Absolutely, a lot can be learned from the internet or books, and a lot of things you just have to teach yourself. The problem (at least in my opinion) is that instead of teaching the best/fastest/most reliable ways to do math, the current way is to teach several other, far more complicated, completely backwards ways of doing it. I think that time could be used for teaching something like doing taxes or something else
useful that most kids don't know how to do when they come out of high school.
Very true, math is one of the most useful and important things to learn. The problem is with how it's taught now. Here are a couple pictures I found that should show what I mean a bit better than I can explain it.
I can tell you off the top of my head that 7 x 5 is 35, that's 1st grade stuff, but even if I couldn't there are far better ways to figure that out. No one is ever going to use that method outside the classroom, so why teach it?
Again, who is ever going to use that method outside of the classroom?