I assume you also disapprove of zed shaw's "Learn X the Hard Way" books (which, btw, have many adherents and praises), which he explains partly here? https://news.ycombinator.com/item?id=7207283

The irony is that even in painting, there is a fair amount of "rote" or repetition needed before ones "creativity" can be explored.

This may be somewhat tangential/distracting, but I find the whole notion of 'creativity' problematic - many artists also think so (“Amateurs look for inspiration; the rest of us just get up and go to work.” ― Chuck Close).

I tend to think that a certain amount of rote arithmetic is required, and, well, if the student doesn't like it, I'm not sure what to do about that. Reading and spelling are the same way... if you want to be a fluent reader, you need to put the time in.

What I learned in elementary school is OK. (There my objections would center more around the cohort system being terrible, but that's another objection. Also, I have to qualify that because the education system considers screwing with elementary math education one of their primary mandates.) But math education flings itself off the rails when it starts doing symbolic manipulation. (And if anything, every time they screw with it they're flinging themselves off the rails harder and sooner.)