Oh, don't get me wrong: I was served very well by today's standard math sequence. I learned fascinating stuff in precalc, and calculus was a revelation and a profound joy. Prof. Benjamin's argument favoring statistics instead was a tough sell for me.
But I'm a theoretical physicist. As much as I hate to say it, structuring the entire standard math curriculum so it works best for kids like me (or even for the top 10% of students) just isn't reasonable. (Ideally, a solid gifted program could fill that gap.) I think that we agree on that.
I'd like to think that there are ways of introducing concepts from physics or statistics that do highlight the underlying structure of the field, even if the students don't yet know all of the math they'd need to work through the details themselves. If I find a perfect way to do it, I'll let you know!
One approach I've seen and thought was interesting is the course schedule offered at the Illinois Math and Science Academy.
Their pre-calculus courses have been somewhat radically reorganized into a curriculum called "mathematical investigations" which orders the topics according to more of a practical progression. So, for example, bits of linear algebra are pulled all the way up into precalc because they're useful in geometry, and will also work better with the science curriculum. Perhaps physics teachers inheriting students who already understand vectors, for example.
Then the calculus curriculum is split into two tracks, one more basic, and a more intensive one for students who anticipate going into fields that require more calculus.
But I'm a theoretical physicist. As much as I hate to say it, structuring the entire standard math curriculum so it works best for kids like me (or even for the top 10% of students) just isn't reasonable. (Ideally, a solid gifted program could fill that gap.) I think that we agree on that.
I'd like to think that there are ways of introducing concepts from physics or statistics that do highlight the underlying structure of the field, even if the students don't yet know all of the math they'd need to work through the details themselves. If I find a perfect way to do it, I'll let you know!