I'm not intimately familiar with the standard math curriculum, so I don't want to guess at what could be replaced without losing too much.
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 que...
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?