Pardon my elitism, but only the absolutely best students need to learn trigonometry or calculus. I'd much rather high schools offer useful classes like personal finance or civics or creative writing than make average, uninterested students take a trig or calc class that they will have absolutely no use for later in life.
High school fails in this purpose when it wastes time teaching trigonometry and calculus to those who have no need for it. The majority of people do not graduate college; of the ones that do graduate college, many will never use trigonometry or calculus in their occupations or personal pursuits.
It makes no more sense to teach every high school student trigonometry and calculus than it makes to teach every high school student how to retread tires or operate a band saw.
If kids are going to spend half of their time for 13 years (!) in school, I sure hope they’re learning all sorts of useful things. Drilling them on geography or historical dates or the content of 19th century “classic” novels, &c., certainly isn’t the only important thing in the world.
"Not every student necessarily needs to learn every thing" is essentially the point I'm making.
Please, by all means, demonstrate a place where a person who doesn't know calculus is at a disadvantage interacting with the technology of the world around us. Until then, I'm calling bullshit.
At SOME point, true. But that point is very, very far off, and very few people ever get there.
It is possible to understand what the normal distribution is, and how to lookup significance values, without worrying about how to calculate it. This is how virtually every non-statistician does it, and is what statisticians themselves do more of the time.
The point where you have to calculate it and prove properties about it does require Calculus.
Unfortunately, calc generally requires trig. It should be taught while teaching calculus.
I'm sorry, but this is not a good idea. What Calculus requires from trig is a solid understanding of what sin, cos, and tan are (else the derivatives of the same won't make sense), and a solid understanding of trig identities for use in integration. Both uses require several layers of abstraction on top of the idea of trig. My experience is that it is a bad idea to layer abstractions on top of material before making sure that that material is solid.
I therefore want people to have a solid understanding of trig before they arrive in a Calculus course.
That said, I think that a lot of the use of trig in integration is a now useless skill, given the widespread availability of programs like Mathematica that can solve all of those problems very quickly and much more accurately. It was once important for people to learn those skills, but now it doesn't seem that useful to me.
You should be able to verify that the integral differentiates correctly. But integrating complicated expressions isn't in my view that critical of a skill.
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.