When can asking a question during lecture be offensive?
Asking questions is a good thing, but you need to make sure that the questions you ask are appropriate. The best thing to do is judge for yourself whether or not a majority of the audience might be interested in your question.
An example might be that the lecturer has made a mistake, or has forgotten to define something in a mathematical derivation. In such cases, perhaps you could whisper to the person next to you for a quick second opinion.
If a concept has been neglected or poorly explained, then you should ask for expansion or clarification if you think that most of the class will be in the same boat.
These aren't always easy judgements to make. If you're uneasy, save the question for after class. You can also simply ask the lecturer if he or she minds you asking questions, or your classmates if they thought your question was a good one. Good questions enhance the learning experience for everyone.
The bottom line is that most good professors like to have some interaction with the class. Many students audience don't like to say anything, so it's often up to just a few students to ask any relevant questions. But more than one question every ten minutes or so can start to get tiresome for the lecturer, so unless it's a tutorial class you shouldn't turn it into a Q&A session.
From my experience in college as a student who asks questions (as opposed to those who stay silent even if they do not understand what they're listening to) you can divide the process into the student's part (asking) and the lecture's part (answering). The student's part is the one you have control over, and so there are at least two possibilities:
- The question is pertinent: it adds to the discussion, is useful to the general audience and it does not disrupt the lecture.
- The question is not pertinent: it is too deep (save it for later when you can meet the lecturer in a one-to-one basis), it is too shallow (you were not paying attention, or lack previous knowledge needed for the present course, etc.), or it is irrelevant (you're trying to correct or point out some insignificant mistake or make an appreciation that does not help anyone except your ego).
If your question is not pertinent then do a favor to everyone (including yourself) and don't ask it.
Now, if the question is pertinent it is up to your appreciation and experience in that class to figure out whether that particular lecturer will welcome it or not. Some lecturers will be happy to answer anything they think adds up to the discussion and to be corrected whenever they are wrong. Others will feel that their students are being intrusive towards their work and even get defensive if they're pointing out a mistake.
Examples:
I once pointed out a mistake a lecturer had made on the board and he dismissed me implying I was clearly wrong without even giving a thought about what I was saying. Right after class I talked to him privately and he was happy to acknowledge I was right.
I did the same with another lecturer and he immediately admitted his mistake and thanked me for pointing it out. Asking a tricky question to this same lecturer he admitted he didn't know the answer but came the next day with two sheets of paper where he had worked out the answer after class during his own time.
To sum up:
It is your responsibility before asking to make sure yours is a good question. But it is also up to your judgement to decide whether asking that particular lecturer that particular question benefits you or not.
You should not always resort to Google. If the professor feels bad if you ask in front of the class, note down the question and either ask at the end of the class on one-on-one basis, or ask in a separate meeting during their office hours. Consider asking TAs too.
This is not the ideal solution though, as asking in the class provides others the opportunity to ponder on the question.
One litmus test that you might want to do before asking the question is, whats the point of the question, and whats the point of the current lecture. Are you asking a question that goes deep down some unnecessary details, or does it ask for a piece of information thats relevant and important?
Another way to test your questions is, what would I lose (or what would I be not able to do) if I don't know the answer to that question.
One more way can be that before asking the question, you verbally clarify what you understood, and then ask which bit you didnt understand. Similarly, verbally clarify what details you know, and then for which scenario, you need the additional information. That would not only justify it as a legitimate doubt, but also clear the context of question A LOT in your own mind.