One of the mathematicians most often cited when Reform math advocates critique traditional math is Paul Lockhart’s A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form. His book opens with an allegory about a musician, who awakens from a nightmare in which the “curious black dots and lines” that “must constitute the ‘language of music’” become the center piece of what has become a universally mandated music curriculum:
It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory.In Lockhart’s nightmare, the mission of the primary and secondary schools is:
To train students to use this language-- to jiggle symbols around according to a fixed set of rules: "Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way."As for the higher grades:
The pressure is really on. After all, the students must be prepared for the standardized tests and college admissions exams. Students must take courses in Scales and Modes, Meter, Harmony, and Counterpoint. "It's a lot for them to learn, but later in college when they finally get to hear all this stuff, they'll really appreciate all the work they did in high school."But luckily:
Waking up in a cold sweat, the musician realizes, gratefully, that it was all just a crazy dream. "Of course!" he reassures himself, "No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression. How absurd!"Lockhart stacks the deck just a tad by imagining that no one except the music professionals actually get to hear what music sounds like. Transposed to mathematics, this would be the equivalent of not telling students that the symbol 10 stands for the number of fingers on their two hands, or that the symbol + stands for the process of combining two different quantities into a single quantity. In this respect, Lockhart’s nightmare is completely irrelevant.
But in nearly all other respects Lockhart's nightmare was my reality. During my 12-odd years of piano lessons, I had to:
*practice meaningless drills until I learned how to read those curious black dots and lines to the point of mindless automaticity
*practice meaningless scales to the oppressive tick of the metronome
*practice even more meaningless and repetitive finger exercises to the point of mindless automaticity and a punishing buildup of finger muscles.
Surely true musical artists like Vladimir Horowitz and Misha Dichter weren't forced through such mindless, trivial, time-consuming, soul-crushing tedium. Surely, from the first day they lay finger tips to keyboard, they grasped immediately the beautiful patterns in the lines and dots before them, and, as their souls communed with Scarlatti and Chopin, the music coursed seemlessly out of the tips of their fingers.
Just imagine how many other people might have discovered the joys of piano playing if they, too, had enjoyed the same freedoms as the professionals must!