Some thoughts on dumb multiplication: Dumb multiplication is where you go 23 x 31 ----- 63 the answer obtained by multiplying 2x3 and 3x1 and writing the answers under the columns they came from. Now how many people do you know who multiply numbers this way? How many of you can admit to currently thinking that multiplication works this way? As teacher I have seen this kind of multiplication way too many times for it to be an accident. There is something seemingly very natural and intuitive about multiplying numbers this way, and its entirely WRONG (as of course you all know). But why is the illusion so persistent? I have seen kids revert back to this dumb form of multiplication persistently after I have shown them the proper methods many times. Somehow it is the default way to multiply in the same way that heavy-objects-fall-faster-than-light-objects was the default way to describe gravity for many centuries, so intuitive was it that it was never actually put to the test and proven to be WRONG, an act that could easily have shown its falsity in a matter of minutes, anywhere in the world. Even today there are people who will regard gravity as acting in this way, suggesting that there is something inherently credible about this mistake, just like the mistake of dumb multiplication. If dumb multiplication really worked, then 11x11 would be a really interesting calculation: 11 x 11 ------ 11 We have just found a number that multiplies to make itself. Does anyone know of a good way to rid students of this misconception? Ive not found it yet, which goes to show that being a nice guy about it doesnt make the mistake go away. Maybe the old ways were better after all: a good caning for doing it wrong? Hmmm... I think Id rather just let the mistake-makers be the way they are and not get worked up about it. Multiplication by hand, whether done correctly or not, is more of an intellectual exercise than a requirement for life. Like a crossword that keeps the brain stimulated for a while, it doesnt really matter that the answers written into the boxes are spelt correctly or are even genuine words. What matters is that a challenge to think abstractly has been accepted and some thinking has occurred. So go forth and multiply, as absurdly as you wish! And if someday you discover along the way that your preferred method is giving you preposterous answers, then you will have taken the first grand step towards arithmetic sentience. To paraphrase Yoda: Learn? There is no learn! Only discovery by ones own effort there is! Hmmph! -DC
Posted on: Mon, 14 Jul 2014 09:51:24 +0000
Recently Viewed Topics
© 2015