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How Japanese Kids Learn To Multiply

magicalmaths.org

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Re: How Japanese Kids Learn To Multiply

#91

Post by zainny »

tokenadult wrote: post #9

The more important difference between mathematics education in Japan and mathematics education in (say) the United States is how hard the problems are and the encouragement to pupils in Japan to try to figure things out for themselves. I put instructional methodologies to the test by teaching supplemental mathematics courses to elementary-age pupils willing to take on a prealgebra-level course at that age. My pupils'…

Timothy Gowers (mathematician, fields medalist) actually wrote about this phenomena quite recently as well: http://gowers.wordpress.com/2012/11/20/what-maths-a-level-do...

Re: How Japanese Kids Learn To Multiply

#92

Post by asdf333 »

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...

ditto. i am japanese and did not learn multiplication this way.

it was more through a sing-songy multiplications table nininga shi nisanga roku ..and so on..

Re: How Japanese Kids Learn To Multiply

#93

Post by niels_olson »

My sister-in-law is a Japanese school teacher. I showed this too her and she said she does not recognize it at all. My mom has a master's in math education and teaches at the local junior college. I'll let you know if she has any comment on this.

Re: How Japanese Kids Learn To Multiply

#94

Post by theyak »

tokenadult wrote: post #9

The more important difference between mathematics education in Japan and mathematics education in (say) the United States is how hard the problems are and the encouragement to pupils in Japan to try to figure things out for themselves. I put instructional methodologies to the test by teaching supplemental mathematics courses to elementary-age pupils willing to take on a prealgebra-level course at that age. My pupils'…

Teachers in the U.S. who expect students to struggle with math problems instead of just giving them answers after the student puts in the most minimal effort can get in big trouble for doing so. (Source: My math teaching career.)

Re: How Japanese Kids Learn To Multiply

#95

Post by shn »

it's hardly practical. Yes, interesting, but I would not use it at all. The way I know how to do multiplication "manually" is superior than this. You line up numbers on top of each other. Then you start multiplying first digit of the bottom number with all the digits of above number, from right to left and adding any carry over. You start writing the result on the same column you are multiplying. Then you add them all.

    123
    123 
  x______
    369
   246
  123
+________

  15129
That's what I learned in elementary school and have been using since then. It's interesting to know how others to do it.

Re: How Japanese Kids Learn To Multiply

#96

Post by wilhow »

This method does not convey any understanding of the problem. I'm not sure it's a good idea in the long run. It'll create a class of people who know how to solve a particular mathematical problem, but don't understand why.

Re: How Japanese Kids Learn To Multiply

#97

Post by signa11 »

shn wrote: post #95

it's hardly practical. Yes, interesting, but I would not use it at all. The way I know how to do multiplication "manually" is superior than this. You line up numbers on top of each other. Then you start multiplying first digit of the bottom number with all the digits of above number, from right to left and adding any carry over. You start writing the result on the same column you are multiplying. Then you add them al…

> That's what I learned in elementary school and have been using since then. It's interesting to know how others to do it.

well, i generally do it using a 'covolution approach' like this:

     45
   x 86
   ------
       0 (5*6 == 30) -> take the units place, and put '3' as carry over
      4  (6*4+8*5+3 == 47) -> take the units place, and put '4' as carry over
    36   (8*4+4 == 36)
-------------

   3640
-------------

with sufficient practice, you can multiply arbitrary 3 digits in approx 10-15 seconds or so ;)

[edit-1]: my formatting sucks, cannot seem to align stuff nicely at all.

Re: How Japanese Kids Learn To Multiply

#98

Post by sinker »

It's a neat trick, but the method doesn't do much to reveal why multiplication works as it does. Most students will just sit there drawing lines and counting intersections without understanding why it gives them the right answer. Memorizing a routine without understanding why it works is just one step above memorizing a table.

Re: How Japanese Kids Learn To Multiply

#99

Post by pm90 »

JPKab wrote: post #58
graeme wrote: post #21

Earlier quoted context omitted.

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 h…

Its kind of subjective though. In my schooling, when we moved from basic arithmetic to "word problems" as these were called (i.e which required you to formulate the mathematics yourself), I was completely lost and intensely dreaded the process. It seems a bit silly saying it, but at that time I didn't understand that I had to actually understand what the problem was asking of me. Before then, learning math had been "if you see A, do B" and I would frantically search for "patterns" to similar problems. It took me a long time to realize that the problem itself was telling me how to formulate the solution.

There is an amusing end to this story. When I entered college, I realized that this pattern-finding approach to solve math was used (in vain for the most part) by many of my classmates to try to game exams. It seems that it had worked well for them through high-school, but failed miserably at college.

Re: How Japanese Kids Learn To Multiply

#100

Post by Natsu »

talmand wrote: post #25
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 hate to disappoint you, but mathematics is nothing but a gigantic collection of tricks, rules, games and the like written in language impenetrable to outsiders.

If a mathematical paper had said something about graphical isomorphisms with a two-dimensional lattice, the average person would have been impressed, without understanding a word of it. But show them children doing it and suddenly it's a cheap trick.

Actually, thanks. That gives me an idea for the next time I have to explain higher math. I'll just find a way to show it to children first. They're usually easier to teach, anyhow.

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