Understanding Multiplication

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Do you want to understand and be able to multiply in order to:
a) help you (or your child) with life in general and the education that counts, or
b) just help you (or your child) pass the next math test?

If your answer was b, you just saved yourself some time and effort for the next few minutes. You don’t have to read any further. But you’d be costing yourself (or your child) years of frustration. Passing a little (or big, standardized) test is just jumping through an artificial, meaningless, hoop. You don’t have to be a slave to the school system.

If you really need to beat the system, you need to game it. You need to learn math much, much better than they teach it to you in public schools. Then their tests will be a joke, and you will blow them away without being intimidated. But if you just want to learn enough to get through the next test, brother, you are digging your own educational grave.

It doesn’t make sense to accept their dogma, and then blame them for feeding it to you. Do something about it, now. Pick a subject you feel you’re lacking in, and then find alternative ways to supercharge yourself at it. “Ah speet on yo’ steenkin’ test from a high altitude!”

This is going to sound like heresy, but here it is - If you have a test that you don’t really have a good chance of passing because you don’t understand the material, don’t just cram and hope you’ll pass - Forget about the test, totally! Plan to fail it, but use that time to find a better way to learn. Go to the library, scour the internet, ask a friend, or check a bookstore for in formation related to the subject, and don’t stop looking and learning about it until you understand it better than anyone else in your class. Being “good enough” will never make you good enough. Make sure you can “speet on the steenkin’ test.”

Then, instead of just failing the test that you would have failed anyway, you fail the test, but actually learn the material so you will not fail any more tests on the subject, and you’ll be on your way to real knowledge.

Imagine this scenario:

Little Smike is faced with a test of basic multiplication, which his schoolmaster, Mr. Wackford Squeers, is going to give on Friday. Now, Mr. Squeers knows nothing about multiplication except for “the multiplication tables” (a posters of which he has hanging in various places on the walls of his classroom). And all he knows about how to teach or learn them is to “just shut up and memorize them!,” although he’s never even taught his class anything about methods of memorization.

Smike has tried and tried. He has shut up, he has stared at “worksheets,” he’s spent time with flash cards, and has even suffered through silly songs and rhymes, but he just doesn’t get it. Is Smike stupid, or does Smike just need a way to understand multiplication, instead of just learning how to parrot back meaningless information? Isn’t it often the smartest people who have the hardest time learning, because the methods of teaching are so insipid?

Mr. Squeers laments the fact that, though he is working so hard, his students just don’t seem to learn. What could be wrong with the little urchins? Why don’t they learn, despite his best pedagogical intentions?

Being from a family of administrators, Mr. Squeers subscribes to the time-honored platitude of, “You can lead a horse to water, but you can’t make him drink,” in order to excuse his ineffectiveness. He has certainly taught the little tykes well. Why don’t they just learn? (Perhaps he’ll have to thrash them.)

Poor Mr. Squeers. What he doesn’t realize, is that if they haven’t learned, he hasn’t taught. He can inculcate, threaten, or test them to the high heavens, but that’s not teaching. Perhaps if he made the water taste better. Perhaps if he offered the horse some milk, some lemonade?

You can make a horse drink, you just don’t always have to use water. You can teach multiplication. You just don’t need to use the times-tables.

Luckily for Smike, there is a new assistant in the class, a Mr. Nickleby. Mr. Nickelby knows an interesting method of multiplication, which he learned from a magician while touring with a traveling stage company.

The method requires the use of basic addition and subtraction, rather than “multiplication tables.” It is counter-intuitive, but much more effective than the tables.

Unfortunately, Smike hasn’t been taught addition or subtraction adequately, because the class had to rush to “cover material” in because of the “No Child Left Unstressed” Act. But Mr. Nickleby has a plan - What if Smike spent the time between now and Friday actually learning simple addition and subtraction? That he could manage, it’s much easier than memorizing meaningless “multiplication facts” from a chart.

To make it even easier, Mr. Nickleby shows Smike a simpler way to add than is taught in most of the better schools. He uses a tool called an abax. And he teaches Smike how to subtract from left to right, instead of the old, less effective method. This builds Smike’s confidence, even though Smike hasn’t learn anything that will help him on Friday’s “multiplication facts” test.

On Friday, Mr. Squeers snickers as Smike fails the test miserably.
“Nickelby, old boy, it seems like your ’star pupil’ is a miserable failure,” he chortles in his schadenfreude*.

“Yes, Sir. Failure there is for sure, Mr. Squeers.”

By the following Monday, though, Smike is the only child in the class that has a through understanding of basic addition and subtraction. He can perform these operations from left to right, without paper, quicker than than even Mr. Squeers can do it with pen and paper.

With that, Nickleby helps Smike parlay that knowledge into learning the basic multiplications up to ten-times-ten, in about five minutes. Smike will never forget what eight times seven is again. He will never struggle or be insecure about “multiplication facts,” whereas most of the other students had forgotten them by the weekend.

The moral of the story? School sucks, but education doesn’t have to.

The next few posts at the Chronicles will be about a Roadmap to Multiplication. I’ll be outlining the skills anyone would need to get a deep understanding of multiplication, and how to get those skills.

*Schadenfreude - “taking joy in the suffering and misfortunes of others.”

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