Eh, I'll try to address all of these, but it's late and I wasn't really anticipating so much opposition (because I forgot about this thread).
May I ask which subjects? (not trying to be an ass or anything, just not aware of what these could be)
Ah I must have misunderstood then, I thought he meant subjects to be taught in high school, not subjects to which higher math could be applied.
(No, you were right the first time.)
Just to name a few that are generally not a requisite in the general curriculum or are heavily underrepresented (in a very disproportionate way): nutrition, parenting psychology, home financing, and software application literacy.
If most math classes (or just a significant enough minority of math classes) were integrated (pun unintended) into other subjects, then where would the math majors take classes? And if there are no math majors, then who would go on to become math professors/mathematicians? Who would teach math to others? Who would discover new mathematical techniques? Who would prove them?
To put it very plainly, the number of people who go into a pure math field aside from the pyramid scheme that is math education today (i.e., we need math teachers to train tomorrow's math teachers!), are insignificant in number. If you wanted to become a mathematician? Simple. You would do that in college as a course of study, much like you do with every other profession. Put it to you this way, how many people go into medical fields compared to becoming mathematicians? Which, realistically, do you think would be of greater benefit to emphasize?
Besides that, if we combine math classes into everything else, then we would never be able to teach enough of the theory behind it. If you are teaching a calculus/physics class, do you choose to teach the Chain Rule and then rigorously prove it, or do you quickly teach the Chain Rule and then explain how it can be used in computing acceleration and velocity? By combining two different, distinct subjects, into one learning environment, you lower the detail you can explain and teach of each.
Not so. You will be teaching more that is relevant to the student and less that isn't. Things that are relevant to the subject would actually get more instructional time. Your problem seems to assume the impossibility of simply having twice as much time for physics classes (to students who intended to go into a related field).
(if you are only bringing in a single concept (like with the statistics in your education class), then it is understandable to simply slip it in rather than create a whole new class to learn one thing, but as far as learning larger things (such as all of vector calc, a separate class is needed).
The former is far more often the case than the latter. I don't know the applications of vector calc, so I could only take your word on it having a very high universal value to several specialized fields. For the sake of argument, assume that an entire semester or year of vector calc can be universally applied to five different fields. Students then need to be made very aware of what those fields are.
Also, I'm going to be inclined to argue that high school should prepare you for higher education, even if you don't plan on attending it. I don't believe we should 'dumb down' curriculum in order to accommodate those with different aspirations.
It is not a dumbing down in the least bit. Specialization is becoming increasingly important in competitive markets. A different curriculum for an individual is not a worse one simply because it has less emphasis on math.
It may also be good to note that while not only would each class suffer from combining in math, but they would suffer as a whole because no class could assume you have the relative maths behind it without a class to teach those specific parts of math you might need, and introduce needless redundancy. I've seen professors who are surprised how little was covered in previous courses (or just the lack of general student knowledge on a subject), this could only be worsened by such changes.
This would actually be less of a problem, because it would ensure that emphasis went to skills related to the career path (so you would get emphasis on more of the necessary skills, and more likely to have the ones you needed for your program). If there are issues, it lies solely in the curriculum management of the school. That's true regardless, really. If there are excessive redundancies or gaps in the curriculum, then your school needs to reevaluate their program.
Just so we're clear, I want my Algebra teacher to teach me how to FOIL even if he can't tell me why I'll ever need it. It turns out I'm an engineer and knowing how to do that has been fairly important over the last 9 years. My teacher, however, shouldn't have to know whether or not I'll be an engineer before he decides whether or not to teach me how to FOIL. He should teach it to me regardless of whether I'm me (an engineer) or Noc (an artist), because he's an algebra teacher.
Most likely your classmates won't feel the same way. Regardless, basic algebra is fundamental enough that I wouldn't suggest removing it from the curriculum. Now, on the other hand, if FOIL were something that only applied to a handful of specialized fields, it would be very inefficient to teach it to the 98% of students not going into any of those fields who could be learning something that they might actually use. I won't address the, "He should do his job because it's his job," point.
Also, Kachi, I think that where you're running into so much resistance is that some people value education regardless of whether or not it is required for your job/career/whatever. It appears that you do not, and if that is the case, I believe that's an irreconcilable difference.
