Being not-so-Genius

So I came across a post on Facebook from Be Genius which I'll reproduce here:

This is why the Japanese are better at math. Once you figure this out it'll blow your mind...

The lines and numbers above may not make any sense at first, but according to William C. at Themetapicture.com:

“The lines over the circles are color coded. Notice the single red line and 3 blue lines representing "13" group together while the single green and 2 black lines take their own group. [Simply] draw your first group of lines in one direction then your second group of lines going over the first, count the groups of intersections and there's your answer.”

Well, this has really gotten up my nose for some reason.  This tool is not "why the Japanese are better at math," and it doesn't even really explain "why the Japanese are better at standardized math tests" (I suspect the reasons for that are an emphasis on rote memorization).

Really, this is a manual tool for doing two-digit multiplication...and it isn't even a very good one at that.  If curious, this blog has a pretty good explanation for how this technique works (it is indirectly FOILing).  For me, what this technique most critically lacks is facilitating any sort of insights as to "what is going on in the maths" - the fact that it takes a blog post to describe is somewhat telling.

Try the technique with 18 x 19 (= 342):

  

You're sure as snot not going to count in the lower right...so hopefully you've memorized your single-digit multiplication tables (8 x 9 = 72), there's 8 + 9 = 17 on the diagonal, and 1 in the upper-left.  It's not as simple as just concatenating together these numbers (as the simple =156 example might lead you to think).  The upper left represents 100s, so that's really 1 x 100 = 100, the diagonal 17 is 10s, so that's really 10 x 17 = 170, and then the lower right is 1s, so that's 1 x 72 = 72.  Combine these by addition: 100 + 170 + 72 = 342.

(That's a lot of lines to draw!)

Now, try to see if you can figure out how to use this tool:

Same answer (and a lot fewer lines to draw!).  Crucially to me, you could probably figure out how this works on your own, without resorting to a blog post...and that is the power of the tool - it is closer to how the math works, not just some sort of accelerative technique that gets you an answer more quickly than the "multiply and carry" technique so many of us (of a certain age, at least) were taught in primary school.

Where this tool gets even more powerful is when Algebra gets introduced...remember the FOIL method?

                     First     Outside   Inside    Last 

(A + B) x (C + D) = (A x C) + (A x D) + (B x C) + (B x D)

Doesn't the solving the problem 18 x 19 with this square look suspiciously like (10 + 8) x (10 + 9)?   That's because that is exactly what you're doing.  So, you can teach the FOIL method by recalling something the students are already adept at, simply substituting different values for the polynomial terms, before getting into more complexities like squared numbers.

The Japanese technique  (assuming that's what it is) doesn't really help you understand that you're FOILing...you're just using a handy accelerator and might as well be using a calculator for all the math it is teaching you...