Conference moira::parenting

Your description of the problems he is having is a good one.  It doesn't sound
to me that his problems have anything to do with using or not using calculators
or memorizing the times table.  It seems to me that he simply doesn't
understand how long division works (or possibly any division, for that matter).
In my opinion, it's really hard to go through the mechanics of something
without having a decent understanding of why it works.

Perhaps you could take an approach of "zeroing in" on the correct answer, and
then show that long division is a way of doing that.  In your example:

  ------
4 ) 397

4 x 90 is less than 397, 4 x 100 is more than 397, so we know the answer is
90-something.  (Or is that a Boomer TV show in the 2050's? :-)  You can discuss
how, for example,  (4 x 93) = (4 x 90) + (4 x 3), if necessary; this is pretty
easily shown with a diagram.

So we take off the 4 x 90 and figure out the rest:

397 - 360 = 37

  ----
4 ) 37

4 x 9 is less than 37, 4 x 10 is more than 37, so take off 4 x 9 and see what
we have left:

37 - 36 = 1  which is less than 4.

Adding everything up, we have 90 + 9 = 99, with 1 left over.

Maybe some approach like this might be helpful.

						Brian

    Does the school offer a tutoring program?

    We work backwards.  Comes from being a switched lefty for me, but who
    knows?  Try what times 3 (or whatever) = 15, type of questions.  It
    took me years to work things any other way, and we weren't allowed
    slide rules (as if I could have used one) and calculaters weren't
    invented when I was in school.  Anyway, Carrie seems to be catching on,
    with that and the point that division is a short cut for subtratcion, as
    multiplication is a short-cut for addition.
    
    meg

    Patty,
    
    I could never get fractions, myself.  I can remember my Mom and
    teacher having conferences over my teacher's frustration.  My Mom
    would make paper "pies" and cut it into separate peices trying to
    give me visual aids.  Still nothing got through for the LONGEST
    time!
    
    And to tell you the truth, I have totally lost my multiplication
    tables after years of using a calculator.  I have to do the same
    thing as Chris does.  Either multiply by five or 10 then do the
    add and subtract.  I think you are at least partially right about
    the calculator.  
    
    I can't offer any advice on correcting the situation, but certainly
    will stand as an example of how bad it can get!   :-)
    
    						cj *->   

    Put an ad up for a college student as tutor either at the
    local library or at a college library.  Your child might
    respond better to a "third-party".  I've already decided 
    that I WON'T be teaching any of my children to drive,
    because they know everything already.

    My daughter (age 9 grade 4) is having the same difficulties with her
    division as well, for pretty much the same reason.  Her multiplication
    is weak due to the fact that she too was allowed to use a calculator.
    
    We now have her tutored once a week for about 1/2 hour.  I spoke to her
    tutor (a teacher at her school) who told me that very often it is just
    a matter of pinpointing what "trick" she needs to use to help her with
    both her multiplication and division.  She is working with Heather to
    figure out what works best for her, and hopefully things will just snap
    right in place all of a sudden.
    
    In the meantime, the tutor is well worth the money, as we find having
    an unbiased 3rd party tutoring her works best (dad and I tend to get a
    little impatient sometimes when she can't grasp a concept)
    
    Good luck
    Rosemary

    
    Thanks for the suggestions!!  Though, Brian, I have to admit that you
    sent my head spinning a little (-:  That's probably something that's as
    clear as day for Chris!!
    
    I spoke with his teacher, and she was STUNNED!!!  She says he does FINE
    with classwork, no problems at all, seems to know his multiplication,
    does all his division as quick and accurate as anyone else.  HUH?!?!? 
    WHO is she talking about?!?!
    
    A few things we found out .... in school, the teacher has written, in
    minute detail, every single step, and where to put what numbers and how
    to figure it all out.  In class he can reference this on the board.  He
    was SUPPOSED to write it down - so she's going to make sure that he
    does.
    
