"(Side rant: why do they teach trig before calculus in high school? That's completely backwards. Trig is a bunch of arbitrary formulas if you don't have the calculus behind them.)"
I'm fairly convinced the answer is that That Is What The Curriculum Does, and Do Not Question It.
None of the subsequent 9 hours of debate since you posted this convinces me otherwise. It's not possible that there's a better way, and we can marshal all sorts of rationalizations about how this is the best way, and the possibility that it might not be simply can not be conceived. If you think that there might be a better way, you just must not be aware of how what we already have is perfect.
Our math curriculum could be significantly improved in many ways, except that this is the general societal attitude towards it that I see, and it turns out that "Fix the math curriculum" becomes an unsolvable problem when you add the constraint "But don't make any changes to it of any kind, not even to merely reorder a few topics". Feh.
I'm fairly convinced the answer is that That Is What The Curriculum Does, and Do Not Question It.
None of the subsequent 9 hours of debate since you posted this convinces me otherwise. It's not possible that there's a better way, and we can marshal all sorts of rationalizations about how this is the best way, and the possibility that it might not be simply can not be conceived. If you think that there might be a better way, you just must not be aware of how what we already have is perfect.
Our math curriculum could be significantly improved in many ways, except that this is the general societal attitude towards it that I see, and it turns out that "Fix the math curriculum" becomes an unsolvable problem when you add the constraint "But don't make any changes to it of any kind, not even to merely reorder a few topics". Feh.