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  1. #1
    keithk's Avatar
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    Default How to Fix Our Math Education - NYTimes

    I found this article interesting...

    http://www.nytimes.com/2011/08/25/op...tion.html?_r=1

    Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now.
    I think this is a great idea, especially for connecting non-math inclined students to real world applications. It certainly could help drive the points home and not leave the students wondering how any of the current math classes will have relevance in their lives.

    Sadly, this probably wouldn't happen any time soon. Fundamental changes to core education would probably take decades.

    Anyway, what do you guys think about getting away from the current algebra->geometry->pre-cal->calc->trig path that is currently used?

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  2. #2
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    I think it's a great idea. *nod vigorously* I am a super recent high school grad, other than studying for the College Math CLEP, the last math I took was in 08. I already remember nothing and haven't used it at all since. Utterly pointless.
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  3. #3
    OE800_85 is offline Baron / Baroness
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    I hate when people say math is pointless. This is why America is crumbling, people.

    You guys all bought mortgages that, if you did the math on, you'd realize in the future you couldn't afford :P. (sorry, had to say it)

    Not to mention personal finance and budgeting, which I'd argue america is probably among the worst performing among developed nations (as it is with its education of math to students)

    I think students need to get over this stigma with mathematics and science. It's for geeks, it's not practical, I can never learn it anyways.

    How about:
    It's for people who want good jobs with a decent salary, it's indispensable in so many walks of life, and if you just go slowly, be patient, ask questions, and practice (I mean, a LOT) it becomes really easy.

    However, making math "fun" is much easier said that done, people have been trying to do it with mixed results for many years, things might not change so quickly.
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  4. #4
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    Quote Originally Posted by OE800_85
    I hate when people say math is pointless. This is why America is crumbling, people.

    You guys all bought mortgages that, if you did the math on, you'd realize in the future you couldn't afford :P. (sorry, had to say it)

    Not to mention personal finance and budgeting, which I'd argue america is probably among the worst performing among developed nations (as it is with its education of math to students)

    I think students need to get over this stigma with mathematics and science. It's for geeks, it's not practical, I can never learn it anyways.

    How about:
    It's for people who want good jobs with a decent salary, it's indispensable in so many walks of life, and if you just go slowly, be patient, ask questions, and practice (I mean, a LOT) it becomes really easy.

    However, making math "fun" is much easier said that done, people have been trying to do it with mixed results for many years, things might not change so quickly.
    Umm, I think that was the point. You don't need geometry, etc. to understand personal finance. People learn how to find the sin and tangent of an isosceles triangle but can't figure out why paying the interest on credit card debt isn't making it go away!

    Higher math =/= common sense math.
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  5. #5
    keithk's Avatar
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    Quote Originally Posted by OE800_85
    I hate when people say math is pointless. This is why America is crumbling, people.

    You guys all bought mortgages that, if you did the math on, you'd realize in the future you couldn't afford :P. (sorry, had to say it)

    Not to mention personal finance and budgeting, which I'd argue america is probably among the worst performing among developed nations (as it is with its education of math to students)
    This bolded part is exactly why I think a change would be good. Give the kids some real-world lessons with math. Let them learn examples that will directly influence and enlighten them as 18 yr olds looking at the option of taking on thousands of dollars of debt for school, housing, car, etc. along with everyday life choices such as "Do I really need to spend this extra $10 right now on eating out?".

    Maybe that would be better in a special money-management class though. Anyway, I think using real world applications to teach math can only help, but I like hearing both sides
    Last edited by keithk; 08-25-2011 at 01:22 PM.

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  6. #6
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    Default +++

    great summation!

    Quote Originally Posted by OE800_85
    I hate when people say math is pointless. This is why America is crumbling, people.

    You guys all bought mortgages that, if you did the math on, you'd realize in the future you couldn't afford :P. (sorry, had to say it)

    Not to mention personal finance and budgeting, which I'd argue america is probably among the worst performing among developed nations (as it is with its education of math to students)

    I think students need to get over this stigma with mathematics and science. It's for geeks, it's not practical, I can never learn it anyways.

