I am a maths teacher and have developed a arithmetic technique that the students seem to like. This may in fact be the way that all teachers teach integer arithmetic. I would be interested in your comments. I call it 'blob theory'.
It appears that students are taught at a very early age to regard 9 - 5 as being 'number operator number' (the number 9 followed by the operator followed by the number 5). I am beginning to think that is the wrong approach.
I would like to promote an object oriented approach to maths (I have worked in the computer industry). 9 - 5 should not be regarded as number operator number but number number (or more specifically integer integer). Firstly you must clearly define what a 'term' is: a sign and then a number. In fact for the younger students I have started calling terms 'blobs' meaning an object that always has a sign in it and a number. For example [-8] [the square brackets mean a circle is drawn around it but I can't draw a circle on the keyboard]
9 - 5 is [+9] [-5]
those square brackets are CIRCLES not brackets.
As soon as you do this is really frees things up. You can tell the students that they can move the blobs anywhere:
i.e. [-5] [+9]
Then you give the students a very good grounding with the number line so they understand how to actually calculate [-5][+9] or indeed [+9][-5].
Now you may be thinking what's all the fuss about but if you teach blob theory the students are able to use it to solve more complex things. For example:
before you do this problem you need to circle the blobs:
Then you can tell them that they multiply [-2]*[+3] = [-6]
and [-2]*[-x] = [+2x]
so the answer is: -6+2x
Anyway, I'll stop there. My point is is that the inclusion of the operator just confuses them. They often write:
-2(3-x) = -6--2x (and have to deal with the two negative signs) or they make a mistake and get -6-x
I have heard many students say 'is that a minus sign or a negative'. Blob theory does not have a distinction!
I have heard that this type of maths has got a name. I would be interested if anyone knew what it is referred to as or if anyone else has used a similar technique?