[Maths-Education] Subtraction

[Judy Mousley]

>At 9:30 AM +0100 10/4/2000, Ian Thompson wrote:
>Most books on teaching mathematics discuss 'the two aspects of subtraction:
>'take away' and 'difference'.
>Since the most efficient way to solve difference problems is usually by
>addition, and since 'difference' is commutative whereas 'take away' (and
>subtraction generally) is NOT, why do we persist in linking difference with
>subtraction?

Many 'difference' problems can be solved by adding on. However, the 
solution (while a missing addend) is actually the solution to a 
subtraction equation. (I know that's academic, but think about how an 
algebraic representation of the same sorts of problems would probably 
be solved.)

Which method is efficient depends somewhat on the numbers involved. 
To find the difference between, say, 26 and 1927 I would be likely to 
subtract. But to find the difference between 96 and 1927, I would be 
likely to add. 'Efficiency' varies from person to person. Given that 
some people use subtraction for difference problems, and that people 
need to se connections between the processes, I think we should ask 
"Why not link it with subtraction?"  I do feel, though, that there is 
too much emphasis put on solving difference problems one way-but that 
situation is no different from the solving of many other sorts of 
problems in school.

I am not sure if I have told the following to this list.  I was 
observing a Year 2 class, where a difference problem arose. The 
teacher said to a girl who could not work out how to proceed "What is 
the difference between 6 and 9? (long pause) Come on-you know 
that-what is the diffference between 6 and 9. (longer pause) Nine and 
six-the difference?"
The girl replied "One's upside down, but which one?"

Judy