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"School mathematics" is something almost completely different from mathematics. (For an elaboration on this idea, see http://duckduckgo.com/?q=lockharts+lament

• guscost 14y ago
  Math became ludicrously easy for me as soon as I realized how to think about it. It wasn't the same method that they were suggesting in school, and I don't know that my method would work for everyone.
  • ThomPete 14y ago
    As someone who still haven't found a way to think about it I would be curious what you ended up with.
  • drieddust 14y ago
    I will be very much interested in learning what method did you use.After dropping from regular education 12 years ago, I have tried to learn mathematics multiple times with moderate success only. Please try to share your methods via a blog post/elaborate comment if you can spare some time.
    • guscost 14y ago
      All I can finish today is a rather unhelpful rant. I'm very opinionated and angry about this stuff: http://guscost.com/2012/07/29/mathemantics/ http://guscost.com/2012/07/29/mathemantics/ But I'll be sure to put together a follow-up instructional blog that skips the vitriol, as nobody should actually have to just believe me. I do think that the very general attitude toward each problem is the only constant feature, and each topic has to be treated as a brand-new exploration, so I'll need to coagulate a topic to start off with. I'm leaning towards degrees of freedom, coordinate systems and the magic of Euler's formula. Sound good? And if not, I'm serious about the last sentence. What topic gave you the most trouble when you tried to learn it?
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      • drieddust 14y ago
        I have tried to learn discrete mathematics topic however I have never made progress past Calculus. I had multiple false starts on Linear Algebra, Probability,Graph theory,Set theory, and Logic. Somehow books on these topics tends to run into hundreds of pages with multiple exercises of similar type which kinda encourages me to drop it typically when it starts becoming repetitive.I am not sure how to cross this plateau.
        • sanxiyn 14y ago
          In my experience Calculus was a tough nut to crack. This was mainly because it is usually taught in a way that forces you to chew lots of preliminary materials which seem completely unmotivated. But obviously, Calculus was not developed the way it is taught. I found historial approaches more motivating. That means either using infinitesimals (17th century approach), or starting from construction of the real number, say Dedekind cuts or Cauchy sequences (19th century approach).
          • guscost 14y ago
            The original texts are invaluable too. Sometimes ideas don't make as much sense to me after they've been re-explained by a second person.
          • radicalbyte 14y ago
            If you're having trouble then I'd suggest that you pick up Calculus Made Easy by Silvanus P. Thompson. Best book I've read on the subject by a country mile.
        • guscost 14y ago
          Well to be honest, I'm not that far along into probably some of those same books myself, and I still get derailed by random curiosities and end up on Wikipedia or ordering a new book. The latest was a tangent into filter theory and digital signal processing, for a real-time audio project. It's hard to anticipate everything I should be able to do but I have some idea of the general order of things to study personally. If I needed to go in depth about Linear Algebra (and I definitely do), first I'd recall whatever I know about vectors and vector spaces, transformations and matrices and systems of equations, and start gathering articles and seeing if I'm missing any critical linked topics. After I get confident enough, I'd probably skip right to some textbook topic that caught my attention, say normed vector spaces, and try to make do with backward-skipping as a last resort. Of course, that's just an artificial way of making the problem harder, basically, so that it's more interesting than safer but repetitive sets of exercises. The best way to be interested, by far, is to actually want to solve some problem. For now, anyway, I heartily recommend looking for problems that these disciplines can solve, and choosing one to solve yourself.
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• bjz 14y ago
  "(For an elaboration on this idea, see http://duckduckgo.com/?q=lockharts+lament http://duckduckgo.com/?q=lockharts+lament)." For the lazy: http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf
• gcv 14y ago
  Nicely put. I have increasingly come to the view that computer science really is a branch of applied mathematics. My most intellectually rewarding recent work has been on (programming) projects where I get a chance to use some computational geometry and linear algebra. It goes without saying that almost every non-trivial project requires serious thinking about time and memory complexity costs, and I've been surprised to find theory of computation useful when working even on simple parsers (nothing fancy from compilers classes, just straightforward reading of proprietary formats).
