text:
What are strategies for minimizing student questions during exams?
Context: I am an assistant professor of mathematics at a small liberal arts college in the US.
I generally find student questions during tests and quizzes to be somewhat annoying.  I disliked them when I was a student, and they're even worse as an instructor.
To elaborate on my dislike:
As a student I found such questioning very distracting.  I'd be in the midst of trying to solve a difficult problem when suddenly people around me are talking in hushed voices about a problem I had already done.  As one can imagine, it was challenging to pull my attention back to what I was doing.
As an instructor, I want to do my best to provide a good test environment, so I would like to minimize questions that I see mostly as a distraction.  In addition, most courses contain a student or two who I don't entirely trust, so I like to be able to watch the students during the exam to ensure test security, and answering questions can hinder that.  I also don't want students getting up during a test to ask questions, for obvious security-related reasons.  (This problem is easily solved by telling them to raise their hand.)
Most questions fall into the following categories:

Legitimate questions aiming to clarify vague instructions or a typo.
Questions fishing for a hint.
Questions seeking support of a solution method.
Questions asking for confirmation about answer format.

Type 1 questions are not a problem. Type 2 and 3 questions are foolish, because I hardly ever tell students anything remotely useful. Type 4 questions are irritating, because my questions specifically say what format to use (i.e. "show two decimal places," "you do not need to simplify," etc.).
What are some strategies for eliminating questions of type 2, 3, and 4 while not discouraging type 1 questions?
Of course, I can just straight-up tell them that they're not to ask questions unless they believe them to be very legitimate, but I'd like to use a less "adversarial" approach, if possible.

I fail to see the difference between type 1 and type 4.

Fair point--I've edited my question to make the difference more clear.

@DSVA Why not saying openly "we cannot answer that -- it's part of your exam to figure out the answer to this question"?

Just ignoring the question is terrible pedagogy. It is far more helpful to be told "I cannot provide that information during the test" and possibly "your answers must be your own, I can't give hints" than wonder if you are going to check and come back to a student with the information.

I really just hope teachers wouldn't write vague or unclear questions in their exams. After all, isn't making a fair exam part of their job? After that, if there is some lack of clarity left, the students taking the exam should be told to assume a sensible (in the context) situation, and document their assumptions. Actually, they should know to do that even without being told. Afterwards, if a question is deemed to be totally broken, take that into account in the grading, possibly even ignoring that question completely (but you shouldn't need to go that far).

I explain at the start of the first test that, "Questions clarifying what you're reading are okay (raise your hand, I'll come over). I cannot tell you how to solve a problem. My response may be, 'I can't tell you that during the test.'"
If Question #1 comes up, I do as stated. Questions #2-3 get a fairly loud (but polite) repetition of, "I can't tell you that during the test." (Or, "That's what you're being tested on."). Question #4 may get, "Just read the direction carefully" (which itself is a repetition of something I need to say during almost every single class meeting).
I find this public act tamps down on questions as much as I can hope for. The main thing is to be solidly consistent. Counterexample: I was co-proctoring with another professor in their class. That professor got a question, shook his head in disgust, muttered "You should know that", and walked away. Then turned around, walked back, and actually did talk the student through how to solve the problem. This can only encourage more fishing questions like that.
Due diligence: In liberal-arts math courses I have occasionally had students express disbelief and/or outrage that I wouldn't help them during a test. "But you're the teacher, that's your job" kind of thing.

@QPaysTaxes: Yes, that's probably been said by professors at community-colleges (et. al.) a few tens of thousands of times this year.

You ask about minimizing questions, but really from how you describe your motivation it sounds like the real question is about minimizing distractions to you and to the students; the questions of type 2-4 don't bother you per se, but only to the extent that they create a distraction.
Well, it seems to me that distractions can easily be brought down to a level that no one can reasonably find objectionable by imposing a suitable protocol for students to ask questions, and without compromising any student's right to ask any question they think is appropriate to ask or making the students feel like you are treating them in an adversarial fashion. A couple of possibilities that come to mind for such a protocol are:

A student who wants to ask a question should raise their hand and wait for you to notice them. You will then give them permission to get up and approach you in a part of the class that's far enough away from the other students so as to minimize the noise and distraction that your conversation will create. They then ask the question, you answer it, and they get back to their seat.

