Tuesday, September 18, 2007

Division

So far I have largely ignored the way Americans write their division: divisor first then dividend. I learned it differently. Mind you, the algorithm is exactly the same, it's just the way it is written that differs: dividend, divisor and quotient are all in the same line, in that order, and the rest is the same. Now that I teach elementary math I have to train myself to do it the "wrong" way. Can anybody explain to me why the order in which these numbers are written in the algorithm seems to contradict what is being done, or is that just my perception influenced by years of drill I was subjected to? Also, whenever I show "my way" to people they say it doesn't make sense even though it is exactly the same process. Does that show the lack of understanding or lack of willingness to understand?

4 comments:

jonathan said...

"Does that show the lack of understanding or lack of willingness to understand?"

A bit, on both sides. It is not an easy algorithm, and once mastered, few would want to alter it.

Explain that they will have students from places where the set-up was different, then do out the same division (same numbers) both ways, side by side. The lesson is really not to correct the other way, when it's already right.

Does the European layout leave room for decimal expansion of the quotient?

(I was taught differently from both - and then American-style. One day I should blog what my first long division looked like. It really was better than either of the other ways...)

e said...

Does the European layout leave room for decimal expansion of the quotient?

It leaves lots of room.

Ok, I want to know your algorithm. Please :)

jonathan said...

I think I need to scan an image... someone told me once it was called Greenwood or Greenleaf or something like that.

You know, in a box buried in a closet is a smaller box with assorted school papers from grade school, and at least one real live sample, in my awful handwriting. Maybe I'll go dig.

(Without the diagram, we subtract away multiples of the divisor, tracking how many we have subtracted. Place value does not play a role. We sum the number we have subtracted.)

Without layout, for example, 14,536/23 we might subtract 500 of them (11,500) leaving 3,036, then 100 of them (leaving 736) then 30 of them (leaving 46), then 2 of them (leaves 0), and at the last step, sum 500+100+30+2.

Turns out the lack of place value slows you down, but just a bit, unless the dividend has many digits, in which case writing all the 0's can be tiresome.

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