For this post you'll need to know about math operator precidence so very quickly: the basic math operators are add, subtract, multiply and divide. You have to be careful to use the operators in the right order. Here's an example so you can see what I mean...
What is 14 x 2 + 3 ?
Well, 14 multiplied by 2 is 28. Add 3 to 28 gives 31. Easy.
But I speak English and we read from left to right - called a "left to right reading order". What about languages that have a right to left reading order? Then you would add 2 to 3, giving 5... and then multiply 5 by 14 giving an answer of 70. Ahh... now we've got two completely different answers. Who's correct?
The solution is to have a worldwide convention: carry out operators in a certain order then we don't get different answers. The convention is Brackets, Indices, Division, Muliplication, Addition, Subtraction... BIDMAS. If everyone carries out mathematical operations in that order then we'll all get the same answer.
So I'll pose my students the same question: what is 14 x 2 + 3 ?
Then I ask...
"So you say the answer is 28 and I say it's 70. So who is right?"
And, invariably, with some hesitation, they'll tell me I'm right.
When asked why I'm right the answer, invariably, is that I must be right because I'm the teacher.
I'm completely wrong, I've told them the reason why I'm wrong (but, of interest to me, I haven't explicitly told them I'm wrong). They know I'm wrong - but they can't bring themselves to question my authority: "You must be right because you're the teacher".
I close this aspect of my math teaching with a bit of sage non-mathematical advice: always have the courage of your convictions.
I'm very interested in exploring the pupil-teacher relationship - the nature of authority and respect. Is this something you've tried exploring in your teaching? I'd be interested to hear what you think.