Or, if that's not quiet enough, then a slightly more drastic option would be

The student will write their question on a piece of paper and raise their hand. You collect the paper, go back to the front of the classroom, think about the question, write an answer (or something like "no comment" if the question is not legitimate), and give them back the paper. If they are still unsatisfied with your answer, they can ask a followup question by following protocol 1 above.

Finally, I should add that I see some psychological benefit to allowing students to ask even illegitimate questions (e.g., of type 2-4). We should remember that exams are a very stressful situation and induce a high level of stress and anxiety in many students, which can be quite debilitating and hurt their performance on the exam. I think it's important to be as empathetic and mindful as one can to this fact; in particular, giving students the impression that you are friendly and stand ready to answer any questions they may have can go a small way towards reducing the level of anxiety some students will experience, even to the extent of allowing them to perform better (and want to ask fewer questions!). And this is true even if in practice when the students ask an unfair or illegitimate question you give nothing away. So, it may sound a bit Machiavellian, but in my opinion creating the appearance of being helpful can be just as important and useful in an exam situation as actually being helpful.

You make a very good point in your last paragraph--I believe that a significant number of the students who are asking questions are doing it simply to make themselves feel better, whether or not they realize it.
I do try to present a very affable personality to my students, as many of them are already scared enough to be in a math class.  Your answer reminds me of the importance of doing this on test days as well.

When I read that I thought not about students wanting to make themselves feel better, but the "converse" (?) fact that if the students need to devote mental effort to deciding whether it's safe to ask a question in the first place, it's likely to hurt their performance on the test. That would be an argument against coming down hard on students who ask illegitimate questions.

I wish I could upvote only specifically option 2. Sounds like a perfect solution. No talking/whispering, you get to give the exact reply you want without much follow-up arguments, you can still pay attention to the other students while "receiving" the question (hearing vs reading, which you can do while still checking your problematic students), the student will think about how much time do they really want to spend explaining their question, thus making it concise.... tons of advantages and addresses all OP concerns. I loved it!

My approach is approximately "no questions, period" (not after the first few minutes). I'm only in the room to proctor, not to talk about the exam. Even if there are typos on an exam, it is a very mixed thing to "make corrections" during the exam itself, because some people will already have spent time on the thing, etc. That is, "fairness" is sometimes approximated best by "uniformity".
One could follow up on "refusal to answer questions" by observing (to the students) that understanding expectations of format, this-and-that, are a large part of what such exams are meant to test. This may not console everyone, but it is a genuine point, and deserves repetition.
So, yes, even when there have been ghastly typos, I've just kept things as they were. Yes, this approach does entail announcing that, no matter how scrupulous I've been, there may indeed be typos, and that students should exercise their own judgement about that possibility. (Again, even if there are typos, it is not possible to correct them in-exam in a fashion that is clearly fair to everyone, unless it happens within the first few minutes.)
It did take me a long time (30+ years?) to get to this point of view...

Comments are not for extended discussion; this conversation has been moved to chat.

Do you feel the "yes the typos exist, deal with it" approach properly prepares students for life after university? Because in industry it is stressed that the earlier a problem is identified and correct, the less cost and risk there is to the firm. How does that factor in to your approach?

@corsiKa, I see your point, but/and typical "exam" environments are soooo artificial, so unreal, with so many unrealistic/anti-realistic constraints, that normal best practices are not easy to apply sensibly, I think. It is nearly impossible to make an exam that truly tests what one would like to test, I claim... so we inevitably make caricatures. And so on.

Some of my old professors followed this procedure:

Sit down and get test sheet.
Get 5 minutes to read the test carefully (pens down), we were able to ask clarifying questions during this time. This period did not count towards the time limit.
Start of the test, no more questions beyond this point.

Yes, this is a good procedure!

As someone who has encountered problems and issues in tests that only become apparent after some effort to solve them, I think this is a rather poor approach. -- Not all issues (by which I mean actual mistakes in question phrasing) are immediately apparent during a brief 5 minute examination. Poor wording or unspecified edge cases can raise their heads in the midst of solving it, rather than being immediately apparent. (For example, due to a typo on one test I took, a calculated ratio which needed to be approximately an integer for the result to make sense wasn't even close.)

Due to the structure of my exams and the nature of the questions, I don't see this approach working especially well.  That said, I think it could definitely work is some settings!

+1 for a novel approach to consider even if I may not implement it myself.

