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How Japanese Kids Learn To Multiply

magicalmaths.org

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Re: How Japanese Kids Learn To Multiply

#61

Post by saalweachter »

solox3 wrote: post #51
talmand wrote: post #28

Earlier quoted context omitted.

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.

Eh, one example isn't much for statistics. Looking at the average for 1, 2, and 3 digit numbers (ie, [0,9] * [0,9], [0,99] * [0,99], ...), using the sentence " times is ":

English, 1 digits: 6.5 syllables; English, 2 digits: 14.9 syllables; English, 3 digits: 25.4 syllables.

I'll let other people figure out the numbers for their own languages, but I'm guessing most languages will have similar lengths. Numbers tend to be short in any language.

Re: How Japanese Kids Learn To Multiply

#62

Post by sks »

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.

This is exactly the same algorithm as the standard one we use : Multiply all possible combinations of digits and appropriately combine the results. This is just the graphical version of writing down numbers.

Re: How Japanese Kids Learn To Multiply

#63

Post by weirdkid »

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.

I learned the lattice method in the 5th grade in 1981 here in a US public school. I loved it and used it for years afterward. I didn't realize until I was in high school that it wasn't part of the curriculum but only something my teacher thought was useful.

Re: How Japanese Kids Learn To Multiply

#64

Post by a1k0n »

Jtsummers wrote: post #55
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…

> 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 g…

I think calculators for interest calculations makes a lot of sense. I'd be pretty impressed by students doing P(1 + r/M)^N without a calculator, though I suppose you could do repeated tedious multiplications of P*(long decimal number). We definitely used calculators for that 20 years ago.

Re: How Japanese Kids Learn To Multiply

#65

Post by tuxdev »

3chelon wrote: post #43
Aardwolf wrote: post #32

Earlier quoted context omitted.

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.

Actually, this method is one of the most efficient ways to multiply in software. It's called the "Comba" method in that context, and is efficient for multiplying 32x32 words or smaller, due to cache effects and function overhead required by more complicated algorithms. Over about 32 words on many architectures, the algorithmic advantage of the Karatsuba method wins out.

Re: How Japanese Kids Learn To Multiply

#66

Post by numeromancer »

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…

... computation != mathematics.

This is exactly why giving calculators to children who have not yet mastered any method of multiplication is bad.

Re: How Japanese Kids Learn To Multiply

#67

Post by keithpeter »

Aardwolf wrote: post #31
acomjean wrote: post #26

I see the video, but how does this work? on unix/linux I just use bc -l

bc is a pretty misleading calculator, without specifying rounding it thinks 2^(40/1.5) is 67108864. It's not even close. If you trust your finances to that, you could get in trouble.

The man speaks the truth, but I do get a warning

   2.0^(40.0/1.5)
   Runtime warning (func=(main), adr=18): non-zero scale in exponent
   67108864.00000000000000000000
Apparently the ^ function only works with integer powers. The exponential and natural log functions work as expected

http://www.johndcook.com/blog/2010/07/14/bc-math-library/

   keith@xeon4:~$ bc -l
   e(l(2)*(40.0/1.5))
   106528681.30999083085437360438
nice example.

Re: How Japanese Kids Learn To Multiply

#69

Post by saraid216 »

Ntrails wrote: post #24
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 us…

> I don't see how the lines method is any easier than long multiplication

You probably learned multiplication using something similar to the lines method. If you had 3 x 4, you'd draw out 3 circles and then put 4 more circles inside and count up all the small ones. This is just a logical extension of that.

Re: How Japanese Kids Learn To Multiply

#70

Post by Jtsummers »

a1k0n wrote: post #64
Jtsummers wrote: post #55

Earlier quoted context omitted.

> 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 g…

I think calculators for interest calculations makes a lot of sense. I'd be pretty impressed by students doing P(1 + r/M)^N without a calculator, though I suppose you could do repeated tedious multiplications of P*(long decimal number). We definitely used calculators for that 20 years ago.

Well, that particular exercise was something like: You have $P and the interest rate is I% per month, what would you have after 1 month, 2 months etc. It was easily doable at the level that exercise required by hand. However yes, if the formula had been more complicated then calculators would've made sense. From talking to the teachers though, the sense I got at the time was that calculators were never restricted regardless of the difficulty or ease of the exercise.

EDIT: Did mention complex interest, that part made sense to use the calculator for. My observation was merely attempting to point out the ubiquity of the calculator in the classroom. I'd be interested to see the capability of students after a curriculum like that at doing mental and hand calculations, my understanding is that here in Georgia the various classwide exams they take also permit calculators so the students would have little occasion to demonstrate that skillset.

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