From: Pat Ballew (for Teacher2Teacher Service)
Date: Jun 14, 2000 at 17:35:37
Subject: Re: European long division

I was not familiar with a significantly different approach in either
place, and I work with teachers all over the world, so to be sure, I wrote to
a discussion group that has teachers from almost every part of the globe.
Here is a response I got from a friend from the Netherlands who has been a
Math Doctor for a long time and is a VERY good mathematician and educator.
The method is only a minor difference from the one we use here.  If I learn
more, I will forward that to you as well.  Sorry I could not be more help...

------------------Flo  wrote------------------------------

Hi, Pat,

I don't believe that in Europe and South America a "different" (from the
USuAl) algorithm is used. I do know that here, I live and teach in the
Netherlands, we write down a long division in a different way. The
division of 162318 by 78 is written down as:

  78 / 162318 \ 2081
       156
       ---
         631
         624
         ---
           78
           78
           --
            0

Something else:
I have read about experiments of teaching long division in primary
schools in a more flexible and less algorithmic approach. This method
can be more like the way you calculate divisions by head. I don't know
whether this method has made it or is making it to more general use in
class, since I teach in secondary school only. Here is an example of a
division in this method:

Divide 1776 by 12.

            12
  1776
  1200     100x
  ----
   576
   600      50x
   ---
   -24
   -12      -1x
   ---
   -12
   -12      -1x
   ---    ------ +
     0      148

Of course this method is meant to let pupils start with any approach,
and let them gain better strategies. For instance, I used negative
numbers here, while when you start explaining this for the first couple
of times you shouldn't. More gifted children could use them later on to
improve their _speed_.

The _oldfashioned_ long division is more like a computer algorithm,
while in this method pupils might learn to have more 'feeling' for
numbers.

Kind regards,
Floor van Lamoen,
Goes, the Netherlands.

--------------------------------------------------------------------------
Thanks for writing...
Hope this has helped some...

 -Pat Ballew, for the Teacher2Teacher service

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