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    #14482 - 04/23/08 12:35 PM Re: Math intuition, math without books [Re: Dazed&Confuzed]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Originally Posted By: Dazed&Confuzed
    Cathy - can I sign up for your class? Pretty please??

    I was actually researching VCI and PRI and what does those indices mean in the real world. I was surprised to read somewhere that VCI correlates more with algebraic thinking and PRI with geometric abilities ie that math and verbal domains are linked as you stated.


    Thanks, Dazey! It's so fun to teach people who are excited about learning (that's why I like third graders smile .) Teaching a bunch of jaded college students taking a required course that they hate is torture.

    Quote:

    There is a math website I came across and it explained fractions just the way you did and also addressed the importance of doing so. Coincidentally, w/out knowing why or the significance of it, it's how I taught my boys fractions at a young age.


    I'm not sure how significant it is, but it sure makes sense! Otherwise, kids just get a look of panic on their faces when they see two numbers with a weird little line between them. What the heck is that about? It must be hard. If nothing else, exposing kids to higher math will get them accustomed to seeing different kinds of notation. Just like we expose toddlers to the alphabet without expecting them to read right away. Why do we (as a culture) feel like we have to keep math a secret? Why do we send the message that it's "too hard" or "too confusing"?

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    #14483 - 04/23/08 12:38 PM Re: Math intuition, math without books [Re: Dottie]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Originally Posted By: Dottie
    Excellent thoughts, but if my calc student doesn't buckle down and just memorize a few basic trig points, she is going to lose too much time deriving them on her upcoming test!


    That's exactly why I said that rote learning can be a valuable tool for increasing fluency. And fluency is important, not just for tests, but to allow a person to glide over those concepts that have already been reasoned out. If you can't do that, it overtaxes your working memory when you're trying to reason out a new concept that builds on the old ones. Once the pathways are laid down in the brain by that initial "aha", they need to be reinforced by practice.

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    #14484 - 04/23/08 12:39 PM Re: Math intuition, math without books [Re: pinkpanther]
    kimck Offline
    Member

    Registered: 09/20/07
    Posts: 1134
    Cathy - that was wonderfully stated, coming from another mathematician.

    I also never actually memorized anything. I can memorize things. And then immediately forget it 10 minutes after the test. How you would derive your math facts really hit home for me. I couldn't comfortably jump through teachers hoops until I really understood WHY we were doing something a certain way.

    Anyway - thanks for your post.


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    #14485 - 04/23/08 12:45 PM Re: Math intuition, math without books [Re: kimck]
    st pauli girl Offline
    Member

    Registered: 01/29/08
    Posts: 1917
    Cathy - thanks for your example! i printed it out for when we get to fractions. This so makes sense to me.

    I am one of those people who was told that boys were good at math, and girls weren't, and i suppose i believed it. I always got good math grades, but only took the courses that were required. I was thrilled when my college accepted logic courses for math requirements! I do not even have the foggiest idea what calculus is. blush

    But, I do know how to ask for help when needed, and DH is very good at math. So DS4 will be OK. wink

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    #14486 - 04/23/08 12:51 PM Re: Math intuition, math without books [Re: st pauli girl]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Calculus sounds a lot more daunting that it is. Basically, it is a way of cutting curved things into little pieces that have practically straight sides so that we can add them up just like regular old geometric shapes. It's a clever concept which was developed as way to calculate phenomena encountered in physics. It has its own notation--you may have seen integral signs which look like elongated esses. They are for adding things up. The esses stand for "sums". It's actually a very visually based kind of math.

    ETA: I wish more people would take logic!


    Edited by Cathy A (04/23/08 12:53 PM)

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    #14487 - 04/23/08 12:53 PM Re: Math intuition, math without books [Re: st pauli girl]
    Ania Offline
    Member

    Registered: 02/07/06
    Posts: 802
    Loc: Home :)
    Great thoughts, Cathy!

    Can I ask you some questions about Descartes' Cove game, or has this been discussed in a different post already?

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    #14489 - 04/23/08 01:02 PM Re: Math intuition, math without books [Re: Ania]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Originally Posted By: Ania
    Great thoughts, Cathy!

    Can I ask you some questions about Descartes' Cove game, or has this been discussed in a different post already?


    Sure. We haven't played all of it yet. DS is working on the easiest level (Measurement) which is about unit conversions, decimals and metric system. There is other stuff thrown in, though like formulas for volumes and areas of different shapes. I checked out the Algebra level and there were some reasonable tricky problems on there. Good for stretching your brain! smile

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    #14490 - 04/23/08 01:05 PM Re: Math intuition, math without books [Re: Cathy A]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: Cathy A
    I did learn my math facts in grade school but it wasn't exactly by rote. It was more that I repeatedly thought about them until the answers were clear. For example, 7+8=15 because 8+8=16 and 7 is one less than 8. This process builds upon itself--i.e. at some point I had to become convinced that 8+8=16 before I could use that to conclude that 7+8=15. After a while, I felt that I could skip the reasoning part and just go straight to the answer.


