Some parents in Chicago, having heard of us, wrote to ask how they could best get their 8-year-old onto a yet faster track and drive him over higher and higher hurdles. We thought you might be interested in our answer (with their names disguised). Alex has written a great e-mail to them, offering him a place in her Math Circle.
Dear F and S,
Your son sounds wonderful, and it is very important to do the right things for him now. Please read our e-mail carefully, and re-read it, since some of it may not be what you expected to hear.
You want J to grow up loving you, and math, and his friends; having a life full of joy and the pleasures of the mind and the world. You want him to appreciate all the beautiful things in the world the way an artist does, and be someone who will be a benefit to those around him, and who will in turn delight in the achievement of others and of our amazing species. The last thing you want is for him to be driven by doubt and rivalry, living the sad life that athletes often do, never satisfying their own expectations or those of their family.
Mathematics is an art, and like all art, it needs peace of mind, leisure, lack of pressure to let invention and imagination grow. Tests and contests are exactly the wrong setting for doing real math: they foster competition where cooperation is wanted; they take the deep pleasure of mathematics away and replace it by the shallow and short-lived pleasures of winning and then having to compete again: the surest way to neurosis, ill heath and dissatisfaction with oneself, one’s family and the world. This road to ruin you see being followed by so many in our high anxiety world.
Let J’s real delight in mathematics grow by having him enjoy, at leisure, with no time pressure or pressure to succeed, real mathematics: not this problem and that (short-winded exercises that reach down to no depth), but exploring geometry, or algebra, or calculus, slowly, with questions and mulling things over, trying different approaches (many of which won’t work - but that’s part of the fun of exploring!). This is why we wrote our book, The Art of the Infinite, which sets the reader out on paths that go deeper and deeper into the heart of things. This is why we began our Math Circles, where people talk together about serious problems in a non-competitive way, as philosophers and artists do, trying to understand, not triumph over, the world and the human mind.
All parents want the best for their children, but often rush them instead headlong into lives of endless dissatisfaction. Let J have the time to fool around, to try this and that, to get things wrong – because this is the way all great mathematicians have begun, focusing not on themselves or petty successes but on mathematics itself, which needs imagination to live with happily. And imagination grows in a life where the cares of the day are seen to be unimportant. Think of the Eight Immortals of the Wine Cup, laughing at the moon.
With our very best wishes,
Bob & Ellen Kaplan
Thursday, January 22, 2009
Leave Those Kids Alone
My friends and mentors Bob and Ellen Kaplan founded a very collaborative, fun version of a Math Circle in Cambridge. It gives young children the opportunity to work as real mathematicians do - on broad, unfamiliar problems in a playful atmosphere. In my work, I have dealt with hundreds of parents, only a few like this. I wish I had responded so eloquently.