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DS8 can answer questions, but can't tell me how


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DS8 is finishing Singapore PM 2B today. On his review, he is doing word problems, which he likes. He can tell me the answer, but he cannot tell me how he got the answer. He can't even tell me if he is adding, subtracting, multiplying or dividing. He says he just "knows" the answer. I think he knows how to do it, but he doesn't know how to write down what he did. Instead of thinking of 26/3, he says it is a multiplication problem because 3x8=24. But then he couldn't tell me how many were left over. He is probably (according to the school district) gifted in math, so I don't know if it is just that he can figure it out in his head but doesn't know how to write the equations or what. Help!

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It sounds like he has visual-spatial (VSL) gifts :)

 

I'd keep trying to talk through what he did - maybe ask him to teach you how to do the problem because you're not sure how to do it ;). Maybe not all the time with every single problem, but I'd encourage him to explain (orally is fine for now, IMO) on a regular basis. (In my view, which may differ from other people's views, I wouldn't really worry that he doesn't understand the math as much as he may need practice "translating" from the spatial side of his brain to the sequential, language side, practice that is really important and will pay off in the long run.) More complicated problems may be easier for him to explain his process compared to simpler problems for which he can't "see" what someone else wouldn't understand.

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Totally agree with wapiti. I have a kid like this. It will definitely cause problems later if he doesn't learn the skill of translating to expressions/equations. I started not by asking him to do it but by asking questions of him. Did you multiply or divide? Did you first add or subtract? He often (most of the time?) could not answer, but I would tell him how I got the answer and then flip it around whenever possible to verbally express the different ways you could solve that problem. Lots of seed planting...

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Totally agree with wapiti. I have a kid like this. It will definitely cause problems later if he doesn't learn the skill of translating to exp<b></b>ressions/equations. I started not by asking him to do it but by asking questions of him. Did you multiply or divide? Did you first add or subtract? He often (most of the time?) could not answer, but I would tell him how I got the answer and then flip it around whenever possible to verbally express the different ways you could solve that problem. Lots of seed planting...

This is what I do with my child like this. He is much better at 10 than he was at 8, if that helps. He was adding up rows of single digit numbers in his head at the age of 5 and was unable to explain how he did it - he just could. In the earlier years, his math ability outpaced his verbal ability. His verbal ability has caught up, and he can explain his processes now. He is also helpful in explaining math concepts to his brother and sister because he loves to talk and doesn't mind helping others. He will often have a different "take" on math than I do, so we make a good team. :) It just took a bit of time for his abilities to synchronize.
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I have one of those sorts of kids. As a toddler, she could look at a group of objects and just know how many there were, without actually counting them. I get the same sort of answer from her now about math sometimes -- "I don't know how I did it; I just did." She needs training in the processes for when she hits things that aren't just obvious, so I do help her break them down into steps; I don't care so much *what* method she uses, just that she has one, and one that is more than "I just knew it."

 

Studying Latin has helped this child immensely, because it's taught her to work through a process when the answer isn't immediately obvious.

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Banjo, when my dd was that age/stage, I tried to slow down and figure out how she was thinking through the problem. We'd draw it out on a whiteboard to model her thinking. There's usually more than one way to think through a problem. The *trick* is to figure out whether they got there in a way that will *consistently* give them correct results, or if it just happened to work for that one. And *usually* what I found was that her mind had leaped to some later concept. So you think ahead to the way they might explain reducing fractions in a later level or in a pre-algebra class and you realize OH, that's why he's thinking through it that way. Then you just go ahead and draw the diagrams and explain it with the more complete presentation to give words to what his brain has intuited and figured out.

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DS is like this, but I'm a very sequential thinker. So when he asks me if he has the right answer to a multi-part problem, I have to tell him to slow down so that I can figure out the answer step-by-step-by-step. 95+% of the time, he's correct. Drives me nuts that he cannot explain how he got the answer, but that's the whole Gestalt vs. sequential thinking thing.

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