
Anders Ericsson and his colleagues did the key research in the 1990s
(Ericsson, Krampe, and Tesch-Romer 1993; Ericsson, and Chamess 1994;
Ericsson and Lehmann 1996).
Those who wish to read these articles will find them on my Academia page in
the "Teaching Notes" section:
https://swinburne.academia.edu/KenFriedman
These will be available through Saturday, May 10.
For those who wish to read more deeply, Ericsson (1996) edited an excellent
book of research papers on these issues. There have also been several good
popular books on these topics by Geoffrey Colvin (2008), Malcolm Gladwell
(2008), Daniel Coyle (2009), and Matthew Syed (2010).
What we know about human learning suggests that we cannot find enough
talented students to fill out more than one or two entry cohorts a year on a
worldwide basis. The size of these cohorts is likely to be so small that
there would be no need for more than one or two university programs to
accommodate them.
However, there is also the question of financing. Today's educational
framework is complex and available funding has shrunk greatly in recent
years. Given the current context, could even two universities afford to fund
the resources needed for a full dual program in both mathematics and design
as linked sets of skills?
There is also the question of staffing. Teachers in any such program would
themselves need special skills. Even though the teachers might not
themselves have dual skill sets, they would need high levels of
interdisciplinary capacity to work with students whose projects take them
across disciplinary boundaries that the teachers might not themselves move
across. These teachers would need a great deal of methodological
sensitivity, and a capacity to work comfortably in interdisciplinary teams
with the other teachers.
Given this, I can't imagine more than a handful of elite design schools
based in strong research universities with the capacity to develop and
manage such programs.
Even without the demand for high-level expertise in mathematics, our field
faces significant challenges in developing robust research programs in
design at the graduate level. On a worldwide basis, I estimate that fewer
than fifty design schools offer truly robust research programs.
When it comes to mathematics, we can gauge some of the problems by comparing
this with the one kind of design program that requires genuine working
skills in mathematics: product design engineering. Worldwide, we only half a
dozen programs graduate full-fledged product designers who are also
accredited engineers. These product design engineers have a high level of
working skill in mathematics, but not the level of skill for expressive
mathematics that Terry describes. In my view, the challenges of a program
that would train designers to the level of fluent mathematical mastery that
Terry proposes are nearly insurmountable.
Before returning yet again to this debate, I'd be happy to see anyone
whatsoever give answers to five questions.
(1) Are these skills important for ALL designers? If so, why? If not, why?
(2) If these skills are not important for all designers, for which designers
are these skills important? Why?
(3) Let us assume that this level of mathematical skill is important for
some group of designers, no matter how small. How are we to locate
appropriate cohorts of students who have the background required for mastery
in BOTH design and mathematics? Does anyone have an estimate of the size of
these cohorts on a worldwide basis?
(4) Let us assume that there is at least a cohort large enough for one such
class of designers. Let us assume that one university is willing to make the
required investment in developing such a program. What kinds of curriculum
do we require if we are to educate such students at university? How many
years will this take? What degrees will they earn?
(5) Conversely, let us assume the possibility that cohorts are too small to
make attracting students possible. Or let us assume the possibility that
such a program would be too expensive, even for an elite university. Is it
possible that we might meet the need for mathematically fluent designers by
simply allowing the right people to find there way into both fields?
There are in the world today such persons as Mark Burry, John Gero, Donella
Meadows, or Don Norman who sometimes use fluent expressive mathematics of
the kind Terry describes. This is a contrast with engineering design
mathematics of the everyday kind in use at companies such as BMW, Microsoft,
or nearly any telecom provider. The people who mastered mathematics to this
level acquired these skills in different ways and brought them to the design
field without the benefit of a dedicated program. If such individuals are
rare, is it better to let them self-select than to prepare a costly program
for which there may be too few applicants?
So far, no one has pointed to published working examples of design projects
that require and use the kinds of mathematical fluency for which Terry
argues. Not even Terry seems to do this kind of work. Once again,
peer-reviewed publication is the difference between professional mathematics
at the level of fluent mastery. Saying it could be done or should be done is
speculation. Describing possible projects in imagined worlds is fiction. If
there are no published examples of actual design projects demonstrating this
level of mathematical skill, it is difficult to see why designers should
learn to speak this particular language.
Investing 10,000 hours is a real commitment. There are two sets of costs.
One set of costs involves the investment in time required for expertise.
This also involves the investment in time required to teach and coach
experts. Masters in every field generally require expert coaching to develop
their skills.
