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How Japanese Kids Learn To Multiply

magicalmaths.org

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Re: How Japanese Kids Learn To Multiply

#51

Post by solox3 »

talmand wrote: post #28
gklitt wrote: post #5

Earlier quoted context omitted.

Agreed. I went to Japanese elementary school (in college now, so within the last 15 years) and didn't learn this lines method ever. What I found greatest about the Japanese method of learning multiplication was actually the method for learning single-digit products. The Japanese use a system called "kuku" (translated, "9 by 9") which involves memorizing a rhythmic chant that goes through the entire multiplication tab…

It isn't that different, in my American elementary school I had to memorize the multiplication table up to 12x12. But I don't recall anything about the English language being a hindrance so your example is interesting. There doesn't seem to be that much fewer syllables in 7x7=49 in English but I'm assuming that as the numbers increase then the syllables get worse in Japanese as opposed to English? For instance, 148x3…

Using your example 7 x 7 = 49

seven [2] times [1] seven [2] equals [1] forty-nine [3] = 9

七[1] 乘[1] 七[1] 如[1] 四十九 [3] = 7 (without using primary school mnemonics)

七[1] 七[1] 四十九 [3] = 5 (using primary school mnemonics)

Even at that primitive level, a change of language can give you a 23% and 45% speed-up of basic arithmetic operations, respectively.

Re: How Japanese Kids Learn To Multiply

#55

Post by Jtsummers »

graeme wrote: post #21
patio11 wrote: post #7

This is a method that is occasionally taught in Japanese classrooms, but one could also say that of chunking or the traditional long multiplication algorithm. Want to know the real super-secret-special Asian magic math sauce? Practice. (But if calling it kungfu math lets you teach it is a US classroom and get precious instructional hours by calling math cultural studies then by all means Orientalize away.) [Edit: I h…

I tutored a student who counted on his fingers. He was 21. Within 6 lessons, using Khan Academy, I had him adding four digit numbers in his head, multiplying large numbers, and doing algebra. He would learn a technique from me or the video, then apply it in practice drills, then review at the next lesson. Total instruction time was 12-20 hours. I think he did a bit on his own. I concluded that no one had actually che…

> I concluded that no one had actually checked to see if he could understand math. North American students hardly try calculations now; they're given calculators at a very early age.

That was something that caught me off guard a few years ago. In 2008 I was considering becoming a teacher (high school math/technology). For various reasons I chose a different path, but I sat in on some courses at a friend's school to get a 'day in the life of' feel and an opportunity to talk to other teachers. One class caught me by surprise. It was a 7th grade math course, essentially pre-algebra. However, the students did everything with calculators. The lesson that day was on interest, simple and complex, a way to try and tie the concepts down to real world examples. The students did everything with calculators, not one was using pencil and paper to work out the math (though they all recorded the steps they'd done on the calculators). Talking to the teachers, that was how their curriculum was setup, not just a one off case.

That wasn't what turned me away from teaching, but left me confused about how things had changed so much in the 15 years or so since I'd been in those seats.

Re: How Japanese Kids Learn To Multiply

#56

Post by gklitt »

talmand wrote: post #28
gklitt wrote: post #5

Earlier quoted context omitted.

Agreed. I went to Japanese elementary school (in college now, so within the last 15 years) and didn't learn this lines method ever. What I found greatest about the Japanese method of learning multiplication was actually the method for learning single-digit products. The Japanese use a system called "kuku" (translated, "9 by 9") which involves memorizing a rhythmic chant that goes through the entire multiplication tab…

It isn't that different, in my American elementary school I had to memorize the multiplication table up to 12x12. But I don't recall anything about the English language being a hindrance so your example is interesting. There doesn't seem to be that much fewer syllables in 7x7=49 in English but I'm assuming that as the numbers increase then the syllables get worse in Japanese as opposed to English? For instance, 148x3…

Yes, there are examples where the syllable discrepancy is a bit larger between English and Japanese, but I think you're right -- perhaps the syllable difference is not too big of a deal. Now that I think more about it, perhaps the actual advantage may be in the rhythmic nature of the mnemonic. By modifying syllable numbers for various products, the entire recitation gets a kind of rhythmic flow. (watch the video to see what I mean)

All I can say is that in my personal experience learning the multiplication tables in both languages around the same time, it was dramatically easier in Japanese. Perhaps the small reduction in syllables caused that, and perhaps the "rhythmification" was more responsible.