• mseebach 14y ago
  My personal anecdote-backed theory is that the lack of proper math teaching (and yes, a little bit of old school drilling) lays the foundation of more advanced "school maths" subjects being perceived as hard: If you struggle with in-your-head multiplication, then the FOIL mnemonic for binomial multiplication is going to be hard, which makes algebra hard. If you can read the language of maths, you can see patterns and understand things in the same way you can when you can read an article. This continues to spill over until it becomes a negative selector, driving a preference for liberal arts type subjects over science and engineering, not by the positive virtues of the former, but by the perceived (and, probably at this point, real) difficulty of the latter - and further augmented by the fallacy that any college education is better than none. We're happy to drill reading in schools, but loath to drill even the simplest maths. Only the most abject failures are allowed to go through school without being able to read a newspaper article at a reasonable speed and give a summary, but if someone breaks down having to do 12 * 9 in his head, it's fine, he's just not very "sciency". Rant over.
  • sanxiyn 14y ago
    This is completely shocking to me. Is it really allowed not to be able to do 12 * 9 in your head after completing school? I am serious. (Since this is not the case in South Korea.)
    • mseebach 14y ago
      Well, anecdotally, since that's all I have to rely on, yes. I'm fairly certain that if you were to survey the basic maths skills on an average liberal arts college in most of Europe or the US, you'd get a result that would shock you.
    • ht_th 14y ago
      Nor around here when you're leaving primary school. So I assume it is a kind of hyperbole used by your parent. At the same time, however, not having any scientific literacy at all seems to be accepted or even glorifies in Western popular culture. Then again, other troublesome behavior is quite accepted as well, like, for example drinking alcohol. How often haven't I heard a parent proudly tell that his or her child just had her/his first beer. Some bad behavior seems just socially and culturally accepted. And changing culture is hard, so, even though there have been programmes stimulating STEM for decades now, there seem to almost no real improvement.
• spockofborg 14y ago
  I started programming when I was 9, mostly taught myself to convert between hex, binary and decimal at about 13. I say mostly out of fairness: high school did spend a day or two on it one year. Needless to say I dropped out in 9th grade; I learned things that would be applicable in the real world better out of school than in. I was making 45K/yr, starting salary, by my mid twenties. Despite that, I'm going to college currently for my degree. I just got an "A" in intermediate algebra, though it was an up hill battle the whole way. The struggle, aside from it being a 6 week summer class, was trying to convince myself that I wasn't wasting my time; that I would learn something applicable to life outside that or the next three requisite classes. Something, that is, besides helping my kids with their math homework. I've come to the firm conclusion that college math exists purely to perpetuate itself, like a virus in our education system; The only job it prepares someone for is to teach the damn class!
  • spockofborg 14y ago
    side note: As a programmer I specialized in both data compression and cryptology.
  • sethammons 14y ago
    I've found that it is nearly impossible for students to find any math useful until they really understand it. As a simple example, you don't need to know nor understand how to multiply. After all , you could just repeated addition and figure it out. However, there is no need for addition either; you can just count up for a while. point being, the more math you know, the more tools you have. you may never use the quadratic formula outside the classroom, but I use algebra all the time to make my life at both work and home easier. please excuse typing errors as I'm replying from my phone.
• wcarey 14y ago
  It would be interesting to understand how "school mathematics" displaced "actual mathematics" in our educational system. I suspect that part of explanation has to do with computers. The word "computer" was originally a job title (see, for example the Harvard Computers: http://en.wikipedia.org/wiki/Harvard_Computers http://en.wikipedia.org/wiki/Harvard_Computers). It changed meaning in the middle of the twentieth century when mechanical (and later electronic) computers displaced human computers. It seems like much of "school mathematics" is vocational training to work as a computer. Unfortunately, we don't employ people to do computation anymore because the cheapest and worst computer you can but will be thousands of times more productive at computation than a human being. If our mathematics curriculum was designed to train people to be computers, and that profession no longer exists, it's no wonder that school mathematics seems pointless and disjointed.
  • sliverstorm 14y ago
    I think "actual mathematics" was used to refer to abstract and/or high level mathematics, the sort a math major might take in college. While "school mathematics" was used to refer to arithmetic and algebra.
• grrabear 14y ago
  If by "school mathematics" you mean algebra, then I completely disagree with you. Algebra is essential for almost every other mathematical concept, not to mention everyday tasks. Just because a computer can do it easily, doesn't mean that people should rely on them to do simple calculations when they could have easily learned how to do it on their own. That is terribly inconvenient and a waste of resources.