    How about:
    It's for people who want good jobs with a decent salary, it's indispensable in so many walks of life, and if you just go slowly, be patient, ask questions, and practice (I mean, a LOT) it becomes really easy.

    However, making math "fun" is much easier said that done, people have been trying to do it with mixed results for many years, things might not change so quickly.

  7. #7
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    The separation between pure and applied maths is already well-established. The reason maths needs taught as a separate subject is that it is an abstract subject, regardless of whether you take the formalist or constructivist perspective.

    Most maths subjects in primary and high school incorporate some form of application in an attempt to make it relevant; Euclidean geometry always has problems involving mowing the grass or filling baths, algebra has word problems related to industrial production (operations), the exponential function is nearly always introduced alongside problems of compound interest, limits go all the way back to Zeno's paradox, discrete maths (counting) has arranging families in a theatre row, probability has balls in vases, trigonometry has ships sailing or weights hanging and calculus will combine Newton and race cars accelerating.

    Understanding maths in general (in the abstract) lets an individual learn how to then go ahead and apply the techniques in specific situations in order to model events. Only teaching specific models would really limit the student if it's done at too early an age while maths in general is already being taught using applications as described above.

    There was a really cool mathematician called Hardy who wrote a little pamphlet called A mathematician's apology in the first half of the twentieth century. He basically said, "alright, maths is useless but I think it's beautiful." Of course, some of the examples he used from number theory were later required reading for anyone involved in cryptography but it's still a good read.

    There's a reason hard science courses are pretty well paid; they're difficult, challenging and not for everyone (psychology major here, thank you ). These articles are topical and might be considered in relation to the influx of Soviet scientists after WW2, the brain drain from the UK in 1960s and the general requirement for the immigration of technically-skilled individuals. But mostly a case of people writing a lot of waffle

    Any time I read one of these articles, I've got to have a little reality-check. Yeah, we can cite the two rules written above Plato's Academy of "let no man enter here ignorant of geometry" and "know thyself". The trick is to be ruthlessly honest; what's my attitude to maths and what have I done about my own maths education because it's noone's else's fault.

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  8. #8
    Kaz
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    Quote Originally Posted by irnbru
    The separation between pure and applied maths is already well-established. The reason maths needs taught as a separate subject is that it is an abstract subject, regardless of whether you take the formalist or constructivist perspective.

    Most maths subjects in primary and high school incorporate some form of application in an attempt to make it relevant; Euclidean geometry always has problems involving mowing the grass or filling baths, algebra has word problems related to industrial production (operations), the exponential function is nearly always introduced alongside problems of compound interest, limits go all the way back to Zeno's paradox, discrete maths (counting) has arranging families in a theatre row, probability has balls in vases, trigonometry has ships sailing or weights hanging and calculus will combine Newton and race cars accelerating.

    Understanding maths in general (in the abstract) lets an individual learn how to then go ahead and apply the techniques in specific situations in order to model events. Only teaching specific models would really limit the student if it's done at too early an age while maths in general is already being taught using applications as described above.

    There was a really cool mathematician called Hardy who wrote a little pamphlet called A mathematician's apology in the first half of the twentieth century. He basically said, "alright, maths is useless but I think it's beautiful." Of course, some of the examples he used from number theory were later required reading for anyone involved in cryptography but it's still a good read.

    There's a reason hard science courses are pretty well paid; they're difficult, challenging and not for everyone (psychology major here, thank you ). These articles are topical and might be considered in relation to the influx of Soviet scientists after WW2, the brain drain from the UK in 1960s and the general requirement for the immigration of technically-skilled individuals. But mostly a case of people writing a lot of waffle

    Any time I read one of these articles, I've got to have a little reality-check. Yeah, we can cite the two rules written above Plato's Academy of "let no man enter here ignorant of geometry" and "know thyself". The trick is to be ruthlessly honest; what's my attitude to maths and what have I done about my own maths education because it's noone's else's fault.
    Spot on irnbru, very well said.

