A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory…Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music”. 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. Playing and listening to music…are considered very advanced topics and generally put off till college, and more often graduate school.
As for the primary and secondary schools, their mission 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…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.”
Sadly, our present system of mathematics education is precisely this sort of nightmare.
So begins Paul Lockhart’s scathing critique of how mathematics is taught in this country, A Mathematician’s Lament. The book is an expansion of Lockhart’s essay of the same title. I encourage you to read the essay, buy the book, and share your thoughts in comments.