Learning to play the piano is hard – it takes years of practice to get really good, and months of practice just to get to the point where you can even play a non-childish song or two.
Yet millions of people, over the years, have become quite good at the piano, almost without exception using more or less the same approach:
– Take lessons from a piano teacher for half an hour to an hour once a week or so;
– practice from 15 minutes to a half hour a day.
Following that method, you can pretty darn good in a few years. Of course, if you want to get really good, you eventually must ramp up the practice to several hours a day – but even without a grueling practice schedule, you can get pretty good at 30 minutes a day. You just have to be consistent about it for a number of years.
Now, it’s almost a truism that music and math are related talents. I’ve even heard it said that they are the *same* talent. Yet, with rare exceptions, we teach math – I should say, attempt to teach math, since it almost always fails – by lecturing to students as a group for 40 minutes to an hour day after day, year after year, then assigning math homework which, in high school, can run into several hours a night. We do not work one-on-one with a student for a limited time once a week and then give them lots of space to practice on their own, as we do with piano.
Oddly, we do use something much more like piano lessons to teach people in college – at least, the amount of time students get to work on their studies outside the classroom is more like the ratio of piano lessons than like high school. In grad school, it’s gets even less like high school and more like piano.
Once, on a business trip, I sat next to a man who was doing some really hairy wave function type math around some sort of sensor he was consulting on. I asked him how he learned all that math. He told a story of having joined the Navy, having gotten good scores on an aptitude test and getting assigned to work in the radio room. From there, he took whatever classes were available, worked his way through a number of increasingly technical jobs, adding, along the way, to his math chops – until, to my pretty-good-at-math eyes, he was a master.
His closing comment: ‘It’s just like leaning the piano – just do a little work on it every day, and you’ll get good at it.”