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    #14538 - 04/23/08 07:45 PM Re: Math intuition, math without books [Re: squirt]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Originally Posted By: squirt
    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.


    I don't see how it could be harmful. It can be a kind of play and it can be satisfying to figure things out and fill in the blanks. Ask him about what's going on in his mind when he's figuring things out. It's a good exercise to verbalize your thinking process and you may be surprised at what he tells you. My son comes up with all sorts of ways to do problems. Sometimes it's a way of looking at things that I haven't thought of.

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    #14539 - 04/23/08 07:48 PM Re: Math intuition, math without books [Re: snowgirl]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Originally Posted By: snowgirl
    ... the auditory-sequential person is supposedly better at rote memorization...


    My theory on this is that they are better able to retrieve the floating info by using auditory cues (like whispering to yourself, "6,8,48.") It gives them a hook to hang that info on and find it again. Eventually, they can just hear it in their minds.


    Edited by Cathy A (04/23/08 07:50 PM)

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    #14540 - 04/23/08 07:52 PM Re: Math intuition, math without books [Re: Cathy A]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    BTW, my son is sitting on the living room floor doing a math workbook right now. It's way too easy for him but he gets satisfaction out of it and I suppose it's reinforcing those thought pathways... Oh heck, at least he's not watching the TV smile

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    #14547 - 04/24/08 04:25 AM Re: Math intuition, math without books [Re: Cathy A]
    OHGrandma Offline
    Member

    Registered: 01/05/08
    Posts: 830
    Originally Posted By: Cathy A
    BTW, my son is sitting on the living room floor doing a math workbook right now. It's way too easy for him but he gets satisfaction out of it and I suppose it's reinforcing those thought pathways... Oh heck, at least he's not watching the TV smile


    I think the satisfaction of doing arithmetic is why Sudoku is so popular. Some people like crossword puzzles, some like math problems.

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    #14554 - 04/24/08 06:21 AM 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
    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


    Thanks, Cathy, but oh, man! I read that stuff and I only hear the teachers in "Peanuts": "Wahwah-wah-wah." I think I need "Numerical Analysis for Dummies"! I may be in BIG trouble with this little scheme of mine...Much math to learn!

    On the bright side, I spoke with DH about my grand plans last night though (he'd been out of town), and he's all in favor of handling a big math/science project with DS6 on the weekends next year as a matter of course. They'll ask the question and do the experimentation. Then hopefully I can help DS6 with any grunt work to find the answers to his questions. Worst case scenario: he has to ask dad. Not a huge deal.

    There are definite benefits to an English major marrying an engineer! Together, we make one person who may actually be capable of effectively homeschooling an HG+ kid! wink
    _________________________
    Kriston

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    #14558 - 04/24/08 07:08 AM Re: Math intuition, math without books [Re: Kriston]
    AmyEJ Offline
    Member

    Registered: 03/10/08
    Posts: 79
    Loc: Texas
    Originally Posted By: Kriston

    There are definite benefits to an English major marrying an engineer! Together, we make one person who may actually be capable of effectively homeschooling an HG+ kid! wink


    This is what allows me to even entertain the idea of homeschooling in the future! My husband is SO good at math, and I'm SO not! I laugh about it being the subject that drove me to law school. The funny thing is that he's a lawyer too, but for completely different reasons. Anyway, I think he does math much like how Cathy A. has described it (I've loved the posts, by the way!). I've always been amazed at how quickly he can do arithmetic in his head, and finally I asked him about a year ago. He explained that he does it through rounding, usually to 10, then adds or subtracts as needed. I felt so dumb. I'd never even thought about math like that. It just came naturally to him, and I would be bogged down trying to carry my tens the way my teachers had taught me so many years ago. crazy He thought of it as kind of cheating, but I realized how I'd been focusing on something way too literal for my whole life, which is weird because I'm not a black and white thinker. But I think it was how I was taught math and I never thought to look beyond it.

    I started disliking math in about the 4th grade when we had those math competitions to fill in the blanks (Math Factors, or something like that) as quickly as possible. Around that time I got it in my head that I wasn't very good at math, and it's always stuck with me. I will say, though, that despite "hating" math, I loved my AP chemistry class, particularly balancing equations. This wasn't math, though, right? wink That was chemistry, something completely different.

    I feel a little silly now because at age 34 I'm finally beginning to see how a lot of math "works" and I'm actually delighting in it. As I'm explaining things to DD6, I find that suddenly I'm seeing patterns there that I had never really noticed before. I don't know if I was never taught math that way or if I just blocked it out but I would LOVE to take a class taught by Cathy A.! If I went back in time and learned math her way as a 3rd grader maybe I would have done a little better in my high school calculus class, or at least maybe I wouldn't be relearning it at my age now.

    So Kriston: you go, girl! I love that you are exploring this way of learning about math. When you get it figured out maybe you can share it with the rest of us. I'd definitely be interested in that. And I'd love a PM of your notes, if it's not too much trouble.

