From: Jeanne (for Teacher2Teacher Service)
Date: Jul 25, 2000 at 16:16:08
Subject: Re: Decomposing numbers

There is a book called, "Knowing and Teaching Elementary Mathematics" by
Liping Ma which might be of interest to you.  It has a chapter devoted to the
topic of "Subtraction with Regrouping:  Approaches to Teaching a Topic" where
the concept of composing and decomposing numbers are discussed.  Ma conducted
a study that "compares mathematical understanding among U.S. and Chinese
elementary school teachers as it related to classroom teaching practice."  
This book is one of the products of this study.

What the Chinese teachers call composing and decomposing, many U.S. teachers
call carrying and borrowing, respectively.  BUT "carrying and borrowing" and
"composing and decomposing" ARE NOT synonyms.  Let's see if I can give you an
idea of what I read.

In the problem,
     53
   - 16
  ------

our students learn they can't subtract 6 from 3 so they must "borrow from the
5, regroup and make the 3 into a 13."  (I know this is an oversimplication,
but bear with me.)  ...and get answer of 37.

We can look at the same problem in other ways.
     53 =    40 + 10 + 3           Here the 53 and the 16 are "decomposed."
   - 16 = - (10 +  6    )
  ------------------------
             30 +  4 + 3 ==> 37

OR
     53 =    53
   - 16 = - (13 +  3)      Here only the 16 is "decomposed."
  -------------------
             40 - 3 ==> 37

Ma's book has many, many more messages.  I encourage you to read it.

Hope this helps.

 -Jeanne, for the Teacher2Teacher service

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