But there is a second set of costs. Robert Sternberg's (1996) article,
"Costs of Expertise," addresses this. In essence, it is the cost of skills
and experience foregone by those who master a skill. To put it another way,
there is a possibility that those who master mathematics at a high level of
fluency will not have the time, mental, or emotional capacity to master
design at a high level of fluency. I do not argue that this is the case, but
I do argue that it is possible. In fact, I am willing to propose that a
great many people involved in design and design research now do not invest
the time, or lack the capacity to master design or design research. This
accounts for a great deal of the attrition in our field - and it accounts
for the great number of practitioners whose deficiencies render them
mediocre or even incompetent.
Medical education and medical certification tend to weed out true
incompetence, though mediocrity often gets through. This is also the case in
engineering. There is no similar process in most design fields for most
nations.
Given these problems, I'm really wondering where we are to find truly
skilled designers who also demonstrate true capacity and skill for
"mastering abstraction and meta-abstraction along with predicting dynamic
behaviors in multi-dimensional spaces, going beyond linear four-dimensional
understanding of the world, understanding and using limits and disjoints,
moving between discrete and continuous, combinatorics and design theory
(different from what is known as design theory in the design industry),
understanding the calculus of change and feedback, and moving between set
and metrological mapping of concepts" (Love 2014).
At different points, Birger Sevaldsen, Martin Salisbury, Francois Nsenga,
and I have all asked Terry to address these issues. In each case, there has
been no answer, but rather a period of silence followed by a new round of
assertions on the importance of high-level mathematics to design practice.
In my last post (Friedman 2014), in Martin's (Salisbury 2014), and in
Francois's (Nsenga 2014) opening and subsequent posts, we have raised
questions that have gone unanswered.
If anyone can answer any of these five questions or all of them, I'd be
interested to read the answers.
It could be that no one wishes to address these issues other than Terry. In
that case, let silence reign.
Yours,
Ken
Ken Friedman, PhD, DSc (hc), FDRS | University Distinguished Professor |
Swinburne University of Technology | Melbourne, Australia | University email
[log in to unmask]<mailto:[log in to unmask]> | Private email
[log in to unmask]<mailto:[log in to unmask]> | Mobile +61 404 830
462 | Academia Page http://swinburne.academia.edu/KenFriedman
Guest Professor | College of Design and Innovation | Tongji University |
Shanghai, China ||| Adjunct Professor | School of Creative Arts | James Cook
University | Townsville, Australia
--
References
Colvin, Geoffrey. 2008. Talent is Overrated. What Really Separates
World-Class Performers from Everybody Else. New York: Portfolio.
Coyle, Daniel. 2009. The Talent Code. Greatness Isn't Born. It's Made.
Here's How. New York: Bantam.
Ericsson, K. Anders, Ralf Th. Krampe, and Clemens Tesch-Romer. 1993. "The
Role of Deliberate Practice in the Acquisition of Expert Performance."
Psychological Review, Vol. 100. No. 3, pp. 363-406.
Ericsson, K. Anders, and Neil Chamess. 1994. "Expert Performance. Its
Structure and Acquisition." American Psychologist, Vol. 49, No. 8, pp.
725-747.
Ericsson, K. A., and A. C. Lehmann. 1996. "Expert and Exceptional
Performance. Evidence of Maximal Adaptation to Task Constraints." Annual
Review of Psychology, Vol. 47, pp. 273-305.
Ericsson, Karl Anders, ed. 1996. The Road to Excellence. The Acquisition of
Expert Performance in the Arts and Sciences, Sports, and Games. Hillsdale,
NJ: Lawrence Erlbaum Associates, Inc.
Friedman, Ken. 2014. "Re: Maths, the language for everyone, including (fine)
artists?" PhD-Design List. Monday 28 April, 2014.
Gladwell, Malcom. 2008. Outliers. The Story of Success. New York: Little,
Brown, and Company.
Love, Terence. 2014. "Re: Maths, the language for everyone, including (fine)
artists?" PhD-Design List. Friday 25 April, 2014.
Nsenga, Francois. 2014. "Maths, the language for everyone, including (fine)
artists?" PhD-Design List. Wednesday 23 April, 2014.
Salisbury, Martin. 2014. "Re: Maths, the language for everyone, including
(fine) artists?" PhD-Design List. Monday 28 April, 2014.
Sternberg, Robert J. 1996. "Costs of Expertise." In: The Road to Excellence.
The Acquisition of Expert Performance in the Arts and Sciences, Sports, and
Games. Karl Anders Ericsson, ed. Hillsdale, NJ: Lawrence Erlbaum
Associates, Inc, pp. 347-354.
Syed, Matthew. 2010. Bounce. How Champions are Made. London: Fourth Estate.
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