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    #14560 - 04/24/08 07:15 AM Re: Math intuition, math without books [Re: AmyEJ]
    Dazed&Confuzed Offline
    Member

    Registered: 04/05/08
    Posts: 1815
    AmyEJ - I'm so with you!!! I've used Rightstart to teach my son math b/c I don't care for the Everyday Math he gets at school and he was begging to move ahead in math. I feel like I finally understand. It teaches math the way your DH does it. I explained it to DS this way. I can't remember the exact problem, but it was a problem where you could do it the long way and get the right answer or you could estimate to 10, subtract, and get the answer in 1sec. When I was in school, i was the kid doing it the long, methodical way. The kids who *knew* math, did it the quick and dirty way and were several problems ahead by the time I finished the one problem and had time left over to re-check answers whereas I did not. Teaching math this way, I finally feel like I've been let in on some secret! I too LOVED balancing equations in chemistry!


    Kriston: I'd love a PM of your notes as well!

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    #14561 - 04/24/08 07:21 AM Re: Math intuition, math without books [Re: AmyEJ]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: AmyEJ
    When you get it figured out maybe you can share it with the rest of us. I'd definitely be interested in that. And I'd love a PM of your notes, if it's not too much trouble.


    IF I get it figured out, you mean! crazy Those Wikipedia pages scared me more than a little! Seriously, I had to look up *so* many words. It's more than a little intimidating. I did take calculus, both in high school and in college. I can do this, right?!

    I keep reminding myself that that's just the notations and terminology that are throwing me. I don't have to know all that or use all that to teach DS6 that fractals are cool or that problem solving is about finding a fun puzzle of his choosing to figure out. At this stage, I just want to focus on the big picture. If I get bogged down in math the way I learned it, this won't work.

    Outside the box...Outside the box...Outside the box...

    Anyway, thanks for the moral support, Amy, and I'll send you and Dazey a copy of the guy's talk when I get my notes transferred to this computer.

    laugh
    _________________________
    Kriston

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    #14567 - 04/24/08 08:13 AM Re: Math intuition, math without books [Re: Kriston]
    Lori H. Offline
    Member

    Registered: 05/26/07
    Posts: 982
    For my outside-the-box, more verbally gifted than math gifted kid, math will never be his favorite subject. He usually tries to talk his way out of doing it. Yesterday, he told me that when he does math, he gets this strange sensation in the back of his head and it is very unpleasant and the only way he can find relief is to stop doing math and he thinks it could even be some rare sensory disorder and that it might be interesting to see a brain scan of his brain while he is solving a math problem mentally. I keep telling him he is only prolonging the agony, that it is better to just do it and get it over with, but he loves to argue.

    But around the time he turned 5, he came up with his own way of doing subtraction using negative numbers because he found it easier to do it this way. Would this be considered intuition? A kid at acting class had told him about negative numbers and he just thought about it and came up with his own way of doing things. I found that I could do subtraction mentally a lot easier his way, so he actually taught me something. When we told the Kindergarten teacher about this, I think she just thought it was kind of weird. Teachers at this school think kids should only be allowed to solve problems one way- the way the book shows.

    At almost 10, he is having no trouble doing the math in an 8th grade workbook and a pre-algebra workbook and a book with word problems. But he often dislikes the way the book explains things. For instance, the 8th grade workbook starts out with examples of subtraction and these instructions: "To subtract, start with ones. Rename 1 ten as 10 ones. Continue subtracting from right to left. Rename as necessary."

    My son said they should have explained what to do if you have a problem like 1,111 - 7,777. He knows how to do this, but we couldn't find where it showed how to do this on paper anywhere in the book.

    I usually have him do one problem the way the school would make him do it, just in case he ever had to go back to school, and the rest of the time he solves problems his own way. It works for him, for now.

    But I never took calculus. I will probably need to find a math tutor, hopefully someone who really likes math and can convince my son that it is as fun as science and history and literature and arguing.




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    #14572 - 04/24/08 09:02 AM Re: Math intuition, math without books [Re: Lori H.]
    squirt Offline
    Member

    Registered: 03/31/08
    Posts: 323
    Loc: Back in Texas, alas!
    Kriston - I'd like your notes as well.

    About 6 1/2 years ago (note that son is 6 3/4 YO), I got into a funk and gave about 15 boxes of books to the library. With them were all my college textbooks, which I had been saving for over 15 years. There went Calculus, Diff E, Latin, Logic, everything. Boy do I wish I had those back! Lessons learned: don't throw anything away in the midst of post-partum depression and EVERYTHING is worth keeping! Not that the fist part of the lesson will ever apply again!

    Lori - my son figured out negative numbers when the teacher gave him a "2nd grade brain teaser". There were flowers and numbers on each petal and one in the middle. You were supposed to subtract the petal number from the middle number. He did them all backward and got negative numbers, which he didn't know how to notate, so he put "2 but 2 that is less than 0". I explained negative numbers to him and told the teacher about it at a conference as an example of his math skills. She told me "you shouldn't teach him something that we don't learn in 1st grade - that's a 5th grade concept". I read something about "subtraction with renaming" and had no clue what it meant. Now, you've described it for me. Totally counterintuitive to me - unless it's the same as borrowing? Okay, totally rambling now and not contributing.

    This has been a very good thread and I'm glad to hear all of the thoughts, ideas, and theories of everyone.

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