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Students master the multiplication tables by practicing until they can answer immediately. Next, students learn up to 4-digit by 1-digit multiplication with mental carryovers.What do you think?
Interesting post on the subject of mental maths here.
Saturday, February 16, 2013
mental math question
Kumon asks kids to do multi-digit multiplication problems without writing down any of the 'carried' digits:
Interesting post on the subject of mental maths here.
Interesting post on the subject of mental maths here.
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It was the mental math that killed me at Kumon. I couldn't hold it all in my brain to get through level D (long division) when the numbers were large and in the middle, making it difficult to know whether to round up or round down.
I can't keep numbers in my head at all, even phone numbers. I would have failed at this...but, it would have maybe been good to try to train my brain this way. Maybe I would have been a little better than I am.
I presume they are trying to develop working memory, a very important thing. However, there are a lot of indications that working memory is something you're born with. So, pushing too hard in this regard is likely to lead to frustration and rebellion. I'd go very gingerly on it. If the student is able to pick-up on it great! If not, meh, you do what you can...
My nephew is really good at this. Our problem with him is the opposite; he refuses to write anything down and show his work.
Such a simple carry isn't much of a working memory challenge if you do the calculation correctly, where "correctly" means very quickly and automatically. Any slight dysfluency, though, and you have a working memory challenge. This doesn't train your working memory; it tests your automaticity.
The Japanese (as in "Kumon") are big on calculational fluency. A girlfriend of mine in college had been a Japanese regional soroban (abacus) champion. The physical soroban was like training wheels for her, needing to be removed once she reached a certain level of proficiency.
We would be shopping for groceries, and she would decide to compare the per ounce price of two different brands. Her eyes would defocus and the fingertips of her right hand would twitch. She was flipping the beads in her mind. After a second or two, she would read the answer, her eyes would come back into focus, and she would resume shopping.
It's like any skill -- it comes more easily to some than others, but everyone would get better at it with practice.
Just depends on how much practice you want to put in!
I'd guess that kids who are taught this way get LOTS more practice and voila! they seem to be "born that way."
"4-digit by 1-digit multiplication with mental carryovers."
I read this to mean what we all had to do in grade school; track how many digits to carry over to the next column without having to write down a little number on top. I did not read this to mean that they had to do the whole calculation in their heads.
Fast mental math can be fun, but it's not necessary. Most people can easily divide numbers by two because it's a left to right thing. You can then easily multiply any number by 5 by adding a zero at the end and dividing by 2. With a little practice tracking decimal places, you can do this for lots of numbers.
I'm really bad at keeping numbers in my head. I find that if I can see the numbers on paper, I can do much more in my head. If you ask me to mentally divide 347 by 23, I'll immediately lose the numbers. If you write it down and I can look at it, I can do it. Perhaps not exactly, but I will get you to within 2/3 digits quickly, more, if I'm given extra time.
I like to find fast mental techniques that go from left to right. At worst, you get one digit accuracy. Maybe with a little concentration (and writing down numbers) I can get two or more digits. Another technique I like to use is to round one of the numbers and then correct up or down. That also gets me at least one or two digits quickly.
When I was in school (pre-calculator days) we had to interpolate from tables in the back of the textbook for things like trig functions. We used to have interpolation races. It's amazing how easily you can get accurate numbers to within one-tenth of the interpolation range.
This is all very nice, but not necessary unless you were looking at my son's old 5th grade Everyday Math class where bright kids still didn't know the times table.
My son showed me the tip calculator on his phone today. He had a mental race with his girlfriend's phone at IHOP today to determine the tip (to the penny) and he beat the phone. Years ago, I was really worried about how Everyday Math might affect that ability so I had to work on it with him. Don't they call this number sense?
Heh, no, they call it unnecessary! There's that phone there to do it for him.
Just like you don't have to really know any content, because you can always google it.
Is that called internet sense?
Assuming the availability of a pencil and a napkin (not a calculator), this skill is not necessary. But a certain amount of it is a good thing because it does exercise working memory in a slightly different way than we usually use it.
The trick to doing these is to go from left to right. Yo don't try to do the paper and pencil algorithm in your head.
Developing this skill through Kumon has helped my immensely in his regular 7th grade course work. Because he can do this part in his head, he can spend his mental energy puzzling out just what his next word problem is trying to get out of him.
It's possible to finish kumon math program(A to O) in 1 year? I have 20 year and dispose of 7 hours daily and 2 hours on weekends to study.(sorry for my english)
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