Ingenious Math Trick? Not Exactly

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Ingenious Math Trick?  Not Exactly

                I was dinking around on Blogger, and clicked on this ‘Google Reader’ thing.  What I stumbled upon were heaps (and I mean HEAPS) of blog posts by someone named Melanie Pinola.  All of her posts look extremely interesting, but being the math god that I am, I couldn’t help but look at one called Quickly Multiply Big Numbers the Japanese Way.  I was taught math by Indians (I’m white and live in the United States), so I looked at this alternative way of doing things. 

                Pinola basically explains that one draws lines corresponding to the numbers in the problem, crossing the lines of the two numbers being multiplied.  Then, the number of intersections is counted for each digit of the number, and the answer is reached, seemingly with no mathematical skill required.  You can get to the page and watch the video by clicking here.  She says, “I don't know how or why this works. But it's a pretty amazing trick and might make you wonder why we don't teach math the way Japanese teachers do.”

                I’ll tell you why.  First of all, in the video, the biggest digit in any of the problems is a 3.  With only numbers 0-3, this method looks ingenious.  But try it with 789 x 985.  If you want to count 45, 40, 35, 72, 64, 56, 81, 72 and 63 intersections, and then add those up in their respective places in the answer, then be my guest.  I will be solving this problem the normal, ‘hard’ way, in roughly one hundredth of the amount of time you will take.  That’s why.  But, I’m just getting started.

                What Melanie Pinola doesn’t notice is that conceptually, this ‘voodoo/magical’ method of multiplication is conceptually identical to the traditional way to perform vertical multiplication.  The only difference is that instead of using your multiplication tables, you are literally counting each intersection to calculate that 9 x 5 = 45.  At first, this magical Japanese trick seems easier, especially when this video presents it under the best possible mathematical circumstances, but it will usually lead to slowness, and perhaps even confusion.

                Finally, my only other objection to this method is perfectly outlined in Pinola’s quote above.  “I don’t know how or why this works!”  Believe me, from my observations collected over my short seventeen years of life, this almost never leads to success in math.  If you don’t know what the heck you are doing, your doom awaits; the end is near.  What I always tell people is that the reason I am so good at math, not to mention so fast, is that I know what is going on, and why the method I am using to solve it works.  You shouldn’t blindly learn how to do things using strange algorithms that are blowing by you in an abstract blur.  If this is what they are teaching in Japanese schools, then mark my words; it is going to lead to their demise.

                I don’t mean any offense to you, Melanie, for most of your posts look very good from the front pages, and I’m sure you have a wealth of information to offer, but I just couldn’t let this go by.  Please try to understand what you are posting before you post it; you will receive much less backlash.