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Courses Should Calc I be the intro math course in colleges?

  1. Feb 13, 2012 #1
    I've observed that mathematics at college starts with Calculus I. Another observation of mine was that the math content in the majority of high schools is somewhat lacking and as such, jumping straight into a proper college calculus course might be a bad move. I know I'm not speaking for I alone when I say that the treatment of math that I was exposed to in high school was quite meagre, in that a lot of what we learn is just taken on good faith and there is very little in the way of proofs.

    Maybe I find this so annoying because I intend on majoring in math or physics and would be somewhat less frustrated if I didn't have to try find old books all over the internet to assist me in re-learning geometry, trigonometry and algebra before I start university. One of the reasons I'm applying to uni for *next* year instead of this one is because there are many gaps in my knowledge and I won't find peace until I am fully comfortable with all the material.

    Anyway, should the consolidation of these topics in mathematics be the responsibility of the high school, college or should in fact, be that of the student's? Discuss.
     
  2. jcsd
  3. Feb 13, 2012 #2
    Most universities have precalculus as an option. You could take that.
     
  4. Feb 13, 2012 #3
    A lot of schools around my area give college credit for algebra and pre-calculus, and they offer non-credit remedial math courses down through pre-algebra to get people up to speed. Taking one of these courses as well as some gen eds might be a feasible option as well.

    I don't think you need to be very familiar with formal mathematical proofs to do well in calculus; you just need to be willing to spend a decent amount of time studying the concepts. Being good with basic algebra and trig is also a big plus.
     
  5. Feb 13, 2012 #4
    My goodness, cry me a river. I went to one of the worst high school districts in the country. Most of what I remember from high school was fights, drug deals, and gangs none of which I was involved in. Any math or physics I learned in high school was from a couple books my Mom bought me from the local flea market for Christmas.

    When I got accepted to college some were conditional offers where they required me to have completed Calculus 1 before starting in the fall. Most of the kids that I went to school with had completed vector calculus before starting college! Needless to say, I was incredibly far behind of my fellow students. I had to self study my butt off to get through my first semester of college. I never complained that my high school didn't prepare me, blah blah.. If you feel unprepared then why waste time posting sob stories on an internet forum? Get a book and start working, the clock is ticking.
     
  6. Feb 13, 2012 #5
    You went to one of the worst schools in the country and most of the students finished vector calc before college? That's gnarly.
     
  7. Feb 13, 2012 #6
    I'm guessing they were talking about the students in their college. If not I could get down with that. Snort some blow then get jiggy with some vector calculus. Hell yeah!
     
  8. Feb 13, 2012 #7

    eumyang

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    @Jorriss: It sounds like that SophusLies meant that most of the kids that he/she went to college with were way ahead of him/her when he/she started college. It also sounds like that you're thinking that most students in SophusLies' high school finished vector calculus before college, which is not how I read his/her post.
     
  9. Feb 13, 2012 #8
    Most universities expect more of a mathematical background from students then what the students actually learn in high school. Our school even had a lecture in the first weeks of the first term which main point was to tell us that we probably were badly prepared in terms of mathematical background.

    At our programme (Engineering) we we're offered a introduction course in mathematics. A very simple pass/fail course that perhaps corresponds to pre-precalculus. Everyone who took it passed. Then we all took a compulsory precalculus course and few failed it. Though from what I've heard, most people who failed the compulsory precalculus course had a very hard time even passing the calculus I course and these are students with high grades from high schools all over the country. The number of students that failed calculus I in our class doesn't differ from the number of students that failed calculus I in programmes that didn't have a compulsory precalculus course i.e. having a compulsory (or elective) precalculus course does not ensure a lower amount of students failing calculus I.

    Even though I feel that these two introduction precalculus courses (one compulsory) were beneficial for me, I would have managed without them. If the universities doesn't offer precalculus courses then it's up to the student(s) applying to be aware of that matter and what mathematical background that is suitable for the programme/education in question. It is the student, him- or herself, that is ultimately responsible for his or hers education. Simple as that.
     
  10. Feb 13, 2012 #9
    Taking another pre-calc course from the high school wouldn't be a good idea, seeing as it would be the same material that's going to be covered again.

    High school math frustrates me to end. I don't understand why we are taught calculus, differential equations, vectors and complex numbers when we haven't even gone through natural numbers, integers, real numbers and complex numbers and why there was need to expand the set of numbers. I don't get why we do more advanced material when the prerequisites have not even been covered properly. Another example is the use of partial fractions - no proofs, all that one is expected to do is look at the equation and from there, express it into the required "form" and move from there.