    Exactly! This is exactly what Dr. F was saying! If you get it, then the doing is easy and you learn math facts just from daily use. If you don't get it, then you're forced to rely on rote memorization for the doing, and that's painful for a GT kid. Better to start with the concepts and let the knowledge of the math facts come naturally from there.

    Originally Posted By: Cathy A
    My point (I think I have one smile ) is that verbal reasoning can be used to understand math as a language for representing real problems. This is SO important for kids to understand. The way math is taught in school you would think that the math and verbal domains were completely seperate.

    I think that GT kids have the ability to intuit this connection. Mathy kids don't need to have things translated for them this way. Exposing kids like this to math is like immersing them in a foreign language. They will soak it up. Exposing them to calculus at a young age is like letting them read books with big words in them. They may not understand them right away but that's ok.


    EXACTLY! This is something Dr. F said, too, almost verbatim! That's why he believes ALL GT kids are naturals at math, even if they're highly verbal. Because language and math are not separate entities. Our brains don't divide math and language that way.

    Oh, Cathy, you're explaining this SOOOOOOO much better than I did! Thanks! laugh

    Originally Posted By: Cathy A
    This kind of enrichment is beneficial to kids at all levels--without it, math just seems like an arithmetic wasteland to them and they lose interest.


    Again, right on the money. Dr. F said we should, in effect, aim high with these kids. If they don't get it all at age 6, so what? They've got years more to pick up what they missed on the first exposure! But showing them what's out there, what math REALLY is--and it ain't workbooks!--captivates them, shows them that math is beautiful. We don't teach kids to read by diagramming sentences, so why would we try to teach math by starting with arithmetic. Teach them to love it first, then the nuts-and-bolts will come.

    You rock, Cathy! grin You made that a whole lot clearer than I did!
    _________________________
    Kriston

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    #14492 - 04/23/08 01:10 PM Re: Math intuition, math without books [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    OHG: I see what you're saying. Thanks for the clarification. I think you're absolutely right that anything can get old if done to death. Good point. It's not like math facts have the corner on that market! LOL!

    And I'm definitely not suggesting this style of math for a general classroom. I have no idea how that would play, and frankly, I don't really have to know. Dr. F is doing it with GT kids in a GT school, so there's that, I guess. But for my part, all I'm worried about is my own progeny!

    I thought it might work for some of the afterschoolers out there, perhaps in some modified form.

    ...Or not. You know me--I'm not highly evangelical about anything I'm doing! wink

    At least it's made for an interesting conversation! grin
    _________________________
    Kriston

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    #14494 - 04/23/08 01:20 PM Re: Math intuition, math without books [Re: CFK]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: CFK
    Granted, I can kind of be a laissez-faire parent, but I don't really understand the concern here. Kriston, or anyone, if your son is gifted, to the point of being accepted into DYS, is ahead of age/grade mates already in math, doesn't want or like to do math right now, and you are homeschooling so there is no need to be concerned about standardized testing or acceptance into academic programs, then.. why do math at all? Isn't the major benefit of homeschooling the ability to follow your child's lead?


    Well, because I don't think that it's *math* he dislikes; I think it's *my approach to math* that he has disliked. He's fascinated by engineering principles and has always had a mind for patterns and mazes that astounds me. Dropping math altogether doesn't seem like it solves anything, and may in fact mean we'd be missing some opportunities.

    An entirely new approach, however, may be just the thing to light his fire again, a fire that he's always had until he hit school age and workbooks--either the public school's workbooks or mine.

    I can always back off if it looks like that's what's needed. I can appreciate some deschooling time as much as any homeschooler. But before I just give up and hope that he comes to math on his own, I'd rather try to SOLVE the problem, a problem that I feel is mine, not his.

    Does that make sense?

    He's also a lot less far ahead in math than he is in his other subjects. He's reading at the 7th+ grade level, but he's only doing 3rd grade math. I have no trouble with asynchronous development, but I think this has less to do with his abilities and more to do with my teaching. I feel like I'm letting him down, and this offers a different way to give him what he needs. It seems worth a try.

    And BTW, geometry, which I've approached in a far more conceptual and far less arithmeticky manner than our previous math work led us to, has been pretty successful. He's having fun with it. Geometry is one of my data points suggesting going for higher-level, conceptual math rather than arithmetic is going to work better with him.
    _________________________
    Kriston

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