LikePracticingTheViola

The question of the new-new math decade: how do we resolve the need to develop math fluency in children, without sacrificing their ability to think creatively?

This question presupposes that you believe the two to be in opposition - I don't. Math fluency is developed through practice, of the drill and kill variety; it's harder to say how mathematical creativity is developed (and yes, creativity is of immense value in mathematical research -- we don't just sit around thinking about the Really Big Numbers, as one of my grandmothers thought).

But the two really do coexist -- they have to. Mathematical creativity is hard to express when you have to go back to first principles every time you add fractions. But drilling algorithms can be pretty boring. How does the tedium of drilling algorithms coexist with creativity in solving word problems or engineering problems or Fermat's last theorem?

I think learning math is a lot like practicing the viola, which I could never stand to do.

I personally think the tedium of practicing computations is nothing compared to that of practicing viola, or any other instrument, but that's just me. Still, noone doubts that all violists, even the great ones -- especially the great ones -- have had to put in thousands of hours of practice, and probably noone would argue that they weren't necessary.

And how does the need for practice coexist with creativity and inspiration in playing the viola?

Well, pretty much everyone who practices the viola hard, over a number of years, is going to be a competent violist. The concert violists are going to be some subset of those who practiced their fannies off -- in fact, in terms of hours spent practicing, really inspired instrumentalists beat out their merely awesomely competent competitors. That's how you get to Carnegie Hall, after all, and here's a chart to prove it.

How do we deal with the fact that musical practice is boring for most of us? Well, if we don't like to practice, we don't have to play. We opt out if we don't like the arrangement - as I did long ago, and as Ben did this year (although the instrument he is spurning, after a perfect record of non-practice in fifth grade, is actually the cello).

The problem with math is that nobody can opt out of learning it: we all need to be competent at it. An understanding of quantities and numbers and rates and growth are the basis of a lot of thinking in our society. It would be nice if there were a royal road to mathematical fluency, but there isn't one that we've yet found; it takes years for even the most mathematically able child to pick up all the mathematics they'll need as an adult.

Even a merely competent violist has pushed his knowledge of the mechanics of his instrument down out of his conscious brain and into his fingers. This has to happen before a violist can even dream of being creative, because if it hasn't, then his conscious brain is still working on mechanics.

Here is what I saw in my college algebra and calculus classes: people still struggling with the mechanics of math, years after they ought to have had the basic moves down. They didn't practice long and hard enough, and if they ever had the moves down, they'd lost them by then.

So how do you get your kid to practice? You get him into the habit. You provide carrots in the form of praise, trips to Chuck E Cheese, movies, video game time, whatever turns him on. You also provide a stick if necessary. You do what it takes to ensure that your kid does this thing that he needs to do, even if you have to fight with him (this is what Bernie calls being a brick wall, and what Catherine calls being your kid's frontal lobes). You clear out his schedule, if necessary, to ensure he has the time he needs to practice.

And you try to make sure he is taking a line of study that isn't going to let him down in the end.

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