Alternative methods (algorithms) for subtraction

This is essentially an e-mail message I sent to a discussion group; it is slightly edited. The question being discussed was whether schools should teach THE standard algorithm, and make students practice until they can do it automatically. I pointed out that there is no single standard algorithm.

There  several different algorithms that are widely used. Most currently used algorithms are based on the same principles (place value, commutativity, etc.), but the actual techniques are different.

Examples:

1. Left to right addition or subtraction

  7 8 9
+ 4 5 3
-------
1 1 3 2
  2 4         sum: 1242

Possible advantages: fo>

Possible advantages: for most purposes, the left end of the number is most important, so if you are estimating, you don't have to finish the whole computation. In many languages reading goes from left to right; why do we do arithmetic right to left, and with the least important digit first?

I had a student who said she learned this method in England as a child. (Though I may be misremembering.)

2. "Borrow" from the number you're subtracting.

1  4  1  2
-  8  6  6
----------

1  4  1 12
-  8  7  6
-----------
         6

1  4 11 12
-  9  7  6
-----------
   5  4  6

1  0  0  0
-  5  9  3
----------

1  0  0 10
-  6  0  3
----------
   4  0  7

Possible advantages: sometimes avoids lots of "borrowing". Can be explained as a money transaction. (I have $1000 and owe you $593. I don't have correct change, but you do. I borroect change, but you do. I borrow another 10 ones from you, so now I owe you one more 10...)

Another student had learned this method as a child in Central or South America.
 

3. Add up.

1000 - 593

add    total
         593
   7     600
 400    1000    so 1000 - 593 is 400 + 7

Possible advantages: Avoids borrowing and is often easier than the standard algorithm when lots of borrowing is needed.

This method is used by cashiers everywhere.