[tjr]

The (seemingly intended to sound ridiculous) description of teaching music matches pretty well with what I remember from my occasional K-12 music classes. There was also an element of listening to music, but it wasn't particularly interesting. My first exposure to what I see as a serious study of music was in college.

But why single out math in particular? I look back on pretty much all of my K-12 education as fairly trite and superficial, in terms of "doing real work in the subject". My experience with, say, college-level history was much more intense (and seemingly more true to the field of history) than anything in high school. On the other hand, I'm not sure I would be able to do well at "real math" like calculus or graph theory or whatever you wish to deem "real math" if I was struggling with adding numbers and solving equations, and I attribute getting past such struggles to doing bountiful rote exercises...