    In class, they work in groups of 4, and she suspects that he may also
    be getting "help", or at least getting "unstuck" from the other kids -
    she's going to pay more attention and let us know.
    
    THIS was interesting, with the times tables.  He knows his tables zero
    through 5, and there's some trick for 9's that he knows, and tens are
    easy.  So, she says he only 'doesn't' know 6x6, 6x7, 6x8, 7x7, 7x8 and
    8x8.  Because with all the rest, you can flip them around to fit into
    the tables you do know.  Getting that point across is a bit of a
    struggle, but I think he's starting to get it ... 
    
    I guess I'm lucky - I'm too disorganized to remember where I put the
    calculator, so I've been forced to remember my basic math (-:
    

>>    Thanks for the suggestions!!  Though, Brian, I have to admit that you
>>    sent my head spinning a little (-:  That's probably something that's as
>>    clear as day for Chris!!

Sorry, I had hoped a quickly whipped up example might be helpful; obviously it
was too quickly whipped up.

My point was intended to be: I think it is significantly more important to
understand what you are doing in a math problem than to memorize tables and
techniques.  If you memorize, and forget a part, it's gone; if you understand,
you can reconstruct the part you forgot.  This is the basis for the math
curriculum at my daughter's school, and it's one of the reasons we chose the
school.  There has been some controversy regarding these approaches, but I
personally think they are very good.

I was suggesting that perhaps Chris might benefit from having some emphasis
placed on WHY you put this number here and that number there in a long division
problem; I would expect difficulties with multiplication table memorization to
lead to questions about WHAT number to put in those places.  Your description
sounded to me like confusion about the WHY part; perhaps I misinterpreted.

						Brian

    
    Brian,
    
    No ... I think you hit the nail on the head.  Chris definitely doesn't
    have a CLUE why he's doing what he's doing - and I'm not even sure he
    really understands WHAT he's doing.  I'm having a hard time getting
    through to him, because I DO understand it, and he and I are just
    thinking completely differently at this point.
    
    At the suggestion of a tutor, we're going to sacrifice a box of
    cheerios (IF I can keep the 2-year-old out of them (-;), and sit down
    and make groups.  Multiply the groups, divide the groups, add the
    groups, subtract the groups, and try to get the whole concept together. 
    Show him that division and multiplication are just shortcuts for
    subtraction and addition.  SHOW HIM what it means to divide 9 by 3, to
    divide 10 by 3, and why you can't "borrow" and hoping that this will
    all make it a lot clearer.
    
    Working with estimations is something that always helped me "sanity
    check" my math.  he's got no clue about estimations either - maybe the
    cheerios will help that as well.
    
    We'll move on the coins later ... when we get tired of picking lint out
    of the cheerios, and as something more "fun" to work up to.
    
    We're also struggling with a lack of confidence, so the tutor suggested
    we keep the numbers SMALL so that he'll have more successes and be able
    to grasp the concept better.  And, Brian, I'm sur that your explanation
    WILL make more sense to him, since mine, I may as well being speaking
    Russian to him.  
    
    Thanks - I'll keep you posted!!
    
    Patty

    Have you tried flash cards?  Maybe a 15-minute drill on his times
    tables -- I always thought you had to know how to multiply before you
    could divide (ask any amoeba :-)).
    
    Don't know what Chris' interests are, but my youngest brother responded
    very well when my mother bought him a bag of 100 toy soldiers, and when
    he finally got 100 on his times tables, she gave him the bag of
    soldiers.  I'm sure you've tried incentives....
    
    My son is only in 2nd grade, but I spend time with him going over the
    basic "whys" of what he's doing.  I always thought I stunk at math,
    until I started doing this pretty regularly, and he started getting
    better grades on his math tests!  (He does count on his fingers,
    though, which makes me crazy!  I don't say anything, though.)

    To help my daughter with her times tables, we played a version of
    "War".  She had a pile of cards and I had a pile.  I gave her a
    5 second handicap.
    
