American math students ...

This is a discussion on American math students ... within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Originally Posted by Thantos As to the homework question she pointed out about 36 / 6. Well the problem wasn't ...

  1. #16
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    Quote Originally Posted by Thantos View Post
    As to the homework question she pointed out about 36 / 6. Well the problem wasn't to find the solution but to describe how you could go about solving the problem. Making sure students can logically get to the solution is much more important then the solution itself.
    Use a harder problem, then. If someone can't look at 36/6 or 20/4 and tell me the answer immediately is troubling. When I ask for change for a dollar, I don't want someone pulling out a pencil and paper and "clustering".

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    Quote Originally Posted by abachler View Post
    Yes, this is the unfortunate truth, and I took great interst in math above and beyond what was taught in school. We simply don't have access to the resources. Part of the problem is the mistaken notion that all children are of equal capacity. While I don't think we shoudl abandon those that are not as academicalyl gifted, equally horrible is holding back those that are. We need a comprehensive multi-track educational system with a primary focus on core subjects like math science, art, and music with less focus on things like sports.
    Teachers and schools don't have the bandwidth to teach everyone at their own pace. The simple fact is that some people are good in some subjects and not in others. I couldn't grok chemistry if my life depended on it, but I don't think it would fair for the teacher to let the better students suffer by changing teaching methods for me.

    So I'll never be a pharmacist or chemical engineer, which is good for society.

  3. #18
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    Remember who the target is. It isn't adults it is 4th and 5th graders.

  4. #19
    Malum in se abachler's Avatar
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    Quote Originally Posted by medievalelks View Post
    Teachers and schools don't have the bandwidth to teach everyone at their own pace. The simple fact is that some people are good in some subjects and not in others. I couldn't grok chemistry if my life depended on it, but I don't think it would fair for the teacher to let the better students suffer by changing teaching methods for me.

    So I'll never be a pharmacist or chemical engineer, which is good for society.
    I agree that schools dont have the execute capacity to tailor a class to each student, I'm not talkign abotu individual tutoring, but smaller class sizes, 7-15 students, MAXIMUM. Combine this with a mtultitrack class structure (easy medium hard for lack of better terms) where kids that just want a general knowledge of a subject can take Easy math, and kids that excell at math can take hard math. This way the individual class doesnt have to tailor itself to the students, btu the individual students curriculum can eb tailored to meet theri needs.
    Until you can build a working general purpose reprogrammable computer out of basic components from radio shack, you are not fit to call yourself a programmer in my presence. This is cwhizard, signing off.

  5. #20
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    Quote Originally Posted by Thantos View Post
    I can't agree with all of her arguements.

    The cluster method may not be effecient for pen and paper usage but it is great for mental solving. For the 26 x 31 problem I would definately break that up into something like ((25 *3)+3)*10 + 20 + 6 so that it would end up being:
    When I see that, my approach is... 31 is close to 30. Divide by ten to get 3. So what's 3 * 26? You can do that in your head: it's 78. Now multiply that ten back in to get 780. Now you're left with 1, so add another 26 to get 806.

  6. #21
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    Yeah that was how I started to it in my head also but when I got to 3 * 26 I solved it as (3 * 25) + 3. When it came to 780 + 26 I knew that 780 + 20 was 800 immediately so then I just had to add the 6. Luckily with mental math you can take a few more steps without it costing any more time.

  7. #22
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    When I see that, my approach is... 31 is close to 30. Divide by ten to get 3. So what's 3 * 26? You can do that in your head: it's 78. Now multiply that ten back in to get 780. Now you're left with 1, so add another 26 to get 806.
    Yes, that is what I mean by "that method is taught in primary schools in Singapore as a mental shortcut for specific calculations". My memory is hazy now, but I think the students are around 8 or 9 years old (primary 2 or primary 3) when they are introduced to that, so it should be within the 4th and 5th grade thing. In other words, the very syllabus McDermott (McDermitt?) recommends teaches what she condemns.
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    I suck at numbers, I have to see it visually in my mind, which is why I have a hard time when doing things like division of things that don't involve the "grouping" concept with regular integers. Like dividing the length of one side of a triangle to that of another or some such ratio based shenanigans.

