I'm a high-school student in the United States, and from time to time a teacher makes a mistake while writing on the board in front of the class. Usually, the mistakes are minor, such as forgotten punctuation, but sometimes there are more major mistakes.
To give an example of the latter, I took an informal math class during the summer. The teacher, only a few years older than me, was working through a problem on the board, which we were expected to copy down as he wrote. It was fairly convoluted, and most of the class didn't seem to be paying attention.
At one point, the teacher made what I was 90% sure was a mistake in logic. As far as I could tell, one step of the process would work for some numbers but not others, although he claimed it'd work for all numbers. I noticed the mistake early on, but I was hesitant to point it out because a) I wasn't entirely sure it was a mistake, and b) I couldn't figure out how to correct him without being rude and setting myself up as better than him. (In the eyes of the rest of the class, too — I'd previously gained an arrogant reputation, and given that he was a math major at a prestigious university, I definitely didn't know more about the subject than him.) On the other hand, the flaw in logic might confuse other students.
Finally, seeing that no one else was going to see/point out the mistake, I politely asked him to explain his reasoning. He used an example number, which turned out to be one of the numbers that worked. I asked for him to work another example, this time suggesting one of the numbers that I thought wouldn't work. Seeming slightly thrown by my forcefulness, he tried the number — and it didn't work. He then realized his mistake in logic and corrected himself.
I didn't feel right about the way I'd handled it, and afterwards, when I described the situation to others, they said I'd wasted everyone's time and would've been better off directly pointing out the mistake rather than asking him to explain it.
So my questions are:
Is it even worth correcting a teacher's minor mistake in situations like this, or does it just make them look bad?
- Related to that, does it depend on how minor the mistake is? And if so, how can I tell what kind of mistake is worth ignoring?
If it's worth it, how do I do it politely?