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    #167211 - 09/11/13 07:20 AM Re: Math Homework [Re: ConnectingDots]
    DAD22 Offline
    Member

    Registered: 07/19/11
    Posts: 312
    I think Polarbear already gave some wonderful advice. I'll add my own perspective and experience:

    Mathematics is its own language. Some children are native speakers of that language, and some are learning it as a second language. When you know math as a second language, you translate every math problem into your native language and solve it there. When you know math as a native language, you solve math problems without the need to translate your thought process into your spoken/written language.

    When you ask a student to explain their answers in a language other than math, you are asking them to approach math the way MSL (Math as a Second Language) students approach it. Performing this unnecessary translation is an unnatural hindrance to mathy students, who often resist. It's analogous to asking a child to explain how they walk or catch a ball, and has about as much bearing on the actual performance of the task.

    Personally, when I was in elementary and middle school, explanations weren't considered as important as they are today. It wasn't until I was in algebra that my teacher really wanted me to focus on showing my work and explaining my thought process. She wanted to make the point that my intuition wouldn't hold up to the more complicated problems, and we made a deal: I would try to solve a problem of her choice in my head in under a minute. If I solved it, I wouldn't have to show my work to get full credit, if I failed to solve it, an explanation would be required. In under a minute, my problems were gone. Perhaps there is some demonstration of rare mathematical insight that your child could perform for his teacher that would convince him/her that understanding a problem and being able to explain it in English to other people is not the same thing.

    I've grown up to be an engineer, and when I think about math, I can't say I hear a lot of english buzzing around my head. I tend to think in pictures, but not where arithmetic is concerned. That's just recall.


    Edited by DAD22 (09/11/13 07:22 AM)

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    #167214 - 09/11/13 07:36 AM Re: Math Homework [Re: ConnectingDots]
    HowlerKarma Offline
    Member

    Registered: 02/05/11
    Posts: 5181
    I think that is a spectacular explanation, DAD22.

    I had not one bit of trouble "showing work" in calculus and beyond-- but prior to trigonometry or solving simultaneous equations in high school mathematics, I was always sort of flummoxed by what was intended by that statement.

    I preferred-- as a teacher of college chemistry, I mean-- to suggest that students should "demonstrate THEIR process" for an outside observer/reader so that the observer could replicate that problem-solving strategy.

    That's basically the basis of scientific (and mathematical) communication at those higher levels anyway. It just happens that it's also convenient for catching errors in a pedagogical framework, too.

    smile
    _________________________
    Schrödinger's cat walks into a bar. And doesn't.

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    #167217 - 09/11/13 07:56 AM Re: Math Homework [Re: ConnectingDots]
    KnittingMama Offline
    Member

    Registered: 04/04/12
    Posts: 267
    Loc: California
    A quick idea on why having to show your work is an important skill; not sure how accurate it is, so I'd love feedback. If you want to be a computer programmer, don't you have to know how to translate a "word problem" into mathematical terms? Even if you intuitively know that Susie will have 7 apples after her friend gives her 4 more, computers are dumb devices that don't know this stuff. It seems to be that being able to show your work would be necessary for programming.

    I realize not every kid is going to grow up to be a programmer, but at the elementary level, who can say?

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    #167219 - 09/11/13 08:11 AM Re: Math Homework [Re: ConnectingDots]
    blackcat Offline
    Member

    Registered: 05/23/13
    Posts: 2154
    The book "Upside Down Brilliance: The Visual Spatial Learner" gives interesting insights into kids who can solve complicated math problems but can't explain their work or show their steps. My 6 year old appears to be that way, although has an obvious fantasic visual memory and has about a 25-30 point gap between his verbal and performance IQs (performance being very high). I gave him some double/triple digit addition/subtraction problems with regrouping (he had never seen that before) and he figured out the answers very quickly, but his explanation as to how he solved them did not make any sense and was not the way I was trying to show him (i.e. you borrow a ten). I had to re-teach him but he still does not want to show his work regrouping, he just does everything in his head. His teacher is going to love that.

    In terms of handwriting, my DS struggles a lot and part of the problem in math and showing work is that it just takes too much effort to write. His writing looks age appropriate for the most part, but he scores extremely low on tests of fine motor coordination, meaning he has to put a lot of thought/effort into writing (much more than other kids). DS was diagnosed with developmental coordination disorder. If you continue to have concerns, perhaps get an occupational therapy assessment and ask specifically that they test both for visual-motor integration and coordination. My DS is above average for visual-motor integration (so that has masked some of his problems) but on tests of just motor coordination (like the grooved pegboard) he is very poor.

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    #167228 - 09/11/13 09:41 AM Re: Math Homework [Re: DAD22]
    Nautigal Offline
    Member

    Registered: 04/22/09
    Posts: 1032
    Originally Posted By: DAD22

    When you ask a student to explain their answers in a language other than math, you are asking them to approach math the way MSL (Math as a Second Language) students approach it. Performing this unnecessary translation is an unnatural hindrance to mathy students, who often resist. It's analogous to asking a child to explain how they walk or catch a ball, and has about as much bearing on the actual performance of the task.


    Yes! This is beautiful!

    I don't even know how to tell my kids how to "show your work" on something like subtraction. How did I get the answer to 7 - 4 = 3? Well, because 7 - 4 = 3. As DS used to write, "because it is the answer". And no amount of drawing apples or coloring circles is going to make it any easier. It's just going to annoy the pig.

    DS is currently up to about 50% on showing his work in 8th grade math, from the looks of last night's homework. He had approximately every other step written down -- and it was mostly legible, which is something.

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    #167261 - 09/11/13 02:20 PM Re: Math Homework [Re: ConnectingDots]
    erich Offline
    Member

    Registered: 11/11/10
    Posts: 97
    Loc: Illinois
    If problem solving is just procedural, like 8th grade algebra or anything easier, then "show your work" is not that critical. My DS often skips a few steps here or there, where he is used to the mental math.

    But "show your work" becomes very important when kids start working on geometry problems. The thinking is no longer step-by-step. You really have to build the logic network by writing it out clearly.

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    #167274 - 09/11/13 03:41 PM Re: Math Homework [Re: erich]
    puffin Offline
    Member

    Registered: 12/11/12
    Posts: 2035
    it is a skill you will need later but why learn it before you need to.

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    #167279 - 09/11/13 04:09 PM Re: Math Homework [Re: ConnectingDots]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3294
    Loc: California
    Teachers would probably do everyone a favor if they instructed students to write solutions in a stepwise manner and then gave an example.

    I have no idea how one would do this for 7-4=3, barring drawing 7 circles in step 1, repeating in step 2, crossing 4 of them out, and finally numbering 1, 2, 3 in the remaining circles. This seems silly, however.

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    #167293 - 09/11/13 05:16 PM Re: Math Homework [Re: ConnectingDots]
    MumOfThree Offline
    Member

    Registered: 04/07/11
    Posts: 1689
    Loc: Australia
    Oh but Val that is EXACTLY what they want...

    Dad22, beautiful explanation!

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    #167391 - 09/12/13 09:50 AM Re: Math Homework [Re: ConnectingDots]
    blackcat Offline
    Member

    Registered: 05/23/13
    Posts: 2154
    In our school, 7-4=3 would be shown as a "math mountain" with little circles drawn on both sides. All the teachers are very serious that the kids be able to show all their work, even for the simplest addition/subtraction problems. The curriculum is "Math Expressions" which I hear is a good math curriculum, but not for those kids who don't like showing work.

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