    We'd each throw down a card, then she would multiply them and blurt
    out the answer.  If she didn't know the answer, or blurt it out within
    5 seconds, then I did. I always said the entire equation so that she
    would get the association of the two numbers with the answer.  So I
    would say, "Six times eight is 48!"  The winner was the one with 
    the most cards in their pile.  The mission was to make mom lose
    "big time" by not having any cards in her hand in the end.
    
    Diana

    Diana I love that game!!  I'll have to try that .... unfortunately,
    I'll have to do it when Jason is locked in a closet because he LOVES
    cards, math, and beating the pants off of mom!  Chris is *MUCH* less
    competetive.
    
    We went through a lot of numbers, with pennies.  It seemed to help. 
    Concentrating on smaller numbers, gave him the confidence he needed. 
    I'd group them together, he'd move them around to solve different
    problems.  We take 24 pennies (for example), and I'd ask him how many
    piles of 4 I could make, how many piles of 6, 8 etc.  I'd break out 36
    pennies into piles of 6, and ask how many pennies there were
    altogether.  He'd "get" an answer, then I'd have him count them to be
    sure.  It really went a **LONG** way to helping him understand the
    whole concept.  More or less a light went on - a little dim at first
    (and school vacation is making it tougher to keep on track), but I
    think he's getting the idea.
    
    Then I would tell him to pretend the pennies were dimes, and we get
    into the whole "add a place, add a zero" concept, which he FINALLY got
    (we've spent hours on that before!!).
    
    I think that touching the piles, and moving them around, and keeping it
    all fairly simple, made a big difference for him.  Clearly we're not
    just "done", but I think he has a better grip on the principles of it
    all.  And now when he's thinking out a problem, he relates it to the
    piles of pennies, so if it helped in that way, all the better!!
    
    THANKS!!!!!!!! (and I can't wait to whip Jason's but in a game of war!
    (-;)
    Patty

Re: .12

Those activities you described sound WONDERFUL!  It sounds like Chris has made
a lot of progress in understanding how multiplication and division work.  Good
for you!

						Brian

    My daughter Maresa, age 9-1/2, and I play the following game for both
    addition and multiplication facts.
    
    We call it "The Number Game."
    
    Two person game.
    
    Person 1 thinks of a number between 1 and 100.
    
    Person 2 asks the following questions:
    	1)  Even or odd?
    	2)  Above or below 50?
    	3)  Total (for addition) or product (for multiplication) is:
    
    Person 1 answers.
    
    There are only a few possibilities for each, and Maresa can be further
    challenged by asking to name all of the numbers that meet the criteria.
    We switch off and take turns thinking of the numbers.
    
    Example:
    Number is 35.
    
    Clues:  Odd number; product 15 - only two possibilities - 35 or 53.
    	    Odd number; sum 8; possibility of 17 or 35.
    
    When Maresa thinks of the number, she doesn't say if it's above or
    below 50.  I've almost gotten her to that point as well.  I try to get
    her to name all of the numbers that meet the criteria.
    
    Ex.  Number 35
    	 Product 15  - only possibilities are 35 and 53.
         Sum 8       - possibilities are 17, 35, 53, and 71.
    
    Sometimes I'll combine the clue and say that the number is odd, with a
    total of eight and a product of 15; then she has to think a bit more to
    come up with that answer.
    
    We just came up with this game one day, and Maresa likes it so much, I
    have to ask her to stop playing, especially on drives over an hour.  I
    get bored.  Now she wants to start on 101-200 for the numbers...
    
    Catherine
    
    	                                                               

    
    That sounds like a great game!!
    
    Actually, a couple days ago I bought a card game at Learn N Play, that
    has ~45 cards.  Each card has 4 different numbers on it.  The game is
    called "24" or something like that.  The object of the game, is to
    reach "24" by combining the numbers, in any way that will get 24.  The
    first to get an answer "wins".
    