I've followed the first two steps for years, but I strongly disagree with the third.

I've always found it very distracting, or worse, to read other questions before I solve the ones I've already seen. 2. Often you don't know what to ask until well after you've begun working on the question. So, -1.

depends on how long the test is; 5mins could be inadequate. I would argue that 3. is a very bad idea. Often a student won't find the mistake until later on, as @einpoklum says. A blanket 'no questions' is definitely a bad idea. -1

Some practical points:

Spend the time and re-read the exam text "adversarially", trying to think up any possible way to misinterpret them, and correct for it. On the other hand, better to leave some option for mis-interpretation than spending half a page on spelling out the interpretation.
Have another teacher/TA in the course sit down and solve the exam in its entirety, both to catch potential errors/unclear points and to time it and assess difficulty.
Do answer trivial questions (e.g. confirmations) briefly, but kindly and in a supportive rather than derogatory tone. Example: Q: "Am I really supposed to do XYZ?" A: "Yes, those are the instructions." Don't try lecturing people about asking such questions; don't repeat the demand not ask such questions. Instead, try to smile (if you can manage doing that in a non-creepy way), expressing the pride of having brought your student from relative ignorance to the brink of being proven to have mastered the subject matter. I always felt proud of my students taking their exam!
Remember that students' questions while taking the exam may uncover an unforeseen problem with it. This has happened to me quite a few times - both as a student as a TA.
When faced with a "How do I solve this?" question, and declining to answer - have a look at the student's face. If they appear super-stressed, shaking, desperate - consider suggesting they try moving on to the next question/problem and go back to this one later; or that they go have a drink of water and catch their breath. Consider asking "Are you all right?" if you're actually concerned about them. Some people occasionally have 'blackouts', or otherwise become very anxious, and this sometimes helps. It actually 'discourages' useless questions in my experience, because even noticing that a stressed-out student is being attended to with a kind demeanor reduces stress somewhat. That might sound irrational, childish, overly soft, immature to you - but remember you're testing the student's command of math, not the quality of their character or their maturity. Plus - perhaps, for you, an excellent academic who made it to professorship the exams were not that hard and stressful as for other students - don't judge them until you've walked a mile in their shoes.
If you get a lot of questions overall, or about some point in particular - when the exam ends, either stay there for 10 more minutes and indicate that you will listen to issues regarding that question, or hold extra 'office hours' - for hearing and addressing questions about the exam in a little more detail - once you are able to talk about the actual answer, and at more length. This will help you understand what it is people were finding difficult to understand or to solve. Also, this will likely have a positive psychological effect on the students - whether they did well or poorly.

These are some really good points.  I especially like your point about keeping a supportive tone.  The exam is already hard enough for them; it's not necessary to be overly strict with your responses.

I love your point about tailoring my responses to their emotional state--I've been doing this unconsciously, but I think I can be even more effective now that I recognize the value of doing it deliberately.

Having a TA take the test is a great idea. When I was a grad student, "locking in" concepts that I learned as an undergrad was a big part of my learning process.

@sig_seg_v: I'm not sure how your two sentences relate to each other, but thanks for the compliment. Actually, it was an old tradition already in the mass first-semester CS introductory course in my alma mater.

