I come from my own point of view that I have difficulty learning something when it is not likely that I will apply it. I learned basic calculus while learning physics, and it was immediately apparent why calculus was required. Without calculus, the problem domain available in physics is almost so trivial that it feels worthless to study.
Basic trig does have other interesting applications, such as computer graphics and what not, that could probably all be integrated into an interesting high school course. So much of a trig class is about memorizing identities, though, and it's hard to see why you might want to do that unless you had something else to do, like integrals. We end up re-learning trig in Calc 2.
I have heard arguments that setting calculus as a "goal" of math education leaves out the stuff of math that is actually "cool" and makes math seem boring. But calculus is interesting (at least) when you use its applications.
Mathematica can, indeed, solve a lot of problems, but is something lost when students never gain the ability to symbolically solve math problems? I suppose there is a wide space for research in this area, and I haven't heard of much being done.
Basic trig does have other interesting applications, such as computer graphics and what not, that could probably all be integrated into an interesting high school course. So much of a trig class is about memorizing identities, though, and it's hard to see why you might want to do that unless you had something else to do, like integrals. We end up re-learning trig in Calc 2.
I have heard arguments that setting calculus as a "goal" of math education leaves out the stuff of math that is actually "cool" and makes math seem boring. But calculus is interesting (at least) when you use its applications.
Mathematica can, indeed, solve a lot of problems, but is something lost when students never gain the ability to symbolically solve math problems? I suppose there is a wide space for research in this area, and I haven't heard of much being done.