I'm not, nor have I ever suggested that education is only valuable if it enhances a career. But it must enhance something, and the more vital to the person's wellbeing, the better. The fact is, we have a very traditionalist curriculum because we have made no effort to adapt it to the changing dynamic of our nation.
But from the other perspective, that of the educator, it's not a matter of "Would it be cool if people knew this?" Instead it's a matter of resource management, and scrapping things that are less necessary in favor of things that are more necessary that don't get taught. But it's under this logic that schools keep lopping big chunks off of the Art and Music budgets, which is a whole other can of worms. As is the fact that while this budget-slashing is happening, the Football team gets shiny new uniforms and equipment every year.
And it's very unfortunate that those programs are getting scrapped, but that is more of an issue of underfunding than a philosophical perspective. Schools MUST reinforce their performance in subjects like math due to federal regulations that are not supported with additional funding, otherwise NCLB steps in. It's a classic example of demanding more for less. You might be interested to know, by the way, that the current emphasis on math education (when you hear presidential candidates talking about its importance, for example) are based on a couple of things. One is the Reagan administration and its emphasis on these subjects after a study revealed the importance of science (and by association, math) education to the strength of the nation.
The other is a bit more... cyclical (see: silly). Studies consistently find that students depend on math education to be prepared for college! That's why the federal government regulates the college aptitude tests and licenses through accreditation departments (specifically, the Department of Education). This makes sure to test students' mathematical aptitude regardless of what field they want to enter. So, essentially, the federal government finds that students who lack certain math skills aren't prepared for college, because... the federal government has mandated that they know these math skills. So we're clear, that's one of the main reasons why many people aren't accepted into college. They don't score high enough on the tests that are supposed to determine their aptitude for math, and they need to know this math because the government has set this standard because they found that people who don't have these skills aren't prepared for college. To summarize, the reason math skills are so important to college aptitude is mostly due to the fact that the government has unnaturally forced them to be important, rather than having an innate importance in most of the fields.
Now this is all fine if you take the attitude that not everyone can or should go to college, and the world needs burgerflippers and custodians. Obviously that's true to an extent, but it could be a far lesser extent. If the government simply reduces the math requirements, it may magically find that more people who didn't do as well on their college aptitude test are actually more than capable of being successful in college! Now, you may not understand how that could possibly be beneficial, but there are plenty of fields where math skills are only marginally important at best.
...isn't it just something like "don't throw so much money at god damn high school sports"
Oh, and about the football teams, just to fact check-- they often are a source of revenue for the schools. They often (not always) not only pay for their own expenses, but also fund other athletic teams and programs. Concessions and admissions. Go figure.
So you think calc should be taught when it's applied to the subject you're applying it to, right? Well, as an engineer, EVERY SINGLE ONE of my classes uses calc ALL THE TIME. At what point should I learn it? And what if there's a low level class that requires calc, but it's not a required class. Should calc be taught then? Well what about the people who don't take that because it's required? Should I have to learn it again and waste my time because I then take a required class that teaches calc again? What about if I double major in physics and engineering? Why shouldn't there be a class that everyone takes that teaches the math, so that I don't have to be taught the math twice in two entirely different applications?
It sounds like you're talking about college. That's really an entirely different subject. I've been talking about K-12 education this entire time.
But in your example, if you use calculus all the time, then it should be a prerequisite course. In line with my argument, all you're really asking is if I think it should be taught by a general math teacher, or someone who specializes in engineering. My answer would obviously be the latter. Even if there are absolutely no differences between the calculus education you need for a physics program, or an engineering one, it would still be ideal to have someone who can teach the subject within a frame of the applications you'll be using the skills for. As a double major, you could take either Calculus: Physics or Calculus: Engineering and presumably sub one for the other. If they're too different, then yeah, you'd take both. As a double major with some overlapping concepts, you can expect to.
As for taking a class you don't need again, well, that's pretty much college, isn't it? Unless you took a class for college credit in high school, or tested out of the class, there's really no difference there either way. Most people I know have had to take classes that they didn't need. It was a nuisance, but if you already know it, then it's easy. My math classes were easy and taught skills that I didn't need. They did serve the nice purpose of affirming why it was so important that I knew enough math for the ACTs to be prepared for college!