I am also a mathematics professor, though at a large state university.  To be honest, I'm not sure why the questions are "annoying" to you.  Maybe you could clarify this, since it could help you get a good answer.  (In particular you say you disliked these questions as a student.  Again, honestly, I'm not sure why you cared about that.)  I also want to add though that I don't get that many questions on exams: probably about one question per 20 students per exam.  It is plausible to me that it might be part of the culture of SLACs that students ask more questions on exams, but I don't really know.
With regard to the undesirable kinds of questions: I actually find 2) rather weird.  I cannot think of a single instance in 11 years of teaching at my university where a student has asked me for a hint on an exam.  Only very rarely have they asked a question where I think they are hoping to get information out of me that will make the problem easier to solve.  This actually strikes me as being mildly inappropriate behavior.  A lot of SLACs have strong honor code cultures, so you might think about whether/how these kinds of questions are not abiding by the spirit of the honor code.  If you feel that way, you could put something in the syllabus about it.  Then, if a student asks such a question during an exam, you can say "I really can't answer that kind of question. I'll explain more later."  And then you can follow up with the student afterwards that they shouldn't be fishing for answers to exam questions.
With regard to 3): it's similar to 2) but more understandable/legitimate: after all, some solution methods are not going to get full credit.  These types of questions make sense when they already have an answer.  If they are asking something like "Would it be a good idea to integrate by parts?" then that really falls under 2).  You can try to be as clear as possible in your course before the exam and in the instructions of the exam which solution methods you regard as legitimate, but often there is some real doubt.
With regard to 4): if they are asking things that are already stated on the exam, just answer quickly by calling attention to the fact that it's already stated on the exam.
Coming back to the beginning of my answer, I think you should reflect on whether, how and why the SLAC culture encourages students to ask too many questions on exams and also whether you think that students at your SLAC in general get rewarded for asking lots of questions.  (E.g. do you think that other instructors  give out information to individual students in response to questions?  It seems a bit unlikely to me, but I suppose it's possible.)  If it's clear to you that students are not getting rewarded for asking these questions then maybe you could frame it as advice.  A student who is coming up every five minutes to ask a question is probably not getting the undisturbed thinking time that they need to do well on a challenging math exam.  On the other hand, if the practice is really not hurting them at all and just mildly annoying you...maybe live with it?

FYI, in my lower-level courses at a community college, this is an everyday occurrence. Students will not even be able to tell what's appropriate or not. I usually have one student per course who will ask 10 questions per exam. Putting a statement on the syllabus is of no help, because they don't read that either. It's a widespread problem, and for many of us the cycle is frustrating and tiring some days. (c.f., question on certain needy students expecting to use all your office hours every day.)

I added some clarifications about why most questions are bothersome.
I think SLAC culture is a significant factor.  As an TA/instructor in graduate school I hardly ever got questions during exams, but they were common at my undergrad SLAC and seem frequent at my current university.
I think that asking questions is a great thing, just NOT during exams.

@Daniel: Thanks, that's interesting.  Ten questions from one student on one exam?!? Yikes.  One more thing about the way I handle questions in my exams: the students have to come up to my desk at the front and talk to me, and we talk quietly enough so that this should be minimally distracting to the other students.  Fortunately, the classrooms are designed in such a way that a student can walk to the front rather easily.

Also, I don't mean to rub it in, but this semester "all of my office hours" consists of two hours, both on Wednesday.  So it would be okay if a student wanted to show up to both of them....though so far as I can recall that has not happened yet.

Would someone mind qualifying the term "SLAC"? Throughout my (UK) education hardly anyone ever asked an question during an exam; when they have, it was often followed by an announcement to the whole room that "Paper Z, Question X has a typo...", or "Diagram Y is wrong, heed the text...", or the invigilators suddenly decide to write the Date on the board. At my university, the instructors were rarely in the exam room, but were always contactable by the invigilators to clarify any errors in the papers, and the layout of the rooms made communication with individuals rather difficult.

@VisualMelon, "small liberal arts college". A peculiarity of the US system which aims to produce all-rounders by forcing people to take a wide mixture of courses even in tertiary education. At the risk of caricaturing, where the UK system abandoned the trivium and the quadrivium and introduced specialisation from age 16, the US just updated the contents.

some solution methods are not going to get full credit — Say what now? Why would some solution methods be worth more credit than others, if they correctly lead to the same correct answer?

@JeffE: For instance a homework problem early on in the course I'm currently teaching was to prove that a quadratic polynomial with complex coefficients has a complex root.  If a student proved this by citing the fundamental theorem of algebra, they would not get credit, because they're just asserting something that is much harder than what they're being asked to prove...

...Or: a practice problem for my most recent midterm asks students to prove that f(z) = 1/z is holomorphic at all nonzero z directly from the definition.  If a student uses the quotient rule instead, they are not going to get credit, even though their method is correct and leads to the correct answer.

@PeteL.Clark If they actually prove the fundamental theorem of algebra or the quotient rule, they deserve full credit.  (Yeah, I know that's unlikely.)

@JeffE There are methods that lead to the correct result, but are overwhelming for a certain problem or too error-prone. If a student uses such a method, I usually remove a few marks, explaining the reason. It happened also too me, when I was a student, to have marks removed for the usage of a possibly overwhelming method.

