Much is made of Malcolm Gladwell's "Ten thousand hours," the thoughtful insight that to achieve proficiency, the equivalent of five years of full time work is a necessary condition--if not a sufficient one. The Beatles played clubs in Hambourg for ten thousand hours before appearing on The Ed Sullivan Show; Steve Jobs futzed around with computers for ten thousand hours before moving on to enforce his prodigious ability worldwide.
What isn't mentioned is how many people put in the requisite ten thousand hours and achieve competence but not success. My buddy, Kevin, played guitar for ten thousand hours and didn't make it to a German Coffee House never mind CBS. There is something to be said, certainly, for how beautifully he plays. Here's another question: What else could he have done with his time?
One of my clients tells his children that each decision closes doors: "If you drop math, there are a number of jobs that you can't have," he cautions. "A career in actuarial science is not an option if you don't take advanced math courses." Point taken.
But kids who drop math are frequently those who CAN'T go on to a more advanced course, not those who REF-- USE to keep plugging along with the curriculum. If Percival has the ABILITY to take second semester calculus, then by all means, I encourage Percy to learn the integral of one over x. But if he's destined to suffer unnecessarily before getting a miserable D in Calc II, let's allow him to study that at which he might excel.
Don't misunderstand: I'm pleased to be fluent in trigonometry. There's not much I enjoy more than showing a promising student an identity or solving a novel problem. But I wonder what else might have been written on the hard drive of my brain. COULD I have learned to speak fluent Russian in the time I invested studying sines and angles? Could my neurons have been put to different use?
Look back over your choices, those of my gentle readers who are old enough to remember where the two roads diverged in the yellow wood of your past. What might you have done had you felt all the paths were yours to explore?
Choosing to run 50 miles in Nashville a few weeks ago was 11 hours and 13 minutes spent away from other pleasures--playing guitar, for example, or working on my archery. (Not that Eric Clapton has anything to worry about, mind you. And no, I don't actually know a bow and arrow from a bow-tie.)
When we force--or attempt to force--our children to try to excel in those areas in which they have little aptitude or affection, we not only suggest that they bang their heads against the wall but we also forbid them the opportunity to learn those disciplines that they might enjoy and in which they might excel.
Obviously we want our kids to have functional abilities in reading, writing, and arithmetic. But beyond a certain level, don't you sometimes feel that the advanced courses are too--for want of a better word--"advanced?"
After all, most people are able to muddle through life without knowing a whole heckuva lot about logarithms. I don't remember Ed Sullivan asking John Lennon to solve any equations. Or as a brilliant student is alleged to have cheerfully written on an exam that asked her to "find x" in a drawing of a triangle, "There it is!"
As Gilbert and Sullivan's Modern Major General put it:
I'm very well acquainted, too, with matters mathematical,
I understand equations both the simple and quadratical
About the binomial theorem I am teaming with a lot o' news
With many cheerful facts about the square of the hypotenuse.
The joke in the "Pirates of Penzance" is that the MMG might do well to have some military knowledge as well.
All learning is worthwhile--math, language, poetry, history, medicine, mechanics, athletics, survival, geography, music--and at least a cursory knowledge of each is worthwhile. Competence can not be exaggerated. But with such a limited number of ten thousand hours to invest as we strut and fret our hour upon the stage, we have to think carefully about our choices. Because as wonderful as it is to know all there is to know about trigonometry, there's something to be said for being able to speak Russian, rebuild an engine, hit a fastball, and being...
"very good at integral and differential calculus;
[and knowing] the scientific names of beings animalculous:"