Asking questions in class: how can I "exit" a Q&A when I haven't really understood?
The situation is complicated so there is no simple answer. Over time you and your instructor(s) will have to work out a modus vivendi.
From my point of view as a teacher, I want you to try to continue to ask. I find more students hesitant than persistent - and it's the persistent ones who force me to be clear.
At the beginning of each semester and often again later I tell the class that any question that occurs to you has probably occurred to many of your classmates who are too shy to ask, so you will be doing yourself and them a favor by speaking up.
Students often start questions with "this is a dumb question" or "I have a short question". Often neither is true, so those are not good opening lines.
When a student seems to be in the loop you describe in your question and I sense that I am not quite helping him or her or the whole class I may say that continuing to struggle with it right now on class time isn't useful. I might cut the discussion short with "Please see me after class and we'll work this out" or "Can you come to my office hours?"
So final advice: keep asking while answers are useful, be prepared to continue the discussion one on one if necessary. Hope your instructor cooperates.
I don't want the lecturer to feel like maybe they've done a poor job of explaining when perhaps I'm just not grokking an underlying principle.
If you're not grokking an underlying principle, the lecturer has done a poor job of explaining.*
;)
More importantly, though:
Never lie about your level of understanding.
Ever.
If you don't understand, say so. Even if you just say, "I'm still missing something, but I don't want to hold up the class. I'll have to work this out later."
It's up to the lecturer what to do about that—perhaps they'll keep trying to explain—but you've made it easy for them to say, "Okay," and continue, without getting a false idea of the clarity of their explanation.
As an aside: This whole situation illustrates the precise problem with teaching a whole group at once. Self-paced, supervised study, given a proper text (or videos/other materials) and a study supervisor who knows his/her business, is much more effective because the slow students can take the time they need to fully understand, the fast students can whiz through, and the middling students can middle along.
*Don't take this as a blanket statement. Use some judgment. If the lecture is aimed at graduate mathematics students and you never grokked exponents, yes, you are the one at fault. But my first statement is more true than it is false.
My impression is that you see only two ways to react to asking a question and not "getting" the answer: (a) give up, or (b) repeat the exact same question once again (you talk about "asking the same thing over again").
You are right:
I don't want to just say, "Yeah, I'm not getting it, so what now?" I feel like that would be so incredibly rude!
That would indeed be fairly rude (and ineffectual), as it would put the onus on "making you understand" squarely on the shoulders of the teacher, with no sign of you yourself trying to work it out. This seems akin to the stereotype western tourist who just keeps saying the same thing louder and louder if the natives don't understand his language.
I feel a better strategy to work out what somebody you don't "get" is talking about (in pretty much any context) is to ask again, but by rephrasing what you are asking. Of course this should go beyond just using slightly different words to ask the exact same thing. Instead, try to:
- be more specific in what you are asking. "I don't understand, explain again" is very vague, but asking how we got from step A to step B in this proof might be more helpful.
- build upon what your teacher was just explaining. "So you say that A is usually equal to B, but I still don't understand how this allows us to infer C."
- explain detailedly what about the current explanation is throwing you off, and ask where you are going wrong. "I understand that under the assumption that A is equal to B, we can infer C - but why would A and B be equal?"
As a last resort, you can always ask if there are other resources that you can study to on your own. In this way, you don't need to "pretend" to have understood, and it still allows the class to move on.