@JeffE: Something like this happened recently.  A colleague and I gave a preliminary graduate exam (whose entire purpose was to assess their skills; the grade does not appear on their transcript or get used in any other way), and one of the problems asked for the student to establish a certain limit from the epsilon, delta definition.  This student filled several pages establishing basic limit laws rather than directly taking delta to be (say) the minimum of 1 and epsilon over 10.  My colleague took off some points for this....

....because it seemed clear that if the student had been capable of doing the direct epsilon, delta proof, then they would have.  Admittedly if this had been an exam given in a course rather than a diagnostic test we would have hesitated to do this...but the point is that sometimes you want to test a skill rather than "get the answer by any means necessary."  As long as it is clear between the student and the instructor that the problem is testing a certain skill, then I think it's certainly fair to take off for other correct solutions that do not demonstrate the skill.

If students get questions clarified when they ask, suddenly the incentive is for every student to ask about every test problem (even if they don't need it).  This is obviously suboptimal.
Answering many questions is also unfair, as two students might both be confused by a test problem but only one asked -- hence, they are not being tested on the material, but on their willingness to ask a question during an exam.
My solution is to answer almost no questions.  My typical answer is "knowing the answer to your question is part of what's being tested here".  What's being tested includes literacy (reading the directions to the exam and the directions for the problem and interpreting same).  I make exceptions for two cases:

Typos in the problem.
Weird overanalysis of the problem.

In the former case (I made a mistake), I announce to the whole class the correction.  The latter case is when a student is contemplating using very powerful tools from another course, that he or she doesn't really understand, rather than the simple tools available in this course. Then I tell the student that it's not necessary to do it the complicated way.  This happens rarely, so I am not concerned about fairness.

Case 2 is essentially something that falls into "type 4" in my original question, and I think you've done a really good job of capturing the essence of this behavior.

Consider that in many places, for many exams, the proctors have nothing at all to do with the class or the subject matter. They are just there to supervise the room. Clearly, in that environment, there are no questions. If there are flaws in the exam, the faculty will have to make whatever compensations seem least bad after the fact. It might, then, be easiest to set expectations that all exams work this way, even if the proctor happens to be someone who could possibly answer a question. When I was a student of math and engineering back in the dark ages, that's how it worked. You got a test, you did the best you could.
Every student should know better than to use up all the time on one question. Even if the exam is perfect to the letter, there's always the chance that the student just isn't going to find the path to an answer in the available time. Telling students to (a) put a question aside if they are not finding a solution in reasonable amount of time and (b) write an explanation of why you think the question is insoluble is better than answering questions. If the question is broken, then (b) helps. If the question isn't broken, perhaps the student will earn partial credit for a thought process that is partially correct even if it hit a pothole.

Actually there is a half-way house: the proctors are from a different department and know nothing, but the question setters are available outside the room for the first 20 minutes, and the proctors will relay questions of the type "Is this an error in the exam?" and announce any replies which contain corrections.

First, make sure that your questions really are as error-free and unambiguous as possible.  Achieving that quality takes effort, though.  You will need to have one or two trusted TAs actually take the test to ensure that there are no obvious issues.
At the exam itself, announce a policy that if you have difficulty understanding a question, try your best to solve it on your own, and write down your assumptions along with the answer.  It would probably be helpful to state that you have planted no trick questions, and that smart-alecky assumptions won't fly.  Then, stick to your word and accept any reasonable alternative interpretations when grading the exams.
If you do get requests for clarification anyway, answer most of them by simply reiterating the "state your assumptions" policy.  If it turns out that there really was a bug in the exam, own up to it publicly by writing an announcement on the board.

I find magu_'s approach the best if you have to proctor your own class. Our institution solved the issue by having exams proctored by non-academic personnel.
Beside the obvious advantage that they simply would not be able to answer illegitimate questions it is also more cost-efficient. The academics have that time to do their research.

You just have to warn your students beforehand. As in,

Questions about the format of your answer will not be answered. Fishing for hints will not work as I won't give any useful info about the questions to any of you.

Give them a few minutes extra before you start the exam and ask them to read the questions and ask if the questions are clear. Giving them even just five minutes to read and understand the questions and letting them ask anything they want to be clarified will let you have an easier time later on.
Anyway, since you seem to be grading the papers, I'd also like to add that the type two and three are just fine as questions in my opinion, with the appropriate precautions. We had one professor who would give out any hint that you wanted him to give. He would start the exam like so:

You can ask for hints on questions and anything else your want. I will give you whatever you ask for on the question. However, this will mean that I'll deduct points appropriately. If you want the whole answer to a question, of course, I will even give you that, but, that will mean getting no points out of that particular question.

