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How Japanese Kids Learn To Multiply

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Re: How Japanese Kids Learn To Multiply

#21

Post by graeme »

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 checked to see if he could understand math. North American students hardly try calculations now; they're given calculators at a very early age.

Re: How Japanese Kids Learn To Multiply

#22

Post by vog »

rossjudson wrote: post #3

Interesting in that it shows how geometry can related to mathematics, but very laborious when applied to larger numbers. Amounts to adding up the contents of each place in the numeric result one-by-one. The work involved is the sum of the output digits.

> how geometry can related to mathematics

Geometry is part of mathematics!

More generally, it's sad to see this attitude all over the place, as if geometry and drawing were somehow "less mathematical" than writing and symbols. Both, algebra/analysis as well as geometry, have their place in mathematics, and complement each other very well.

The same holds for creativity versus stringency, by the way. A theorem has to be proved (stringency), but how did find that proof? By aternating of stringency and creativity back and forth! And why did you ask the question answered by the theorem in the first place? Creativity and real-world problems (e.g. physics or economics)!

Note that the distinction between geometry/algebra is totally unrelated to the distinction between creativity/stringency. However, more often that not media associate math only with the algebra+stringency part, glossing over the other equally important aspects. This leads to a totally distorted image of the wonderful field of mathematics.

Re: How Japanese Kids Learn To Multiply

#23

Post by keithpeter »

badatmath wrote: post #16

32 year old Japanese here. I can unequivocally say I've never seen anything like this in my life. Possibly the younger generations, but I somehow doubt it, as people are pretty slow to adopt completely new teaching methods. Pretty cool though...

I have seen students from India use this method for small numbers and a partial sum method for larger numbers.

http://wsgfl2.westsussex.gov.uk/Aplaws/maths/multicultural/V...

Google 'Vedic multiplication'. Its all good because it is unusual here in the UK and it looks interesting.

Re: How Japanese Kids Learn To Multiply

#24

Post by Ntrails »

Jabbles wrote: post #11

Great. Now do it for 79*86.

realistically all this or any other process is doing is expansion and taking advantage of the commutative nature of multiplication.

(70 + 9)x(80 + 6)

70x80 + 9x80 + 6x70 + 6x9

56(00) + 72(0) + 42(0) + 54

Guess what - long story short you need to know your times tables. I don't see how the lines method is any easier than long multiplication, which in itself is not hard with a little time and explanation. If you can use the lines, or any other method, as a way of conveying what I did above - then you've succeeded.

Edit: Stars go to italics and I don't know the escape character

Re: How Japanese Kids Learn To Multiply

#25

Post by talmand »

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.

I agree, I don't see how this actually teaches how multiplication actually works. It's a clever method to avoid solving the problem the classic way of using a memorized multiplication table and breaking down the problem into smaller segments. I don't even see how this saves you time once you get up to speed on either method. The only difference is that with my old school way I can explain to you why I get the answer I calculated while this method doesn't seem to offer that ability.

Re: How Japanese Kids Learn To Multiply

#27

Post by badatmath »

keithpeter wrote: post #23
badatmath wrote: post #16

32 year old Japanese here. I can unequivocally say I've never seen anything like this in my life. Possibly the younger generations, but I somehow doubt it, as people are pretty slow to adopt completely new teaching methods. Pretty cool though...

I have seen students from India use this method for small numbers and a partial sum method for larger numbers. http://wsgfl2.westsussex.gov.uk/Aplaws/maths/multicultural/V... Google 'Vedic multiplication'. Its all good because it is unusual here in the UK and it looks interesting.

Yes, now that I recall, I believe this was a very popular topic in Japan a few years ago (I wasn't in Japan to see it first hand). It was referred to as "India-style multiplication," and some guy(s) sold millions of instructional books. http://math.hoge2.info/kakezan/pr04.html

However, don't think it involves the drawing of lines like in the post.

Re: How Japanese Kids Learn To Multiply

#28

Post by talmand »

gklitt wrote: post #5
cincinnatus wrote: post #2

This is cool but not a part of any standard curriculum in Japan despite the title.

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, 148x385=56980?

Re: How Japanese Kids Learn To Multiply

#29

Post by SonicSoul »

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.

calculating it the western way (by multiplying and adding each column) is also a trick. it also can't be done in your head with larger numbers. These are just different approaches. when multiplying small numbers (probably most of the time for average person) this may be a faster approach.
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