    I can bet that even the better math students in my former high school (and it was among the more selective at the time) couldn't do the easier Olympiad math problems. A few of my friends and I are within that category and none of us can't solve any of those.

    The way I see it, if math is to be done, it has to be done properly. I'd rather not do calculus *at all* if it meant that I'd be doing geometry, trigonometry and algebra properly.
     
  11. Feb 13, 2012 #10

    chiro

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    Its important to put the specific areas and focus into perspective with regard to who is being taught and what they will use it for.

    For most purposes, engineers will not care about the construction of numbers of any sort. They will be more interested in understanding how to go from real world problem to the code in the computer that gives them the results they need.

    The applied mathematicians are a little different in that they will have training that has a 'mathematical focus' where its not rare for someone to have analysis and topology but again the focus is very different.

    Then you have the pure guys that really really do all the work for the other guys making sure that what the engineers, scientists and more applied guys/gals do is actually right. They will focus on things like the construction of numbers, the reliability of calculus amongst other things with the focus more on proofs than applications.

    Also the other thing with high school is that it is largely a disorganized collection of a lot of ideas (which have seen going on practicum and reading syllabi) but at the same time its important to see how high school education is structured.

    It is not structured in any way for self-directed learning and because of the distribution of kids, the school will in many cases have to cater for everyone by teaching for the 'average' student and sometimes for the 'below average' student. This varies from school to school but I think you will find that the private and selective schools give greater opportunities for students over say public schools and a lot of teachers no doubt get frustrated by the environment they have found themselves in.

    Also the way the high-school system is taught, it is not really done to teach a very specific skillset: it is more a generalist learning environment. This frustrated me to no end when I was in high school and I thought it was an absolute waste of time, but again you have to understand that education is one of those things where everyone has a different opinion on it and even though everyone might be right in a small way, someone will have to lose out at the very end.

    I think you should take great solace that any decent university out there will make sure that you know what you are doing and that you really understand what you are doing as opposed to "here is this equation for this problem: remember it".
     
  12. Feb 13, 2012 #11
    As was my school. It was the best I could have gone to, in terms of the students they accept and also the worse because everybody - including myself - were a bunch of wild animals. Things were probably not as bad as in "the worst school district in America". Nevertheless, things were still "bad". Fights, drug deals and gangs. They were all there. ;)

    Then clearly *something* is very wrong.

    College *should* be a logical progression from high school. Therefore, it's not up to the student to sort out his deficiencies on his own.

    I'm not complaining for no reason. I see something that's very wrong and I'd like to see what I can do to fix this before things get any worse. Unfortunately, it looks like things are just getting progressively worse, for a variety of reasons.

    Here, it's the idiots who were in the ministry of education. There's a whole different system here that everybody got very much used to and I don't see the situation improving at all unless somebody with some kind of authority gets off his behind and says "This is bad. This system produces mindless buffoons who cannot think for themselves. Do you want to be stupid? Do you want your grand children to be stupid? This has to change!" and the paradox here is, it's to the advantage of "the man" if everybody is stupid and listens to what he says.

    The number of my peers who can have a discussion of their own, without using the "notes" of a teacher to argue their point, is insanely low. It's all too easy to just swallow what you're told, do the way you're told and go home happy with a few As.

    I don't know what's not going on right in the US but from the little I can see, it's not all that good either. It's probably better than here anyway.

    Either that or I'm just another angry teen with too much Rage Against the Machine...
     
  13. Feb 13, 2012 #12
    Probably.

    High schools are divided in a(n informal) tier system and the tier 1 schools select based on grades alone. Tier 2 are slightly less stringent and tier 3 just take in anyone who's applying. Ultimately, they all do the same thing: prepare the students for some standardised exam, which is all well and good (getting the best grades one can get), except that it does not educate.

    If science does not work out for me, one of the things I want to do is set up a not-for-profit school that is solely for students who are *not average*, i.e, everybody who is below average or above average, in any way. I have a big plan and it's probably flawed on many levels because I got carried away as I wrote it out but it involves students being given the facilities to do whatever they want and can do well in, whether that is sculpture and woodwork or math and philosophy. Everybody will also have to go through a core curriculum to graduate but I haven't looked too much into that and will try figure something out when I go to college. One of the things I'm doing now, is helping out to a somewhat less ambitious end, on a much smaller scale. Basically, after school for a few students and trying new things with teaching and learning.

    I can appreciate that *but* if 50 years ago, doing all the math that I'm talking about was the norm, why are things different now? My dad went to high school in the 60s and while he did the same rubbish British curriculum that I did, what he describes to me sounds much better than I went through. He told me that he had a separate exam for Geometry, Arithmetic and Algebra.