I do recall seeing a study somewhere that showed people who spoke Chinese were able to remember more numbers, ostensibly because each digit takes less syllables to speak in Chinese so the total syllables to remember in one's head is smaller.

Re: How Japanese Kids Learn To Multiply

#57

Post by boredguy8 »

symmetricsaurus wrote: post #6

The videos only show the technique using small digits. For the larger digits this method quickly becomes cumbersome. Latttice multiplication is much better for large numbers and deals with a lot of the carrying of overflowing digits which occurs in both normal and "Japanese" multiplication. http://www.youtube.com/watch?v=cijuPxHgZAA edit: spelling

yes, there are no '57 * 86' examples, which would be counting intersections for quite some time.

Re: How Japanese Kids Learn To Multiply

#58

Post by JPKab »

graeme wrote: post #21
patio11 wrote: post #7

This is a method that is occasionally taught in Japanese classrooms, but one could also say that of chunking or the traditional long multiplication algorithm. Want to know the real super-secret-special Asian magic math sauce? Practice. (But if calling it kungfu math lets you teach it is a US classroom and get precious instructional hours by calling math cultural studies then by all means Orientalize away.) [Edit: I h…

I tutored a student who counted on his fingers. He was 21. Within 6 lessons, using Khan Academy, I had him adding four digit numbers in his head, multiplying large numbers, and doing algebra. He would learn a technique from me or the video, then apply it in practice drills, then review at the next lesson. Total instruction time was 12-20 hours. I think he did a bit on his own. I concluded that no one had actually che…

Not trying to disagree with you about the crappiness of this student's education, or how sad it is that he counted with his fingers, but computation != mathematics.

I HATE the fact that American schools force students to do rote computation over and over again, with very little focus on the concepts behind the computations. I hated "math" until my 6th grade homeroom (not math) teacher took the initiative of writing high school level algebra word problems on the board, and not telling us how to solve them until after we attempted them. "A train going from St. Louis is headed toward L.A., and another train from L.A. is headed to St. Louis. they are going 40 mph, when will they pass each other" etc.

Suddenly, when the computation becomes a tool to satisfy an end, rather than the end itself, math becomes interesting.

Re: How Japanese Kids Learn To Multiply

#59

Post by scarmig »

hemancuso wrote: post #10

This does not teach you multiplication as much as it teaches you a trick to get the result of multiplication. I doubt anyone is transferring this abstraction that results in the answer into something they can do in their head or extend on paper to larger numbers. Teach kids to open the calculator app on their phone rather than to do this. No fast way to learn multiplication other than to practice it.

It's also algorithmicly identical to the way people are taught to multiply in American schools now, except it introduces a geometric isomorphism that makes it easier for people to understand what's going on.

Re: How Japanese Kids Learn To Multiply

#60

Post by ianb »

Someone wrote: post #14

This is a variant of http://en.wikipedia.org/wiki/Lattice_multiplication that does not make it as easy to carry tens a column to the left as that method does. I also think lattice multiplication makes it easier to understand for pupils why the trick actually performs a multiplication. So, I would teach them lattice multiplication instead.

Another approach: http://en.wikipedia.org/wiki/Grid_method_multiplication

Of course it's all multiplication, and all essentially the same thing. I find the grid method the least notation-focused of at least these three, and so I think more accessible to assimilation. Maybe I'm biased, I didn't learn multiplication this way but found myself naturally doing it like this in my head and then was pleasantly surprised to find it had a name. It's also amenable to estimation.

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