    A card might have the numbers 7 2 1 9 on it.  An answer might be;
    
    ((9x2)+7)-1=24  
    
    It's a lot of fun, but boy, some of them are hard!  They don't
    necessarily go in any order, and you can only use each number once.
    
    AND, Chris got 105 on his division test .... so something must have
    worked!!  (-:  (100 +5pt bonus question).
    
    THANKS!
    Patty

    My son too was having a lot of problems with math because he had not
    memorized their facts.  So, I signed him up for the Kumon math program.
    
    This is a Japanese method of tutoring chidren in arithmetic.  Your
    child will be tested and he will start where he is doing well (not where his
    class is).  So, he might start with addition and subtraction.  
    
    Then he will have worksheets seven days a week to do at home.
    It's a lot of drill.  After nearly getting a D in 4th grade arithmetic
    last year, David got an A- on his last 5th grade report card.  I
    attribute it to the constant, daily practice he gets in Kumon.
    
    The parents check the work every night and keep a log.  The
    teacher sees him twice a week.
    
    I live in Westord, MA.  If you'd like, I can try to get you more
    information.
    
    The program costs $70/month.
    
    PS Long division is hard no matter what.  They are teaching a new way
    to do math that hopelessly confused my son.  I finally taught him the
    old-fashioned rote way, and he was doing it well in a few minutes.
    
                                 

    If you have more information on this, I'd be interested !!
    
    ESPECIALLY after last night, and having Jason-my-math-wizard-son,
    throwing an absolute fit trying to figure out when to/not to borrow
    tens, in subtraction.  Sigh.  I'm starting to take this personally (-:
    
    -Patty

    My daugther Jessica is in third grade this year.   She has been tested
    by doctors for ADD and was considered to be on the borderline.  No
    medication was prescribed.   She has been receiving SPED services for 
    speech, math, reading, reading comprehension since kindergarten.  
    
    This year her class has really started getting into more math concepts.
    She is expected to do 40 addition fact problems in 2 minutes.   The
    first time she took the test, she probably got 12 of the problems
    answered with only 2 wrong.   As the year has progressed, she has
    increased the amount of problems that she has completed, but the number
    of incorrect problems keep growing.   Yesterday she brought home a test
    that had only 30 problems answered, but more than half of them were
    incorrect.  At this point, I feel what she is doing is she is striving
    to get all 40 problems completed, and she is not even noticing what the
    problems are, she is just guessing, trying to complete the 40 problems.
    The majority of the other kids in her class has moved on to subtraction
    because they can get 40 problems correct in 2 minutes.  We also use
    flash cards everynight for 15 minutes to try and help her learn the
    addition facts. During these 15 minutes, we go over and over the
    problems that seem to give her the most difficulty, such as 8+7, 7+6,
    5+7.   Also she is being tutored 1-1 with a teacher at the school for
    her math weakness.

    When she had her evaluation back in January for her IEP, it was
    documented in the IEP that she needs "THINK" time.  If she is asked to
    answer a question, she can not give the answer right away, but if she
    is given time to think about it, then she can answer the question
    correctly.   The teacher has even mentioned that she needs this "THINK"
    time on more than one occaision.  
    
    So, I called her teacher up to talk with her about my concerns that
    Jessica  seems to be getting worse instead of better, and that perhaps
    the math expections should be modified.  Her teacher told me that she
    did not want to modify the math expectations for her, because if she
    doesn't know these facts, then math concepts will become harder and
    harder for her.   She said that she was concerned as well about Jessica
    seeming to get worse instead of better, so she had her aid take Jessica
    to another room and work with Jessica using flash cards. Jessica was
    able to get most of the answers.   She seems to have a problem with
    short term memory and confidence.  So instead of having Jessica take
    a two minute time written test, she will be tested orally.  Jessica's
    problems with processing information seems to be related to her
    "short term" memory.  

    So, I was wondering if anyone had any suggestions or knew of some
    literature about the "short term" memory and what I can do at home
    to help improve the short term memory.
    
    Thanks for any info.
    
    Sarah