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

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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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