    I feel like being lazy right now so this'll be short. Almost every other sentence in that article made me think of a counterpoint instantly. Irnbru summed up almost everything that occurred to me. The "real value" of maths is their abstraction. You learn how this stuff "really works" so no matter what situation you run into, if it applies, you can use it. Also, the authors mention more than once our falling behind other countries in maths but actually never say how those countries' kids are taught their maths. Unless all these countries that are kicking our butt pulled ahead of us by making the changes the authors are suggesting I'd say their point is dealt a lethal blow.

    Honestly, I think we as a people need to decide whether we want to "educate people", "prepare them for life" or "get them jobs". I think these three things have both a lot of overlap and a lot differences between them. They definitely are not synonymous. An early apprenticeship in many fields better prepares you for success in that field than unfocused, general liberal arts-style schooling usually does. So people more concerned about employment problems for kids than their "abstract education" should push for that.

    But personally I'll keep my impractical armchair educational abstractions thankyouverymuch .
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  9. #9
    ryoder is offline King / Queen
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    I sort of disagree with the math gurus here.
    Tying a real application to a mathematical concept is so important.

    Here is an example. In HS physics we were given two equations that modeled the velocity and acceleration of a dime dropped from 50 ft high, for example. Then we were asked questions like, how fast is it going at time T? How long until it hits the ground?
    I noticed back then that these two equations looked similar. There was something about them. Once I did 50 problems I had it down pat but I was still spoon fed both equations.
    Fast forward to the next year when I took calculus.
    We were learning how to calculate the derivative of a function. I was concentrated on the abstract and how to perform the calculation.
    I watched a function derive from specific to less specific and it somehow looked familiar. Then I realized what the heck I was doing.
    I suddenly got chills on my arms when I realized that I was now capable of computing the acceleration equation that always accompanied the velocity equation back in HS physics.
    So I raised my hand and asked my teacher. Hey, isnt this derivative useful in determining acceleration equations from a velocity equation? Isn't the constant C at the end of the equation lost since it has no bearing on the acceleration, just like what happens when you take the derivative of something?

    She said yes. At that point I realized that you could do something useful with calculus. I was shocked.


    Another story involves video game programming. I got an A in calc 3 because all of the practical applications of spatial math, vectors, dot products, intersection of a ray with a plane in 3-space were screaming at me. I realized that by learning this math I could write a kick ass 3d game.

    Applications are very important.
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  10. #10
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    Quote Originally Posted by ryoder
    Tying a real application to a mathematical concept is so important.
    ...
    No disagreement here; especially when the example you gave was pretty much the same as the one previously given

    edit: This is application -> maths, rather than maths -> application. Some concepts in maths, even those delivered at a relatively early age, really don't have any application. Previous edit timed out, trying to add some content in an attempt to communicate the position.

    Some half-baked analogies which describe the over-emphasis of application over actual maths:

    Learning to play songs on a piano or guitar without studying and practicing scales.
    Learning a language without studying grammar.
    Learning to play chess or go without studying opening/endgame/shape.
    Learning 'about' psychology without studying statistics.
    Learning to play a sport competitively without the rules.
    Learning CIS without picking up a programming language.

    Okie, the fourth example is specifically mathsy, but I hope overall that the gist is there. In each example, people could do fairly well and some exceptionally talented individuals could still do very well. Ultimately, people who go into the technical/abstract will have a much better understanding of their specific field and also have learned general (higher-level/abstract) information which could also be applied to other fields. That's pretty much what maths is.

    Interesting question that came up once was, "What is Maxwell's theory of electromagnetic radiation?" The only meaningful answer is, "Maxwell's theory of electromagnetic radiation is Maxwell's field equations."

    Someone stated in another thread that they drill their kids with their times tables and basic arithmetic. I fully applaud and support this approach - you've got to have the basics down. To be honest, if anything I think that there is a slight over-emphasis in 'applied'-type problems in maths classes; put x into y to get z, write down z and get a point. I'd rather see a return to the more classical style of maths where actual proofs were studied and taught in Euclidean geometry from a relatively younger age.

    A lot of people don't like maths. I'm pretty much one of them. It's still our own responsibility to actually do the work, however.
    Last edited by irnbru; 08-26-2011 at 02:04 PM.

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