Euclid-style geometry could probably be compressed or skipped entirely without much loss. It's got some interesting stuff, and it's the only introduction most people will ever have to mathematical proofs, but I think the emphasis on geometry in the curriculum is largely an accident of history. I would be in favor of replacing that with basic statistics.
Although, considering how breathtakingly messed up the bulk of math instruction is, this discussion feels like redecorating the staterooms in the Titanic. Find a typical high school senior and ask them a question about basic geometry, or to solve a system of two simple linear equations, or to figure out the height of a tall building using a measuring tape and some angle measuring device and a calculator. These are all skills they will have learned at one point, and they will probably have completely forgotten. If indeed they ever truly understood any of it.
If there's a way to teach math better, we could probably get big gains there. I don't know how, though.
This guy says that the problem is that high-school math education is structured to prepare people to learn calculus in their freshman year of college. But only a small minority of students ever takes calculus, and an even smaller minority ever uses it. And not many people ever make much use of pre-calc subjects like algebra, trig, or analytic geometry.
Instead, high-school math should be structured to prepare people to learn statistics. Probability and basic statistics, he argues, are not only more generally useful than calculus, they are also more fun.
I have to agree with him. What do the people here think?