Different graduate advisors react in different ways to the situation in which a student is asked a question during or after a talk or other presentation and the student can't answer the question or doesn't answer the question well or correctly. The situation of interest can be a research talk in the home department, a conference presentation, or any other moderately to very important setting in which the student has to answer questions on the spot.
Let's also assume that the student is not extremely inexperienced, is not being asked random questions about irrelevant topics, and is not being questioned in a hostile way; i.e. the student can reasonably be expected to know the answer to the question or at least to have some intelligent thoughts about it.
Once it is apparent that the student can't answer the question, some advisors will jump in and answer for the student, or will correct a wrong or incomplete answer.
Some advisors will sit quietly and let the student deal with the situation.
Of course the difference between intervening and not intervening relates in part to personality factors -- e.g. some advisors take questions very personally and cannot bear to let there be any doubt about the research. I find it annoying in department seminars (and even, in one case, an oral exam) when an advisor gets defensive about questions that seems to cast doubt on the validity of the research, even though the questioner is merely trying to see if the student can articulate the research motivation.
The decision to intervene or not to intervene can also of course vary with circumstance.
Even so, to the extent that some advisors have an Advising Philosophy about whether or not to intervene when a student can't answer a public question about a research project, the following may be considerations:
Intervening ensures that the question is answered. This can be important in some situations, especially if the reputation of the research and research group might be affected by a student's inability to answer questions about the work. Answering a question may also help the discussion move forward to other (possibly more interesting) topics. Intervening can be done in a friendly and constructive way.
Not intervening emphasizes that the student is a researcher and must take responsibility for the work they present. If the advisor intervenes, this may signal to everyone that the student may be carrying out a research project that he/she doesn't really understand, and that the advisor is the 'real' scientist -- the one who really understands the work. Not intervening might be a respectful thing to do in some circumstances.
There are positive and negative aspects of both, and of course ultimately the specific context of each situation guides the response. I am also not addressing in this discussion the reasons why a student might not be able to answer a (reasonable) question; the advisor and the student may both be partly responsible for a lack of preparation.
I suppose that some students would want their advisor to step in and answer the question, and others would be embarrassed by this, so it's not possible to give general advice about whether it's a good idea (from the student's point of view) to intervene or not.
There is no single answer to the question of whether to intervene or not when a student is flummoxed by a question, but perhaps we can all agree that it is not a good idea for an advisor to say to the student (in front of an audience) "Come on. You know the answer." Sighing loudly, rolling and/or closing the eyes, or gazing forlornly at the ceiling or floor are probably also not constructive.
Lately I have noticed that I have been moving from a slight tendency to intervene to a slight tendency not to intervene, though I don't yet know if this is a real trend (perhaps related to my age) or just an advising fad this year. What I do know is that whether or not I intervene, it is (almost) as painful for an advisor as for a student when the student stumbles during questioning during or after a talk.
8 hours ago