When you’re trying to explain to a student a subject you know very well, there can be an enormous temptation to start out with “It’s easy. You just…” You must resist this temptation.
The problem is that for you, if it’s a subject that you know inside out, everything feels this way. After all, you can’t even remember a time when this stuff wasn’t easy.
So you start giving what you think will be a simple explanation. Except that part way through, you realize that it’s only simple because there’s something else that’s also simple, which you’ll need to explain first.
And then you realize that that simple thing relies on two other very simple things. And so on.
It’s not that any part of the explanation is complicated. It’s more that when you know something like the back of your hand, you forget just how many different steps you’ve gone through to attain that level of knowledge.
This may be one of the trickier things about teaching: The better you know something, the harder it is for you to remember that it’s not really easy at all, for somebody who doesn’t already know it.
For me, teaching is actually learning.
I teach 10-12 years old children, and I found more insight in, even a simple arithmetic. For example, I try to teach commutative property of addition (without saying “commutative property”), 1+2 = 2+1. It’s too obvious for many people, so maybe you even don’t have an explanation why this hold to convince the children, … it’s just obvious. But when I try to teach this, I need to come up an explanation. I once use a balance and looking at it from the different direction, or change the order of things doesn’t matter the total weight, and so on. That is connected to 6-1=5 and 6-5=1 (here 1 and 5 are exchanged), and you know the idea of group, then, you want to tell 6/2=3 and 6/3=2, since the commutative property of multiplication, and so on.
One good thing is I was not good at mathematics. So I still remember many of the obstacles. I think I might have a good teaching skill because I was bad at math.
Hitoshi