we're doing horizons k math w/ tucker (he's 4 1/2). my thoughts w/ math for him were for him to see that, for example, 4 apples plus 5 apples equals 9. anyway, we never got that far. he looks at the problem, looks up, and gives me the sum. so i tried for a few weeks to get him to look at a number line, and he will look at it, but when it comes to solving the addition or subraction problem, again, he looks up and then writes the sum without 'solving' it on the number line, or counting on his fingers, or anything.
i guess i'm going on my experience w/ higher math and the difficulty i had comprehending it as a teenager. i want him to have a good solid knowledge base of the 'how' math works so that he doesn't get frustrated later on. in your experience or research do you find that kids that seem to get easier math concepts continue to do well in later, more complex subjects?
oy. the second guessing myself is killing me.
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It's entirely possible that he knows how addition works (or subtraction, etc.), but that *you* don't know his method of figuring out the sum. He might not be able to put it into words right now. But he must have a way of figuring it out that doesn't involve finger counting or a number line. Mine does math in his head a lot, and I have no idea how he comes up with the answers. I do show him things like proper notation so that if he is asked to "show work" for any reason, he will be able to do that. For instance, he knows how to do carrying and borrowing, and can write the problem and answer in a way that would make sense to a match teacher. He can also solve the problem without writing everything down on paper. The only reason I show him the accepted notation is so that if he is ever asked to show the work (we're homeschoolers and need to have "evaluations" once a year), he will be able to do so.
As your child is a few years younger than mine, I wouldn't force him to learn notation or force him to do the figuring in a certain way. It sounds like the way he uses is working fine for him now. When he gets a little older, you can introduce ways of showing his work, but for a lot of early math there is no need to do this.
Kaya is four and has been doing math like this for about a year now. She never really needed counters, used her fingers or a number line. She knows the basics of what a number line is and how to "jump up or down", but she prefers to just do it in her head.
In my opinion, when a kids "gets it" in their own way, they learn it more solidly.
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I used to have the same fears with my eldest, until I asked her for detail about how she was figuring the problem out. Turns out she can "see" it in her head. She's 8.5 now, and it seems to be working for her. . . She'll write a complex problem out just like I would, but instead of starting to work it out on paper, she'll just look at it for a bit and write the answer.
I have been telling her for about a year that she has to show her work sometimes, though. At some point she is going to be subject to testing, and she has to know what *they* are looking for, too. She thinks it's funny how slow *our* way is
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Jennifer
Mom to 3 daughters
9, 7, and 4
How does he do if you take out the spatial (apples) assistance in the equation?
I don't have horizons but often math books do double duty. They show the picture of 4 apples next to 5 apples and then they add in a line graph or counters.
How does he do if you just write 4+5? Does he quickly present the answer or does he find a tool? Fingers, counters, etc.
Some children are just profoundly gifted in something and how they get there is, and always will be a, mystery. They'll never be linear, they'll always "see" the answer, not the course.
I am lucky in that my mother is a gifted coordinator for our county. When I asked her about it, she did a little research for me. After talking about it, we decided to let him do it his way - because he is OBVIOUSLY 'getting' it. I have also taught him the writing it down part - although he really doesn't care to do it that way at all. He knows how - and it has helped visually a little with carrying/borrowing - but he still would rather do them all in his head.
How does he do if you take out the spatial (apples) assistance in the equation?
How does he do if you just write 4+5? Does he quickly present the answer or does he find a tool? Fingers, counters, etc.
horizons has pictures; i print off math worksheets for him to do for fun (he actually thinks of math as something cool to do ) and they just say "14+5=_________"
he does them all the same way.
thanks for everyone's replies. i second guess myself so much -- it's really nice to have this forum, and you terrific mamas, to ease my anxieties
Blake does that too. He's doing Horizons math too. He never used the number lines just looks up and then says the answer. It's nice to finally have a kids who "gets" things.
Justin does this as well. Last night, for example, DH had 8 little mints. Justin said "how many do you have? Do you have four so we can each have one?" and DH said "no, I have 8." Justin said "oh good, we can each have two!"
Math is a different concept than English... knowing A WAY to do it is the goal. It does not really matter what the way is...Justin certainly did not drag out manipulitives or write out a division problem, but solved it "in his head."
I think he's on the right track!
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~Michelle
Christian homeschooling mama
to a Jumpin Bean (1/01)
and a Pumpkin Head (4/03)
Do you have cusinaire rods? I like the idea of them being able to see exactly what's going on, and then later they can put that knowledge on paper. That's why I thought Miquon would be good for my ds, because it doesn't seem as "dumbed down" as a lot of the programs.
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Ann
mommy to Morgan Phillip 5/24/02
and Elisha Nicole 5/10/05
and Bethany Alyssa 1/5/08
I need a picture of Bethany and Dannielle's dog Sugar.
i'd be curious as to how much he does understand.With some of my children as soon as they had the four basic operations down we moved on.heres some links to some cool sites.... www.picciotto.org/math-ed www.rightstartmath .com I use the math games alongside the miquon stuff.We love the al abacus! If you have a relly deep thinker this place is nice.We've used calculus for kids alot.http://www.shout.net/~mathman/
i'd be curious as to how much he does understand.With some of my children as soon as they had the four basic operations down we moved on.heres some links to some cool sites....
me too --- thanks for the links. i'll check them out!
After talking about it, we decided to let him do it his way - because he is OBVIOUSLY 'getting' it. I have also taught him the writing it down part - although he really doesn't care to do it that way at all. He knows how - and it has helped visually a little with carrying/borrowing - but he still would rather do them all in his head.
Military wife of a deployed soldier. 
--- thanks for the links. i'll check them out!
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