I had to ask for a hint once, it was something minor, so he wrote -2 to the side of my question (it was a 20 pointer out of 100), and just gave me the hint I needed. With the hint, I was able to answer the rest of the question, getting 18 points in total from that one. Though, if I couldn't answer the question, I'd have lost two points from my paper and that would be it.
I was the only one to ask for a hint on any of his exams because people thought he would deduct too many points. He was really fair though, a tiny hint wouldn't mean deducting half the point worth of that question from the paper.

During my teaching days, I managed a few exams. I used a strategy that was quite satisfyingly successful:
Right before the exam, I would have told the students that the exam would last at least for two hours. And during the first hour, no one is allowed to talk or ask any questions and I won't be answering any. If you need any clarifications, just move on to the easy or answerable questions during the first hour and give the rest a little thought. I should emphasize again that no one has the permission to talk for one hour.
Then after that, my job was way lot easier because many of the problems were automatically solved already. Although I should confess that my teaching days only lasted for two semesters and this method is not tested thoroughly, yet!

This would be a cause of great consternation for many students - judging from my own experience as a teacer.

Math student here;
Casting my vote for the direct, adversarial approach (particularly if you're not generally adversarial as it will maximize impact.)
This is always going on even in upper level math exams at my med-lg state uni, and it is really annoying. I am always hoping for a rule-nazi of a professor to lay down the law, but half of them don't even bother closing the door let alone addressing in-class distractions like inappropriate questions during exams.

I had similar feelings as a student, but I'm curious if this is a minority point of view.

What you consider an inappropriate question could very well be a critically important one to someone else. I find it highly unfair to impose your (pretty drastic) standard on everyone.

How is it unfair/drastic? That is, what kind of question would be appropriate beyond a simple clarifying question (e.g. in this question is it implicit that blah is a function of bleh)

I am not entirely sure what you mean by type #4, but I will try to address it. From my experience, there are high schools were it is taught that some things have to been done a certain way (like it is only allowed to use only a certain method of solving equations or written division has to been written down in exactly that way etc.) which pleases the teacher. I worked with 10-year old kids which were familiar with negative integers, but always asked whether it is allowed to use them since their teachers "forbid" them to use those in class. When I announce Gauß algorithm, students ask whether it will still be allowed to use the substitution method to solve equations. My math teacher always marked my test's answers as wrong when I wrote them as fractions or roots insted as a rounded decimal number (even when the problem was purely algebraic without a "real-world-context").
With this I want to say that especially for new students, it is sometimes not easy to get used to the concept "everything which is correct and well-argued is allowed to solve the problem". On the other hand, I often find the university lecturers have a hard time understanding this mindset of the students.
So, if you get a question of type #4, try to think if it can be because of this problem. If so, do not dislike it, but answer it honestly. If possible, say beforehand that "every approach which satisfies the following conditions: [...] is allowed".
Of course, if the question literally is "how many decimals should we write down" when it says "write 2 decimals", you can say "read the question again". On the other hand, if you write "you do not need to simplify", this can mean a lot of things depending on the teacher and you may want to clarify this.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
How to deal with students staying hours past the end of office hours?
Background: I am a fourth year math graduate student working as a TA for an introduction to proofs course with a focus on analysis.
I really enjoy the teaching component of my position as a graduate student, but this semester I feel as though students are taking advantage of my generosity.
As is typical for a TA in the math department at my university, I hold a couple (in my case, two) office hours per week, plus additional availability via appointment.  My office hours are nearly always occupied, which generally pleases me.  However, my students nearly always stay well past the point when my office hours are supposed to end, even a couple hours worth in most cases.
In addition, I tend to spend nearly all my waking hours at my office, so I have no problem meeting with students at a wide variety of times.  They are well aware of this, and several of them have requested frequent appointments that do not coincide with my office hours.  Again, the main issue here is that these appointments often last much, much longer than an hour.
I understand that the material of this course is challenging, and I am glad that my students desire to improve their abilities.  However, their behavior is seriously impinging upon my ability to progress in my research.
What are acceptable avenues for reaching a compromise between my need to progress in my work and my desire to assist my students?  So far I've considered the following:

I've attempted to subtly imply that I would appreciate less consumption of my time, but I don't want to discourage their eager approach to their work and they don't seem to be getting the hint.
Alternatively, I could lie about having meetings, other appointments, obligations, etc, but I would feel wrong doing so.
I could obviously just tell them that they can't stay late because I have other work that I need to perform, but again, I don't want to directly shut them down.

