She [Boden] began by assuring us that creativity is not magic or divine, neither is it a special faculty possessed by an elite, but rather an aspect of general intelligence. Most importantly, an understanding of creativity is not beyond the reach of the scientific process. What, then, is creativity? Her answer: coming up with ideas which are new, surprising, and valuable.
Phil then goes on to list the meanings of those latter three terms in the context of Boden’s ideas on creativity. It’s very interesting stuff and highly useful for teachers, and you should go read the whole thing.
One part of Phil’s post/Boden’s talk that struck me in particular was this bit about what Boden calls “exploratory creativity” and how to encourage it — which is what teachers’ jobs revolve around:
Exploratory creativity can only be encouraged in one way: practice! One must learn the conceptual styles, the rules and conventions of the structured conceptual space in which one works. Boden cited an interesting study in which pieces of music from various stages of the careers of famous composers were selected and played to a panel of expert judges. The composers included some who were child prodigies, composing perhaps, like Mozart, at the age of 4. The panel was not told the composer, only the year of composition, and was asked to rate the piece on how adventurous it was – in Boden’s terminology, on whether it exhibited exploratory creativity or transformational. In every single case, even for the child prodigies, it was found that their early work was exploratory, and transformational work only came after a period of around 12 years of deep and devoted immersion in musical culture and history. Practice, practice.
Yes! Everybody wants students to experience exploratory creativity. Entire curricula are being built around the idea. But so often, these new curricula — and the education “reformers” who promote them — emphasize creativity instead of mastery, as though one were the wave of the future and the other an artifact of an outdated 19th-century educational model. But really, you cannot have meaningful creativity without a mastery of the basics, without “paying your dues”. It doesn’t work that way in music, or sports, or creative writing — but somehow mathematics curricula expect to simply upgrade the notion of mastery to the notion of creativity.
You’ll get a sort of creativity that way: the sort that you see in the random crayon drawings of a 2-year old. That’s fine for a 2-year old — I’ve got about half a dozen such drawings on my office wall, and I treasure each one — but I don’t think that’s the kind of disciplined creative work we want math students to be doing.