I think one of the key things we need to remember is that just because it makes sense to us, and it seems like a logical explanation, it doesn’t necessarily make sense to the person we’re explaining it to.
A couple of years ago I worked with a lad who is Autistic. He was in his late teens at the time and although this is an extreme example, I think it demonstrates my point… We were working on fractions.
As I normally do, I explained that if we had a cake, cut it into two identical slices, and I ate one of those slices, I would have eaten 1 out of 2 slices (1/2).
Ok, we were ok so far.
Then suggested that if we cut it into 4 identical slices and I again ate one of those slices, I would have eaten 1 out of 4 slices (1/4).
Ok, this still made sense, and we were both happy with the logic.
I then suggested that we cut that cake into 8 identical slices, and I again ate one of the 8 slices. I would have eaten 1/8.
If we cut the cake that small, it would crumble.
True, I hadn’t thought of that...
My logic, my explanation was perfect in my mind and full of flaws in his.
For the rest of the hour, we didn’t get past the issue of the crumbs, so we had to leave it and come back to it at a later date.
For me, a lesson learned.
Fractions are taught from primary school right through to the end of GCSEs and no doubt beyond at varying levels of difficulty.
So, an understanding of the basics will always be useful so that you have something firm in place to put the following harder aspects on.
Normally, we would look at what a fraction is. Then adding fractions that have the same denominator (bottom number). Then subtracting fractions again with the common bottom number.
Life gets harder once the denominator changes and actually, if you are confident with your times tables, multiplying them or dividing them is actually an easier next step.
But for today, I don’t think that explained much at all, except that we need to remember that just because it makes logical sense to us, it may not to those we are talking to…