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#14496  04/23/08 01:27 PM
Re: Math intuition, math without books
[Re: Dottie]

Member
Registered: 09/19/07
Posts: 6145
Loc: Midwest

Ooh! DOK! I wish we had such a club for HSers my son's age!
It may be time to start creating the things I want instead of just wishing they were around...
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Kriston

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#14498  04/23/08 01:32 PM
Re: Math intuition, math without books
[Re: LMom]

Member
Registered: 09/19/07
Posts: 6145
Loc: Midwest

Dr. F gave some examples of just this sort of intuitiondeadening, cym. People who figure 100/8 by doing long division in their heads, for example. That's not the "natural" way to do it; it's learned. And sometimes that learning can kill the intuition. Do you mean that whoever can figure out 100/8 in their head or just whoever does it the same way like long division on the paper? It's about the method. Long division is one way to get the answer, but if you basically write the problem out in long division form in your head, then you're not using intuition because long division is a method taught to you, not one you would just come to on your own. Yes, pretty much everyone can figure out 100/8 in their heads, I hope! The problem itself has nothing to do with intuition; it's just a way to check how you think about math.
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Kriston

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#14504  04/23/08 02:40 PM
Re: Math intuition, math without books
[Re: Dazed&Confuzed]

Member
Registered: 09/19/07
Posts: 6145
Loc: Midwest

OK I haven't read this article in it's entirity  let me say that upfront  but it sounds like it might be relevant to this topic. Lockhart's Lament I just read all 25 pages. Thanks for sharing that, Dazey! He makes many good points, I think, some the same as Dr. F and some that are more extreme and a wee bit scary... But the focus of the article on the art and beauty of math, the DIY nature of math that current math instruction is lacking makes some sense to me. I like the notion of using the history of math to teach math. I think that gives me a way into math that is interesting and useful. DS6 loves history, and I find it less intimidating to go at it from that direction, so that might be very helpful to me. The article also makes me think I need to go back to the geometry book and be sure I'm not making all the mistakes he named in my use of geometry with DS6! Yikes!
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Kriston

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#14508  04/23/08 03:41 PM
Re: Math intuition, math without books
[Re: Kriston]

Member
Registered: 05/26/07
Posts: 1783
Loc: West coast, USA

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. It's not just painful, rote memorization takes a whole lot more effort (at least for me!) and is less "sticky" than understanding something. I think it's because when you just memorize you may learn a fact but it's just floating there in your brain, not connected to anything. It can be hard to retrieve that floating information. If I know how to reason something out it's like a trail of breadcrumbs to follow back to the memory. Each time I repeat the reasoning process it becomes easier to find and follow the breadcrumbs. If you think about something enough, the trail becomes like a superhighway leading straight to the answer.

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#14510  04/23/08 03:58 PM
Re: Math intuition, math without books
[Re: Cathy A]

Member
Registered: 09/19/07
Posts: 6145
Loc: Midwest

Oh, Cathy! <swoon> You made that whole argument against rote memorization that I was struggling to make so beautifully. the breadcrumbs analogy is ideal! Okay, now I'm not only thinking that I'm having trouble with math, I'm having trouble with language... Wanna write my book for me?
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Kriston

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#14511  04/23/08 04:10 PM
Re: Math intuition, math without books
[Re: Cathy A]

Member
Registered: 01/05/08
Posts: 830

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. It's not just painful, rote memorization takes a whole lot more effort (at least for me!) and is less "sticky" than understanding something. I think it's because when you just memorize you may learn a fact but it's just floating there in your brain, not connected to anything. It can be hard to retrieve that floating information. If I know how to reason something out it's like a trail of breadcrumbs to follow back to the memory. Each time I repeat the reasoning process it becomes easier to find and follow the breadcrumbs. If you think about something enough, the trail becomes like a superhighway leading straight to the answer. Haha, this reminds me of taking beginning Accounting in college. I did very well in Accounting but memorized very little except for terms. Just before a test I would review one note which reminded me when cash was a credit or debit. As soon as I sat down I would write on the test when it was a credit. Everything else was a snap because I could relate it to cash one way or another. Other students struggled to memorize individual transactions and never could grasp the relationships easily.

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#14513  04/23/08 04:11 PM
Re: Math intuition, math without books
[Re: Kriston]

Member
Registered: 12/14/07
Posts: 902

It's about the method. Long division is one way to get the answer, but if you basically write the problem out in long division form in your head, then you're not using intuition because long division is a method taught to you, not one you would just come to on your own. Yes, pretty much everyone can figure out 100/8 in their heads, I hope! The problem itself has nothing to do with intuition; it's just a way to check how you think about math. Good, I was getting worried that he didn't expect people to calculate 100/8 in their heads Honestly it must be a really hard work to do it in your head the same way like you do it on the paper. I am not going to try to figure out how DS5 does it. I am afraid he could loose me somewhere in the middle It's not just painful, rote memorization takes a whole lot more effort (at least for me!) and is less "sticky" than understanding something. I think it's because when you just memorize you may learn a fact but it's just floating there in your brain, not connected to anything. It can be hard to retrieve that floating information. If I know how to reason something out it's like a trail of breadcrumbs to follow back to the memory. Each time I repeat the reasoning process it becomes easier to find and follow the breadcrumbs. If you think about something enough, the trail becomes like a superhighway leading straight to the answer.
I am the same way. I took heaps of math and computer classes and exams and it was such a relieve since I just had to get it so to speak. I didn't have to memorize it, as long as it made sense I was fine. I hate when I have to memorize things, I don't usually see a point in doing that and the results show it.
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LMom

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#14514  04/23/08 04:15 PM
Re: Math intuition, math without books
[Re: Cathy A]

Member
Registered: 09/19/07
Posts: 6145
Loc: Midwest

Oh, Kriston! <melting> Do you know how great it is to have people be interested in and appreciate my pet theories ? Ok, maybe that's enough of our little lovefest LOL! Well, I'm really thinking that maybe I can just get YOU to teach me how to teach math! Everything you've written could come right out of Dr. F's talk, and if I can make you melt just by telling you how brilliant you and your theories are, then maybe I can buy you off more easily than I can buy him. Yes, I think I'm saying that you might be a cheap (math) date, but I mean that in the nicest way!
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Kriston

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