Should we teach maths like music?

"High School Geometry: the instrument of the devil"

Via Scott Aaronson, I read this glorious rant by mathemetician Paul Lockart about maths teaching in schools. 

Now, I don't agree with most of it, and hope to discuss why in a future post, but it is such a pleasure to read a critique that isn't by a laudator temporis acti who took his O-levels in the 1970s and has been sulking about it ever since. This bit, in particular, is splendid:

"“The area of a triangle is equal to one-half its base times its height.”  Students are asked to 

memorize this formula and then “apply” it over and over in the “exercises.”  Gone is the thrill, 

the joy, even the pain and frustration of the creative act.  There is not even a problem anymore.  

The question has been asked and answered at the same time— there is nothing left for the 

student to do. 

"

Much as Stephen Fry is the stupid person's idea of what a clever person looks like, an exam that require the rote memorization of  endless formulae before plugging in a series of random numbers is what some non-physicists  think a physics paper should looks like.