Brian Foley is a guerrilla-math teacher and professional magician. He teaches methods of thinking and learning used by master magicians. If you are serious about teaching multiplication, you owe it to your students to check out his ”Numbers Juggling” e-book, e-course and videos at http://learn2multiply.com
Teachers have uttered the mantra of "you must show the work!" since any of us can remember. But is there any good reason for it?
The only reason that would make sense is to find out if the child understood the problem.
But if a child can consistently get the right answers to multiplication, or other math equations, what good reason would there be for him or her having to show work? Does the teacher think the child doesn't know how to do the problem? That would be crazy, because the child clearly just did the problem!
In English class, when they ask a pupil to read a paragraph, and s/he does it well, do they say, "Okay, now write an essay on how you knew how to read that?"
How nuts would it be to ask a kid in gym class how they ran that mile, or else the running wouldn't count?
What if, in history or social-studies class, students were required not only tell you who won the Battle at Gettysburg, but prove it, with archeological facts. It might be a nice exercise once, but for every question?
"Hey, Picasso, put down that brush and write a 300 word essay about why you put two eyes on the same side of that woman's head. If you can't, I'm afraid we'll just have to rip it up and do it again right, won't we?"
No wonder Einstein said, "Education is what remains after one has forgotten everything he learned in school."
All too often, the wonderful experience that should be school is turned into a learner's nightmare because of ill-thought-out pedagogical dogma.
Schools seldom take into account that different students have different learning styles. Misguided efforts like the "No Child Left Behind" act (what a cynically sinister misnomer!) would have you believe that there's one thing to learn, one way to learn it, and one way to test it. (Maybe more than the name is sinister!)
People who do not understand people who are "different" have a hard time reaching them. The loss is on both sides.
If you'd like some insights to the problem and some possible solutions, you might find them at http://mathmojo.com/chronicles/2009/04/16/why-do-we-have-to-show-the-work/
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