LeftoverPi

The short version is this--they take out basically everything that a musician loves about music, and the curriculum consists of a bunch of pointless exercises that would accomplish nothing except making practically every kid who was forced through it hate "music". Not that they would have any idea of what music is--all he has the kids doing in his hypothetical school is transposing sheet music from one key to another, by rote. Never getting to experience the beauty of music--only the most drudgerous parts of it.

Even if you don't read any of the rest of it, I highly recommend the first two pages.

I have used the "music analogy" several times myself, in conversations. The way I usually do it is I say "Suppose that, all their lives, people were forced to take 'music classes', and in those classes the only thing they ever did was practice scales and chords." They never hear music--never get to experience the nearly infinite variety in jazz, country, hip hop, classical, rock, etc. Those kids would grow up thinking they hated music, when what had actually happened was that they never really got to see what music was really about except for a very narrow technical piece of it.

(Note--I'm not trying to say that I'm the first person who came up with that analogy. I doubt that Lockhart is either. I think Keith Devlin, in one of his books (maybe the Math Gene?), said something about trying to get our society to appreciate mathematics is like trying to get people who have no ears to appreciate music. The mathematicians see the beauty in mathematics, but they have no way to "play" it for everyone else. (Even though the most accomplished composer may appreciate his own music at a much deeper level for completely different reasons than I do, I can still listen to the composition and derive great joy from it--Devlin's point is that it's very hard to do the same thing with, say, a proof in algebraic topology).)

Lockhart's introduction of the idea of worksheets where the students have to transpose sheet music into another key is, I think, particularly brilliant in that it captures so accurately the relationship between math worksheets/textbook exercises and "real" math.

I did a similar piece for fulcrum.org, where the analogy was based on mountaineering. If you liked the analogies at the beginning of Lockhart's essay, you might like this one as well:

http://fulcrum.org/features/mountain.html

I'll also mention another thing I think I saw on the Math Forum on perhaps on the math-teach listserv. Someone said that it is very unlikely for anyone to be able to accurately claim that "they don't like Chinese food". Their point was that there are so many varieties of Chinese food, it's highly likely that the person would find something they liked if they looked around a bit. But our general exposure (in America, at least) to Chinese food is very limited and we have a completely incorrect idea of what "Chinese food" means. What we eat may very well be Chinese food, but it in no way represents all of what is native to that country. And the same can be said for mathematics. People say that they "don't like math", but in reality they have only been exposed to a tiny slice of the pie [one half of the double entendre of "leftover pi", btw]. It seems very likely that the vast mathematical landscape, if we allowed or encouraged people to explore it, would have something for pretty much anyone.

Back on topic, I think Lockhart has done us all a great service just in these first two pages. As he notes himself, we're up against a huge problem, as we have decades of heavily reinforced and widely believed misconceptions about mathematics to knock down. I think that analogies like this are some of the best tools for taking the first chunks out of the wall.