Is it appropriate (as a current student) to ask professors questions not directly related (but related enough) to course material?

Question

I am an undergraduate mathematics major. During office hours I asked a question to a professor which was not a homework problem, but which was related to a homework problem (and I had made the connection clear). He answered my question fine enough, but at the end he said, "My office hours are for students to ask about [course he is teaching] only," and he said my question was not relevant to the course.

So, I asked (as politely as possible), who in the department should I ask if I have a question (as he was clearly implying not to ask him anymore)? He said, ask your teacher if the question relates to his class, but not otherwise.

Obviously I understand the importance of self-study, but am I expected to not ask anyone for advice on any questions that aren't word-for-word out of the textbook or problem set?

What is the typical attitude of professors toward students asking somewhat tangential but not totally off-topic questions? Is this normal behavior? I want to have realistic expectations for my professors in the future. I'm an underclassman and relatively new to the field of mathematics so maybe I just have wrong expectations right now. Hopefully some of you who are more experienced in academia can help me out here.

Edit: There was no one else in line after me to see the professor at office hours.

Answer 1

As a former mathematician and academic, the interaction you describe strikes me as unusual. Certainly not the norm, and not in general what you should expect! Most of us, I suspect, learned most of the math we know via self-study, with the benevolent guidance of mentors as we went along. And as pedagogues we generally like helping people explore their interests in math, even when only very loosely connected with the matter at hand.

That being said, it is worth noting that university professors' time is pulled many ways, and in many cases their formal incentives are not at all aligned with spending their time opening the minds of random students on random math topics. At research universities, their career success depends on research productivity, and they may have little time for teaching to begin with, and helping students learn outside of the curriculum may not be high on their priorities. At more teaching-focused colleges, one hopes the desire to help would be strong(er), but teaching and administrative loads may be higher and they may feel their time is limited. In either case, if others are waiting for office hours they may feel those whose questions are directly related to the curriculum take precedence; and if their office hours are poorly attended (perhaps for a reason....), they may start feeling entitled to be using that time for lecture prep or something else unless someone comes with a directly relevant question. In my opinion, they shouldn't, but they may.

The basic advice of "find someone else who is less of a grumpster" applies. Beyond that, whether with this individual or someone else you approach, there are certainly things you can try to increase the positive response you'll get for "extracurricural" questions:

1. Make an appointment / "ask whether you can ask" and indicate roughly what you want to talk about, and recognize you know it's past the curriculum itself. Be willing to come another day.

2. Demonstrate enthusiasm and curiosity, avoid projecting entitlement. Professors want to stimulate the former, but we're pretty jaded about people who come across as if they feel they have a right to answers to whatever level of detail they feel like, or get irritated that the question they asked has a more complicated answer than they were clearly hoping for.

3. Do some reading/research beforehand, and indicate you have done so. There is a shift from highschool, where you are taught, to university (undergraduate and graduate), where you are being helped to learn. Show you are making that shift!

All of the above may well be things you are/were doing, and you just have a grumpy professor. Sorry about that. But I'm summarizing them anyway, since any academic or ex-academic will have stories of students whose keenness was infectious, as well as those whose non-stop, entitled questions were a pain in the neck!

Answer 2

It’s not normal, and your question was appropriate. Your professor was being a bit of a jerk and is not at all representative of mathematics professors. If it were my office hour and I was not busy answering other students’ questions about class material, I’d welcome questions on any subject whether related to the class or not. Other professors might prefer not to get into prolonged discussions about other topics; that’s reasonable if they say that politely, but even so that doesn’t mean you did anything wrong by asking the question.

By the way, no offense, but your question is too long. Try to cut down the length and focus on what’s important - perhaps you will find then that people become more receptive to your questions and don’t respond irritably.

Answer 3

It is hard to make a firm judgement here, but it does seem to me, like I think it does to you, that the professor is dodging a bit. Maybe a lot. But there could be many reasons for it other than a dislike of you personally.

My own practice would be to accept any and all questions and, if I can't answer them, to say so but try to point the student to a source for an answer. But I was (mostly) never inundated by students during office hours, requiring me to ration my time.

But if the professor is untenured then time may be a very scarce resource and he may just need to get back to his own work, giving teaching a lower priority than it (perhaps) should have. The same is true for a top level researcher or one who has a lot of grad students with research to manage. Undergraduates often get the short straw, but this is an institutional problem.

But, I think that you have a right to ask any professor of math any math problem that occurs to you. The worst that should occur is that you are pointed to some resource. But you might also be told that you don't yet have the preparation to grasp a full answer and there isn't time, here and now, to develop it.

But there is another possible issue if it is just this professor. Some professors are on the autism spectrum and have a hard time in personal interactions. Maybe he just interacts badly with everyone and wants to retreat into a private world. Not ideal, of course, but some people like this have other qualities that compensate.

I would recommend, however, that you don't give up seeking his guidance altogether, but restrict it to courses you are taking with him. Seek other, perhaps better, guidance elsewhere.

But, yes, you should be able to ask any math question of any math professor, though you may need to find an appropriate time to do so. Some professors will let you schedule an appointment for discussions. You might also be successful joining with a couple of other students for a joint appointment on some topic of mutual interest.