In his A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form, Paul Lockhart 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. He proceeds to describe just how tedious this curriculum is for all concerned:
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.And then, of course, he famously proceeds to connect this musical nightmare to the way K12 mathematics is supposedly actually taught: all meaningless, mindless drill.
As Alfred North Whitehead writes back in 1911, however, mindlessness is often a virtue:
It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.Furthermore, while no sane piano teacher would ever make "curious black dots and lines" the centerpiece of music instruction, some of the best ones give top priority to mind-and-soul-numbingly tedious muscle exercises. I was reminded of this reading an accomplished pianist's recent New Yorker memoir about his "Life in Piano Lessons." Here's an excerpt (the student/narrator is Jeremy Denk, and the teacher is William Leland):
Learning to play the piano is learning to reason with your muscles. One of the recurring story lines of my first years with Leland was learning how to cross my thumb smoothly under the rest of my hand in scales and arpeggios. He devised a symmetrical, synchronous, soul-destroying exercise for this, in which the right and left thumbs reached under the other fingers, crab-like, for ever more distant notes. Exercises like this are crucial and yet seem intended to quell any natural enthusiasm for music, or possibly even for life. As you deal with thumb-crossings, or fingerings for the F-shart-minor scale, or chromatic scales in double thirds, it is hard to accept that these will eventually allow you to probe eternity in the final movement of Beethoven's last sonata. Imagine that you are scrubbing the group in your bathroom and are told that removing every last particular of mildew will somehow enable you to deliver the Gettysburg Address.Of course, a certain amount of grit and gruel also underlies good writing. The Gettysburg Address doesn't just happen, either.