  9. #24
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    I have a feeling that clustering would also help later with higher level algebra and beyond because there are times when stopping and thinking out the problem, recongizing the "clusters", grouping the clusters together, and then solving those, is a lot easier and less error prone then trying to tackle it all in one go or using some predefined algorithm. For example problems when you need to insert two terms that are equal to 0 (ex: x - x) but help you factor out the problem and reduce it down.

  10. #25
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    Quote Originally Posted by Mario F. View Post
    The real problem with Math as I've perceived it during my days and as I seem to perceive in my daughter's progress (thankfully a terrific student. I'm 7 feet tall with pride) is Environment. More than ever before math needs to be taught in a context and in a less abstract manner.
    I couldn't agree more. I was never one for math (I flunked H.S. algebra)... That is until I joined the Navy. It's amazing how fast you can learn the calculus of of a torpedo shot when the bad guys are hot on your, ah, backside. And yes I used a calculator. I'd have pulled off my boondockers and used my toes if would have gotten me a firing solution any faster.

    Maybe if I'd been taught algebra in a less abstract manner I wouldn't have flunked it. Of course being dyslexic didn't help but that's a whole different can of worms.

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    BTW, did anyone else catch the bit at the end about the "inability to work alone" of her colleagues in math classes when she went back to school in the late 90s? Anyone else kind of notice that here in the overwhelming majority of newbie questions that could be solved with a book and a little bit of self-study?

  12. #27
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    I dismissed that argument since I'm not sure of what she meant. Certainly not basic math (the context was her university student colleagues), and since basic math was the issue at hand, I can't see how it fits in her reasoning.

    You make a good point. But then, again, the problem is not the actual algorithms. If we followed that reasoning, the problem with her colleagues was instead laziness.

    I generally agree with her arguments. I see nothing wrong with the traditional algorithms. They have been used for centuries(?) and they still produced good math students, scientists, geniuses, moderate students and bad students. And, speaking of laziness, they give nothing to it, whereas all the others are highly questionable.

    On the other hand, the fact the proposed algorithms are easily recognized as a mirror of how we do mental math is yet another testimony of the traditional algorithms abilities. After all the latter is the ones we learned.

    Simplifying math teaching to the level of those proposed algorithms is a mistake. The problem students have with math is not one of basics. No student has more trouble understanding more complicated issues later in college because they can't do a division. They can! Naturally there are exceptions, but that's what they are; exceptions. Instead students find certain concepts simply hard to understand because math is taught to them in a completely abstract manner and becomes essentially a memorization discipline. This is what kills it (and even more so in these rushing days).
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    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

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    That argument was based on one of books stressing "group problem solving". I think a lot of the newbies that post here are too quick to throw up their hands after trivial effort (or none at all) and ask to be guided through the solution. Even after a nudge in the right direction, they stop after minimal gain and come back for another spoonful.

  14. #29
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    I think it depends the way in which the question is asked. When you're around someone that knows what they are doing then usually quickest way to get an answer is to ask. Often you can get the same answer in a couple of seconds compared to a couple of minutes (or more) if you had to look it up somewhere. On a forum its different tho as its usually quicker to look something up than wait for a reply, and, lots of trivial questions get spammy.

  15. #30
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    Well, lets not forget those books are meant for children. Basic school, and even 5th - and 6th grade to an extent - are characterized by group activities. And it's an highly successful way of teaching children. Math is no stranger to that. Stressing group activities is the meat of basic school.

    Despite generally agreeing with her, I still don't see the validity of that argument. Besides I highly doubt her university colleegues where taught from those books she so well criticizes. So, again, that argument makes little sense to me and could even turn against her. Apparently she also goofed when proposing those Singapore text books, from what I read on a post by laserlight. I think, she makes a good point when exposing the somewhat ridicule of the proposed algorithms, but lost it in the conclusions.

    I can however generally agree on the dependency on others. Although I'm not sure how much of that is due to basic school teaching methods. I'd risk... very little.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

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