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    #13303 - 04/08/08 11:44 AM Re: Question about algebra and radical acceleration [Re: Dottie]
    snowgirl Offline
    Member

    Registered: 02/24/08
    Posts: 361
    Just to chime in on the subject of drill and rote memorization, the most effective method may well depend on the preferred learning style of the particular child. According to Silverman's theory of visual-spatial learners (which, by her estimate, are about 30% of the student population), VSLs do not learn by drill and repetition, or rote memorization, but by seeing relationships, whereas auditory-sequential learners may need some repetition to reinforce learning and fare much better with rote memorization.
    http://www.visualspatial.org/Articles/appendc.pdf (or for a fuller discussion of VSLs and math, see http://www.visualspatial.org/Articles/mthstrat.pdf and *especially* http://www.visualspatial.org/Articles/algebra.pdf )

    Incidentally, on the local evening news the other night there was a segment about recent improvements in math in a particular local school. The school had switched to Singapore math, which, according to the news story, required less drill and used more visual representations. I know I've seen discussions of that curriculum on these boards, and I admit I don't know anything about it, but I did find the news story interesting.

    just my two cents--
    smile

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    #13313 - 04/08/08 02:08 PM Re: Question about algebra and radical acceleration [Re: Val]
    Lori H. Offline
    Member

    Registered: 05/26/07
    Posts: 982
    I recently bought an 8th grade Spectrum Math book since my nine (almost ten) year old son might try to take the Explore test next year and I was curious about what 8th grade math looks like. I also noticed that it didn't seem very different from the lower level math books, so I now use problems from the 8th grade book when making up a math worksheet for him to do. He also uses Aleks middle school math online but he doesn't do it every day because he likes to do a variety of things. He likes doing multi-step word problems from a book called Calculation Capers for grades 5-8 and he did one on taxes the day I did my taxes. Some days we work on mental math which I think is good for a kid with handwriting issues. We have done math with decimals for years. He learned how to figure out 1 percent of a number by moving the decimal point years ago when we got a credit card that gives us a 1% rebate every time we use it that goes to him. It was easy for him to build on that knowledge. We also have a pre-algebra workbook that he sometimes uses.

    He likes doing a variety of math problems. He absolutely hates a worksheet full of the same type of problems. I like it that he does this because I don't have to worry that he needs to review anything.

    We just started reading a book called Painless Algebra by Lynette Long, Ph.D. but I think we will probably wait before really going more in depth with algebra because my son is more of a verbally gifted kid. He will probably learn all of the math vocabulary and how to spell the words correctly before he really gets into doing challenging algebra problems. I actually got the book for me because I was afraid that I wouldn't remember how to do algebra. He seems to like the book so far. He likes telling his sister that he is learning algebra.


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    #13314 - 04/08/08 02:18 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: Dottie
    I've found our homework also to be very non-rote. This approach might not be best for weaker students, and it never seems to be enough for the really advanced, but it definitely encourages higher level thinking skills!


    Hmmm. Could you give me some examples of non-rote that should be rote instead, Dottie? Aside from the math facts and spelling that I mentioned--which pretty much just have to be memorized--I can't even envision what you could be talking about that would be better as memorization than concept. What higher level thinking skills are involved? Analysis? Synthesis? Or just application of knowledge to solve the problem? (which isn't a whole lot higher on the pyramid than memorization...)

    As for the wacky word problems, I think those are always an issue for kids, but they're also the way math comes to us in real life, so I tend to take those in stride. I have a yard I want to fence and I need to know the perimeter, how much water does it take to fill this container, etc. It all comes with story-problem baggage. My DH hated word problems until he hit physics and realized that THAT was why they'd had all those words cluttering up his math books for all those years! LOL!

    _________________________
    Kriston

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    #13324 - 04/08/08 03:30 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: Dottie
    But the weaker students would surely benefit from more repetition in some basics of any of the math concepts (long division, fractions, etc).


    Well...I think it's like Texas Summer wrote some time ago: there are 2 sets of skills you need for math--the "tools," which are the rote knowledge of math facts, and the "concepts" which are more like the way things are done and why you're doing them. Two separate parts, and often two different ways of learning the parts.

    Repetition is usually required for memorization of math facts. In our case, DS6 has mastered virtually every part of the *concept* of even multiple-digit multiplication--that it's about multiple sets of like groupings, carrying, etc.--but he currently lacks the *tools* because he's not yet ready to memorize his times tables. He needs both to progress (or at least a good work-around until he does the memorization). Repetition would/will help him learn those tools when he's ready.

    OTOH, repetition was NOT necessary to help him with the concepts. He picked those up right away. Some kids can probably come to understand the concepts through repetition of the tools. But I don't think that this is most kids. I do think the way math concepts are usually taught is to have the class do multiplication problems ad nauseum and hope the child gets why things are done that way. But I do NOT think it is very effective.

    For example, when my father was a very young child, he could do multi-digit math problems of all sorts in his head, giving the answer the second you finished saying the problem. Wow, right? But he did it backwards, starting with the 1000s (or millions, or whatever) place instead of the 1s place. When he got to school, the teachers saw that he was using the tools "wrong" (never mind that his conceptual grasp was ideal and that he always got the right answer fast!), so they drummed it out of his head. He can't do it anymore. They focused on the tools, not on the concepts.

