Great. Now do it for 79*86.
I'd rather 86*80-86 == 6880-86 == 6794
I do that too, round to the nearest multiple of 5 or 10 and fix it at the end :D
How Japanese Kids Learn To Multiply
41–50 of 103 posts
Re: How Japanese Kids Learn To Multiply
#42I wouldn't learn how to multiply from the Japanese. They are clearly pretty bad at it. http://en.wikipedia.org/wiki/File:Bdrates_of_Japan_since_195...
Re: How Japanese Kids Learn To Multiply
#43nice trick for numbers with each digit smaller than 5
I think only smaller than 4... I wonder if this works in binary :D
That was my first thought, so I checked, and yes, it does. You just change the carrying rules. But by the time you've accounted for the number of digits you'd need to do anything useful, it's fairly useless except from a theoretical computational perspective - even when converted to logic circuits, I'm guessing it's not the most efficient solution out there.
Re: How Japanese Kids Learn To Multiply
#44This 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…
How widespread are abacuses (Soraban)? I saw the below article [1] (and listened to the corresponding podcast) and the speed mental abacus calculations seem incredible.
[1] http://www.guardian.co.uk/science/alexs-adventures-in-number...
Re: How Japanese Kids Learn To Multiply
#45My revelation came while taking Linear Algebra and Discrete Math in college as an Engineer/CS student. It really abstractly told me why these things were happening and how to deal with them plus giving me a real survey to mathematic techniques. The technique is a bit gimmick, but works for that part of world vs. what we do - which is also gimmick on adds/subtracts on multiple numbers. Its less about what we are teaching our kids, and how to handle it efficiently. Anyway, drawing lines is nothing more than adding numbers like what we do. I see nothing special about this.
Re: How Japanese Kids Learn To Multiply
#46This 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…
The podcast I tangentially mentioned above talks about Soraban, and Japanese people learning Kuku:
Re: How Japanese Kids Learn To Multiply
#47The 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'…
I know that there was a previous link on HN about the math education approach and materials used by Phillips Exeter which very much followed this approach. Where the students are allowed to discover the relevant mathematics in a structured way so that by the time they learn the "standard" way of expressing a line they understand intuitively why it must be so.
It was very interesting, and actually quite similar to the way I was taught physics in university tutorials - I think I've commented on HN before about the way we "discovered" an approximation similar to Born-Oppenheimer as part of a cleverly designed series of small group tutorials.
edit: I just noticed that the previous link was in fact posted by you.
Re: How Japanese Kids Learn To Multiply
#48A good way to introduce this starter is to put up a map of the world and get learners to point out Japan. As a teacher you can then move into how Japanese Pupils learn to multiply.
Shouldn't the focus be on teaching kids to multiply, rather than teaching them that "all Japanese people do it this way, look how strange"? How do the Germans do math? What about Indians?
It really frustrated me that the author chose to illustrate a potentially very helpful teaching aide by focusing so much of the apparent strangeness of Japanese culture. Not exactly setting a very good example.
Re: How Japanese Kids Learn To Multiply
#49This 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…
How widespread are abacuses (Soraban)? I saw the below article [1] (and listened to the corresponding podcast) and the speed mental abacus calculations seem incredible. [1] http://www.guardian.co.uk/science/alexs-adventures-in-number...
(n.b. They're called soroban here -- mentioned so that folks would be able to look it up more easily.) One is generally exposed to them as a curiosity in math classes, but if you want to get good with them, you go to an after-school cram school. There exist many, even in Ogaki, which specialize in nothing other than abaci. The secret to good abacus use is, again, to drill the "'()#'% out of it.
Re: How Japanese Kids Learn To Multiply
#50This 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 desagree completely. It's not a trick. This is exactly how multiplication works. The idea behind 2x3=6 is
| | |
-+--+--+-
-+--+--+-
| | |
(I'd like to use bigger lines for the dozens.) This is exactly what happens in the method. See: http://imgur.com/S5nOh
If I had to use that in a class I would first use the "all graphical" representation, then the "mixed" representation and finally the "algebraic" representation. The lines are still there, but almost invisible.
--
I understand that most of the times nobody should use any hand method to multiply two four or five digit numbers. But some properties of the hand method are important, for example:
* Why to use approximated calculation you use the first digit and no the last digit?
* Why is possible to calculate the last digit of the result using only the original last digits of each number to multiply?
* How is this method related to polynomials multiplication?
* How is this related to the casting out nines check?
* Can you imagine the multiplication of a large number by 2 using this method? 3?
Most of these topics are not explored in a usual K-12 math course, and perhaps it's a good idea because some of them are a little tricky. But the proof of how this method works lies in the structure of the decimal representations of the numbers and the algebraic relations between the sum and multiplications. I think that for small children a graphic method like this one can give some insight of these properties, without all the details and formalizations.