Ultimately, I would love to find some systematic way to decrease the strain that they place on my schedule.  One trick I have utilized is the deliberate scheduling of an office hour immediately before the taught class, since both me and any students have to leave at that time to go to class.  Are there other things like this I could do?
I'm not merely looking for a solution for this semester, because I'd like to prevent this problem in the future as well.

You don't need a "trick" to solve this problem. They're staying past the end of your scheduled office hours because you have been tolerant of this so far. (I suspect they completely missed your subtle hints.)
It sounds like you have made it too easy for them to use you as a crutch, rather than doing the work on their own and then coming to you with specific, focused questions. (Very much like this situation.) It's not good for you and it's not good for them.
At the end of your scheduled office hours, say (with a smile):

Thanks, everyone, for coming! Don't forget that if you need extra help, you can also schedule an appointment with me.

You can do the same thing at the end of a scheduled appointment:

It seems like we made some progress here. If you realize you still have questions after working on this some more, you can schedule another appointment.

Then if you need more of a reason to usher them out the door, grab your jacket and announce that you're going out for some coffee/air/exercise/something to eat.
If you think students are using office hours productively and genuinely need more time with a TA, consider letting the course instructor know - perhaps he/she should hire another TA to offer extra support.

@AegisCruiser One option would be to actually schedule some meetings at the end of your office hours. I assume you do meet with someone during a week, even if it's not a large part of your time.

@JessicaB But in that case, you are hiding the true problem, right? You don't tell the students that the true reason is you can't spend so much time on the office hours. So why wouldn't you simply say this?

@yo' True. It's one way of making things more enforceable though. I can imagine it being hard to get students out of your office if you're still sitting there. If you are locking the door, there's more chance of them going. It doesn't directly address the issue of them taking up too much time, but I think it would help to send the signal that you have other things to do too. I spent the summer explaining to people that I do not get three or four months holiday just because I'm not actively teaching students at that point.

Sadly, and I have seen this often, many students will be annoyed for having come to office hours and not been 'served'. To me that attitude generally indicates a lack of preparation and patience, and even as a student seeing that attitude is discouraging. If I were in OP's situation, I would still have ill feelings about turning away students. Then again, it must be done, otherwise how can you advance as a graduate student? You can't put the rest of your responsibilities on hold... it's just something you have to get used to I suppose.

Yep.  The end of the office hours are when you say they are.   The demands on your time are only going to get worse as your career progresses.  Learning to set boundaries now will help you quite a bit.

Help vampires keep sucking if you keep giving up blood...

I would also add that your students are adults. They should be capable of receiving information and making necessary adjustments.

I would add that it might be a good idea to impose a time limit on scheduled appointments and to start actively enforcing it. If a student can only make a 15 minute appointment rather than an hour long one, they will be forced to be concise in their questions, stimulating them into doing more preparation work. When the students get used to this, you should ostensibly be able to cover their needs in your office hours, so then the option of having an exceptional appointment outside hours becomes available again: 15 minutes of your own time is much easier to accommodate than an hour.

@Jessica B: So why not go and say what the reason is and then start closing up shop? Then you're not "still sitting there", and you're telling the truth. I don't understand why there seems to be this need for hiding/lying/dancing around the real issue. Why not just be blunt and say that you have to now tend to your other responsibilities/work? "Thank you for your time, but now I have to get back to work."

(cont'd) If they hang, then gently ease into creating an impression of busyness, by moving stuff around and getting things out, motioning to the door if necessary, or if your work really involves you leaving, then to start moving out of the office and shutting up shop. Neither would be too far from the truth. These students are (usually) adults and presumably intelligent, so they should be able to understand.

People vary. Cultures vary. Students have a tendency to be selfish, just like everyone else. The grown-up approach might work, but it's also possible it won't.

@mike3 I would go even further. It's none of the students' business what you're going to do after they leave.  It doesn't matter if you're going to spend the next hour reading StackExchange and playing Angry Birds.  Once office hours are over, they're over.

