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 Subject: RE: Best & New way to teach Long Division Author: Daniel44 Date: Jun 11 2014
On Jun  9 2014, Howard58 wrote:
> The long division procedure still uses repeated subtraction, but in
> an efficient way. My suggestion to everybody is that one should put
> in all the missing zeros at each step, as the procedure then makes
> total sense.  Also it can then be easily explained.

My question
> is: Why are we still teaching long division?

The only argument in
> its favour that I have come across is that it helps kids to
> understand place value. But if you don't understand place value then
> you have absolutely no chance of understanding long division.

I feel like the argument that long division goes hand in hand with division of
polynomials is a too week to be repeated. I can't really see a way that it'd
help high schoolers to learn normal long division immediately prior to
polynomial long division. (Can synthetic stand on its own to teach the concept
of polynomial division?)

I think what it comes down to is the difference between computing division and
expressing division. I think long division is still the best method of
calculating a single expression ratio between two numbers. It's possible to get
a whole number answer from any of the methods listed on Jeff's website, but the
methods other than long division do not become more precise than a remainder.
Though, the argument can be made that adjusting a remainder to a fractional
component of a mixed numeral is more precise than any decimal expression. I
think that to a young student a decimal answer to n digits is more apparently
precise.

If you want to express that division is the fundamental operation in fractions,
ratios and rational expressions, I don't think that long division is the way to
do it. In this case Jeff is right to claim that Long division is a computational
shortcut, and Howard is correct to question.