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    #14516 - 04/23/08 04:39 PM Re: Math intuition, math without books [Re: Kriston]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    I'm happy to help. I've never heard of Dr. F but this thread caught my eye. I have done some thinking about math pedagogy just for my own amusement, though. Mostly, I inflict my theories on my mom, who says that she has some kind of inability to learn algebra.

    My mom is a very smart lady and she was a whiz at arithmetic in school. Geometry proofs were intuitive for her and she is a logical thinker. Somehow, she says algebra just doesn't stick in her brain. She can listen to someone explain a problem and it makes perfect sense at the time but she can't reproduce it on her own. I have always wondered if it is just a matter of finding the right way to explain it to her or if she truly has some kind of math disability. I often wish I could do experiments on her <rubbing hands together>....

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    #14517 - 04/23/08 04:45 PM Re: Math intuition, math without books [Re: Cathy A]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    LOL Cathy! Most people I know who were good at geometry weren't so good at algebra and people who were good at algebra weren't as good at geometry. I personally LOVED algebra and although I did well in geometry I hated proofs with a passion. I saw absolutely no point in them. Anyone else out here love one and disliked the other or is that just a phenomenon I've noticed in the few people I've discussed this with???

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    #14518 - 04/23/08 05:02 PM Re: Math intuition, math without books [Re: EandCmom]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    It's supposed to be pretty common, I think.

    Doesn't one of the books about being visual-spatial mention that liking geometry is one sign of many that you're a VS learner, while liking algebra is one sign of many that you're auditory-sequential?

    I don't have that backwards, do I? Proofs always seemed pretty sequential to me, but the figures are obviously VS...
    _________________________
    Kriston

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    #14519 - 04/23/08 05:11 PM Re: Math intuition, math without books [Re: EandCmom]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Geometry has never been a passion for me, although I liked doing the proofs and writing them out neatly and logically. It seemed satisfying. Algebra just seems like a means to do calculus, which I love.

    Abstract algebra (rings, fields, etc) I can do in a mechanical sort of way but it doesn't seem intuitive to me at all because all I can think about is blobs with arrows pointing to them. Algebraic geometry is similarly opaque smile My degree is in applied math and the way I think about math is mostly visual. Numerical analysis makes a lot of sense to me. By the way, that's something that can be understood with relatively little algebra skills. You need to learn about infinite series which are usually intriguing to kids and full of interesting patterns.


    Edited by Cathy A (04/23/08 05:15 PM)

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    #14525 - 04/23/08 06:03 PM Re: Math intuition, math without books [Re: EandCmom]
    Dazed&Confuzed Offline
    Member

    Registered: 04/05/08
    Posts: 1815
    EandCmom: I read that VCI (on the WISCIV) correlates with ability in algebra while PRI correlates with ability in geometry. It goes along w/ what Cathy said earlier about the verbal side of math. I don't know if that's accurate or not but could explain the cases you were referring to.

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    #14527 - 04/23/08 06:13 PM Re: Math intuition, math without books [Re: EandCmom]
    squirt Offline
    Member

    Registered: 03/31/08
    Posts: 323
    Loc: Back in Texas, alas!
    Originally Posted By: EandCmom
    LOL Cathy! Most people I know who were good at geometry weren't so good at algebra and people who were good at algebra weren't as good at geometry. I personally LOVED algebra and although I did well in geometry I hated proofs with a passion. I saw absolutely no point in them. Anyone else out here love one and disliked the other or is that just a phenomenon I've noticed in the few people I've discussed this with???


    I loved Algebra but saw absolutely no reason for the proofs in geometry. I mean, really, we know what the angles are and which is which and how they relate, so what's the point?

    After having read all of this thread, I like the theories of teaching math but I have a question. If my guy LIKES doing workbooks, is there any harm in that? Will it stifle his love of learning or will he eventually get bored with them and want to move on to other things. I don't actually teach him out of them - just provide them.

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    #14531 - 04/23/08 06:55 PM Re: Math intuition, math without books [Re: squirt]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Nope, squirt. I think that if he's happy, let him go to it! Child-directed is what it's all about, I think. Especially at a young age.

    Mine's just bored and antsy.

    And Cathy, can you tell me more about numerical analysis. What is it? Can you point me to any resources for it? It sounds like something my infinity- and pattern-loving boy would totally adore!!! Thanks for the tip!
    _________________________
    Kriston

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    #14534 - 04/23/08 07:11 PM Re: Math intuition, math without books [Re: Kriston]
    Dazed&Confuzed Offline
    Member

    Registered: 04/05/08
    Posts: 1815
    YEs I'd like to hear/read more about numerical analysis as well.

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    #14536 - 04/23/08 07:35 PM Re: Math intuition, math without books [Re: Dazed&Confuzed]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    A quick and dirty description is on Wikipedia http://en.wikipedia.org/wiki/Numerical_analysis

    Here's a description of Newton's method for finding roots of equations. http://en.wikipedia.org/wiki/Newton%27s_method
    If you apply this to complex polynomials you can generate really cool fractal pictures like the one at the bottom of the page.

    I love fractals, too. Check out the Mandelbrot set:

    http://en.wikipedia.org/wiki/Mandelbrot_set


    Edited by Cathy A (04/23/08 07:36 PM)

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    #14537 - 04/23/08 07:40 PM Re: Math intuition, math without books [Re: Dazed&Confuzed]
    snowgirl Offline
    Member

    Registered: 02/24/08
    Posts: 361
    Barging in here, Kriston, you have the VSL angle correct, that Silverman says auditory-sequential learners are better at arithmetic and algebra while VSLs are better at geometry except for the proofs, which are sequential. Also keep in mind that the auditory-sequential person is supposedly better at rote memorization, while the VSL learns best by seeing relationships. And remember, the right brain is the place for intuition smile

    You may have seen this article before, but I'll throw it out here for you just in case any of the points seem relevant to your current thought process: http://www.visualspatial.org/Articles/algebra.pdf

    thanks for all the food for thought!
    smile

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