    In the last paragraph, you sounded a little like my stats teacher. :D

    Getting there's harder than I thought it would be. Mostly because of some personality traits and me still figuring out how to effectively learn...
     
  14. Feb 13, 2012 #13

    chiro

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    I have a few thoughts on this.

    The first thought is to realize that if you ever do go into some venture whether its not-for-profit or for profit, try and specialize in some way. You can't be all things to everyone even if your someone like Apple: make your goals as simple as you can without sacrificing your vision and if you think its too broad, then go back to the drawing board.

    My second thought is talk to as many people that you want to help. We probably have an over-representation of high level ambitious students here on PF, but I get the feeling that we have a very under-represented below-average kind of person on PF: I'm not taking a cheap shot at anyone but I have noticed that a lot of the people here are often at the high end of the curve and it is nice to see people that want to change their lives on here who get the kind of honest and reliable feedback that they need to make a change.

    So yeah speak to the kinds of people that you want to help: they will give you the kind of insight that I think you seek for this particular kind of venture. Also speak with other people that are closely involved like the teachers: they may not provide the answers that you want to hear, but if you suspend your disbelief for a little while I think you will find that you get some pretty good advice from them if they are honest and not completely biased and narrow in their thinking.

    That is a really good question.

    It used to be that if you went to university then that was really something: it meant that you were very bright and very hardworking. Also getting first class honors was considered quite a feat and something that was looked at in the most admirable circumstances.

    Nowadays everyone is going to university and in many places the standards have dropped (I didn't say all places!). Also the amount of people getting 4.0's is increasing dramatically and in some places the standards are dropping immensely.

    But I don't want to paint everything with one brush because there are of course, places out there that exhibit extremely high standards and really do demand that their students are very bright and very motivated.

    One thing that you should realize is that having a world full of smart, critical and educated people is not a good thing for a power controlling hierarchy: these people want you to do the job but not think too hard as to become independent enough so that you can really take more control of your life. The indoctrination of school is a great way to handle this "problem".

    Remember that to really appreciate heaven, you need to experience hell first.
     
  15. Feb 15, 2012 #14
    Thank you. :-)


    In my opinion, that's a problem. I think many of the things that I find wrong with uni would be fixed if university was not seen as a logical route after high school. Many graduate jobs could be done by high school graduates or perhaps by high school grads with some professional training afterwards. That's how it used to be. Why the change? Were universities always more concerned with $$$? Why and when did this happen?

    Who gets to decide if that is a "problem"? Should there be a "power controlling hierarchy"?

    I'm not so sure on that but that's what keeps most people going. I'm open to the possibility of being disappointed...
     
  16. Feb 15, 2012 #15

    chiro

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    It might help if you become aware of the history of the education system and also the differences between the different regions and the approaches used (like the Eastern and Western approaches).

    The education system that we have had many influences that were based on the needs of the industrialists. They needed workers who had enough training to work on the factory floor to do their job or in some other similar capacity.

    I don't know too much about the university system, but I do know that it was certainly in a different league than that of high school and it was only reserved for the brightest and the best of students. Some interesting insights have been reading biographies of people like Newton and Gauss which give hints about the kinds of education systems and what kind of people were accepted into these places.

    Whether there should be not be is not really the point: the fact is that there is a hierarchy and the structure has been designed in a way where the control mechanisms are very effective in making them limited to outsiders.

    Also one thing that might be you a bit of insight into this, is that many people don't want to deal with an extra responsibility that they don't have to and this mentality has allowed people that want the control to go in and get it.

    As a result, the people that just want to focus on their 9-5 (or 9-8 job nowadays) just want to go to work to earn enough to feed their family, send their kids to school and indulge in a few hobbies while they are happy to ask someone to worry about everything else so that they don't have to.

    Not surprisingly it allows people that are power hungry to get power because no-one else wants that kind of responsibility.

    I'm not advocating that you only focus on the 'hell'. What I'm saying is that the bad or the 'real' learning experiences help you appreciate things, gain empathy, and can actually prevent you from making major mistakes down the line.

    I would kind of equate this situation to having a spoilt rotten child that has never been disciplined in their entire life. Imagine that kind of person in that situation being say 18 years old.

    Now imagine the problems that come with that, especially if reality really hits that person where they had to deal with the world 'just like the rest of us'. They will fall much harder than the person who has had a few bruises on the way.
     
  17. Feb 15, 2012 #16
    Very well said.
     
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