    For my part, I don't recall anyone explaining to me why we did math, say long division, the way we did. We were just expected to "follow the leader." The better you were at imitating the teacher exactly, the better your grade. When I got to calculus, I was a goner because we were expected to think, not to imitate, and I had no idea how to do that in a math class. It had never been asked of me before.

    Of course, these are non-NCLB examples--two old ones and one from home school. Maybe things in school are different now? I just still don't understand what, exactly, is different. Please forgive my denseness, but I really would like to know!

    K-
    _________________________
    Kriston

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    #13325 - 04/08/08 03:42 PM Re: Question about algebra and radical acceleration [Re: Kriston]
    incogneato Offline
    Member

    Registered: 10/25/07
    Posts: 2231
    Loc: up in my head.......
    Maybe the more successful students in your calculus class were homeschooled!


    hee hee hee hee

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    #13327 - 04/08/08 04:02 PM Re: Question about algebra and radical acceleration [Re: incogneato]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    LOL neato!!!!

    I do think things are different now in school. My children have been up and performing in front of their peers since kindergarten and have no fear of public speaking whereas I never did an oral report until 7th grade and about DIED to be in front of people for the first time. Also, in kindy last year, my DS now 7 was doing some pre-algebra type work!!! I asked the teacher about it and she said they were introducing the concepts at that age to get them ready for more difficult pre-algebra/algebra conceps later on. My DS10 has already done some algebra type work this year also. I don't believe I saw an "x" or a "y" until I was in 8th grade when I took algebra.

    I honestly think my kids are doing much harder work at an earlier age than I did (of course that was a long time ago so maybe I can't remember everything wink).

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    #13329 - 04/08/08 04:25 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    Originally Posted By: Dottie
    kids get very little repetition on any one skill.


    Oh yea this is soooo true. My DS10 has a math test pretty much every 4 days on some new concept. They move very, very, very fast in math. Luckily he catches on pretty easily and the teacher does do comprehensive tests every few weeks to make sure they are getting it, but there is virtually no drill involved. You have to move fast to keep up!

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    #13333 - 04/08/08 04:36 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    But WHAT is different? Can you give me a specific example? HOW are they making it conceptual? To be honest, what it sounds like is that they just aren't doing much teaching at all, either of tools or of concepts. Navel-gazing isn't teaching, and that's the impression I'm getting of it (albeit perhaps wrongly).

    I don't call word problems conceptual (and those have always been around anyway). Is there more to it than that?

    FWIW, DS6's workbook from 1st grade was no different than the ones we used when I was in school from what I could see. Not conceptual at all. Lots of repetition of the tools. I saw there were maybe more manipulatives in class than we used, but nothing else seemed significantly different. Certainly nothing "on its head" about the math he was doing. But that was only 1st grade, so I realize I don't know much here...
    _________________________
    Kriston

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    #13337 - 04/08/08 04:45 PM Re: Question about algebra and radical acceleratio [Re: EandCmom]
    kimck Offline
    Member

    Registered: 09/20/07
    Posts: 1134
    Originally Posted By: EandCmom
    Originally Posted By: Dottie
    kids get very little repetition on any one skill.


    Oh yea this is soooo true. My DS10 has a math test pretty much every 4 days on some new concept. They move very, very, very fast in math. Luckily he catches on pretty easily and the teacher does do comprehensive tests every few weeks to make sure they are getting it, but there is virtually no drill involved. You have to move fast to keep up!


    Do you know what curriculum it is? We are using 1st grade Everyday Math and it does have this kind of model. But it still seems very slow. And the spiraling! I swear it was after x-mas break when we actually got a NEW concept. I got a note today that it was a goal by the end of the year to have the kids memorize a small sub set of single digit addition. I'm quite sure we knew the whole addition table in first grade. I did go to an extremely kill and drill private Catholic school. We memorized incessantly without reason - all the presidents, countries and capitols, etc etc etc. So great for visual spatial me. crazy I'm saying this as a mathy person with a mathy kid that goes to a very NCLB test score focused school. This is a school that hired a full time teacher this year just to focus on bringing up math scores for the bottom third of the class.

    I remember sitting and learning long division trying to figure out WHY it worked. When I taught DS addition and subtraction with renaming I had to come up with a proof with manipulatives why this really worked. Once we did that, he was good to go. But before that, he didn't want anything to do with it. That and he can do a lot of 2 and 3 digit addition and subtration in his head.


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    #13338 - 04/08/08 04:51 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Thanks, Dottie. That helps. I see now. It doesn't seem like navel-gazing (smirk), and it does seem better than the old-school method overall.

    I guess I like the more intuitive start, but then I'd also want to make sure they drill sufficiently on the tools. I don't know why they can't do both. Neither is sufficient on its own, I don't think. Though 6 problems is a lot better than the 50+ we'd have to do...and none of that "do the last 10 that are hardest and skip the rest" stuff for us either. Ugh. That right there was enough to make me hate math forever. Calculus just put the nail in the coffin!

    A more conceptual tack would have appealed to me, for sure.
    _________________________
    Kriston

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