Dear Terry,

Thanks for your reply. I confess my skepticism with respect to the amount of time required 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 2014a).

On this, I wait for your reply. While I agree that most people go wrong on mathematics at some stage where they get blocked, I still question the difference between high-level useful mathematics and the fluent level of mastery your description requires.

I’d like to see some evidence to demonstrate the degree of time in learning, training, and practice required.

To put it in comparison, I know based on experience that I can help students who already speak English at a solid level to write far better than they write when they walk into my classroom. If they are using English as a second language, this assumes, for example, that they are like my former Norwegian, Swedish, and Danish students. They studied English since they were six or seven years old. They watch English-language television programs in English on the national and local television stations, and they watch English-language movies in English at the theatre and on DVD. Many have lived in the United States, Canada, or England for one or two years – often mastering local accents and dialects to the point where they sound more native than I do after 30 years outside my English-speaking birth country.

When those students walk into my classroom, they have their 10,000 hours and then some. Many students who learn to write better English also improve their written Norwegian, Swedish, or Danish. The crucial factor is that these students have put in their 10,000 hours.

I do not see similar improvements in students who start at a lower level of competence in spoken English.

While native English students also improve, relatively few people write well. People must learn the skill of writing well in any language.

For people to write well takes practice. Whether we are talking about students or working scientists and scholars, fluent mastery takes additional years of practice. I, too, write better now than I did in the past. Deliberate practice, continual study, and occasional coaching from editors and reviewers account for my continued improvement over the decades.

It remains the case that few scientists or scholars write well, even in their native language. Many excuses are made for obscure writing, and there is a high tolerance for obscurity. This masks the lack of deliberate practice.

From this I draw an inference that may or may not be correct. Most people cannot master expressive written fluency in their native language. Only those people who spend at least 10,000 hours in speaking, reading, and writing a second language seem to master expressive written fluency. Only those who spend years of deliberate practice in writing their native language write well. If this is the case for a natural spoken language for daily use, I just don’t see how your assertion can be correct that “pretty well everyone is capable of doing maths at a high level” (Love 2014b) by "teaching mathematics fast" (Love 2014b). Where is the evidence for this claim? And what do you mean by "fast"?

What you are saying here runs contrary to the massive empirical research of experts in general psychology, the psychology of learning, science education, sports psychology, and other fields (Ericsson, Krampe, and Tesch-Romer 1993; Ericsson and Chamess 1994; Ericsson and Lehmann 1996; Ericsson 1996). Several expert journalists and one champion sportsman tell the same story (Colvin 2008; Coyle 2009; Gladwell 2008; Syed 2010).

These authors argue that human beings require something like ten years of deliberate practice – roughly ten thousand hours – to move from beginner to master. My experience is similar to theirs.

Therefore, I am skeptical of your assertion that there is some swift road to mathematics to the level of fluent, expressive mastery. We are not talking about workaday mathematics, but EXPRESSIVE FLUENT MASTERY. This is the level you describe as “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 2014a).

If you have a different story to tell, with evidence to support your claims, please tell it. There’s no rush: I’ll read it when you post it.

Those who wish to prepare by reading Ericsson’s work and that of his colleagues will find the three key articles on my Academia page at the top of the “Teaching Notes” section:

https://swinburne.academia.edu/KenFriedman

These will be available through Saturday, May 10.

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.

Gladwell, Malcom. 2008. Outliers. The Story of Success. New York: Little, Brown, and Company.

Love, Terence. 2014a. “Re: Maths, the language for everyone, including (fine) artists?” PhD-Design List. Friday 25 April, 2014.

Love, Terence. 2014b. “Re: Ten Thousand Hours for Expertise.” PhD-Design List. Saturday 3 May, 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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Terry Love wrote:

—snip—

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.

—snip—




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