From: Chris <cmpalmer2@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2001102220:30:41
Subject: a German algorithm

I teach in the U.S., where we generally use the "little house"
algorithm:

     3122
  ---------
15) 46830
    45
    __
     18
     15
     __
      33
      30
      __
       30
       30
       __
        0


However, over the last few years, 
I have had several students who grew up in Germany.
They did many algorithms differently from the way we do it, here.
Long division was one of them...they do the division algorithm as a
multiplication problem.  For example:


       3122
 15 x ______ = 46830
                45
                __
                 33
                 30
                 __
                  30
                  30
                  __
                   0


They actually went through essentially the same thinking process.
They just wrote the algorithm differently on their paper.

The most interesting thing about this, to me, was the fact that some
of my students, who had previously not understood how to do a division
problem, understood the division algorithm in this manner.
I think this is because seventh graders do not think of division as
divsion.  They naturally think of division as multiplication, and the
German algorithm does that, as well. 
      

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