A lot of the common core math examples I've seen actually mirror how I've always done math in my head.
I think it's good to try to find an approach that explains why the answer is what it is, instead of memorizing the tables and procedures that were emphasized when I was learning it.
I agree, math is taught horribly. When most people who graduate high school think that math is dumb and not applicable to the real world then you have a big teaching problem. When I was in school I always understood the concepts of "higher" math but always screwed up because I messed up the algebra or trig, mostly because I was lazy and those things were taught as something you have to simply memorize. Just googling "trigonometry gif" gives me a better understanding of trig than I ever got in school.
That being said, even though this kid was correct and understood the problems there was some sort of break down between what the student knew and what the teacher wanted. I don't think there can be a standard way of explaining the concepts of math. Different kids pick it up in different ways. Maybe Tavin just thinks vertically, doesn't mean he's wrong.