@JeffE: So then why not just use what I had suggested, only with "but now I have to get back to work" replaced with "but now my designated meeting time is finished."?

Or warn them first "office hours are over in half an hour, we'll have to end then" :)

3 every time.  As a teaching assistant, you are employed by the university.  They employ you for office hours.  You have no obligation to anyone, including the university, outside of those hours.
If instead of being at work, you were sitting at a table in the pub with beers in front of you (which out of hours you are entitled to be), would you accept students coming to you to ask questions?  If not, why not?  And now, why is your situation here any different?
The solution is simple – print out an A4 notice saying

Student enquiries between 9 am and 5 pm, please.

and stick it to the door.  If you particularly want to break your own rule for a particular student/question, that’s up to you.  But you’ve then established that outside of these times, you have a right to not be available.

I would add that students I've dealt with in this situation have been understanding when I said that I had other work that I needed to do.

I think that if you carefully consider the whole set of things you've said, you'll see that you already know the answer.
First, there is the negative situation that you want to stop:

"Students are taking advantage of my generosity"
"Students nearly always stay well past the point when my office hours are supposed to end, even a couple hours worth in most cases"
"The main issue here is that these appointments often last much, much longer than an hour"
"Their behavior is seriously impinging upon my ability to progress in my research"

Second, while you do want to solve this problem, you revealed some results you don't want as you solve it:

"I don't want to discourage their eager approach to their work"
"I don't want to directly shut them down"

Third, there's what you've tried so far to get them to use less of your time:

You have office hours (presumably posted) that state an ending time.
"Subtly imply that I would appreciate less consumption of my time."
"Deliberate scheduling of an office hour immediately before the taught class"

And finally, it seems like your goal is:

"Compromise between my need to progress in my work and my desire to assist my students"

Frankly, it looks like the real problem (to me) is that you want students to leave when they've taken up a reasonable amount of your time, without you having to directly tell anyone it's time to go.
But you have to ask yourself, why on Earth would they do that? All you've done is bend over backwards to accommodate their use of your time at every turn! And even if you had been more clear, there is a difference between what's reasonable and what's realistic. It may be reasonable for them to value your time more (by using less of it), but it's completely unrealistic for you to expect that to happen, without you doing something to make it happen somehow. People are fundamentally selfish and will use as much of your time as you don't stop them from using. It's up to you to stop them.
You want a compromise without changing your own actions, but that's not a compromise. Part of the compromise you have to make will be giving up some degree or quantity of your apparent wishes/goals in order to get others that you value more. Specifically, you may have to disappoint some students from time to time, and until you're willing to do that, you'll continue to feel like a doormat and be used like one.
It basically comes down to this: You need to decide what you want, and then make that happen. You don't know what you want right now, besides wanting to not have to deal directly with the problem of students taking more time than you wish. Except... I think you do know. You want the problem to fix itself, but know deep down that it won't. What you're afraid of is true: you have to do the hard thing and set limits.
Also, I would like to suggest that setting limits on student use of your time is not "shutting someone down" or "discouraging eager work". Saying those things is, in my mind, just a means to avoid the unpleasantness of having to tell someone to leave and being firm about it. If students need more help than you can give, that's not your problem to solve for each and every student. Live in the real world, where you have a limited amount of resources and you must apply them wisely. Your resource of time is being misused, and you must stop that. It is not fair to you to be used all the way up. Students have to study by themselves eventually, and you need to give them a reason to do that.
Here are some ideas.

Communicate. Actually tell them what's going on and ask for help. Hold a meeting with all the students, or print up a flyer, or put each student's name in a book and check it off once you've communicated this. Tell them, "Dear Student, I love helping all of you, and wish that I could continue helping you in the way I have until now, giving you all of my time and energy. However, as much as I hate the idea of leaving you hanging, I have to reduce the time I'm spending, and from now on I'll be ending office hours at the stated time and appointments after 1 hour." Ask for them to brainstorm with you how to fix the situation. Ask for their help directly. Ask how they actually want to grow as people and if just relying on you is their idea of true personal growth? Whatever you decide on and you clearly say will happen, do it.
Delegate. Brainstorm with the students to find ways to use your time more effectively. Suggest they set up their own study groups. Get the more advanced/smarter students to tutor the less so. Assign a student to come and kick people out for you.
Be consistent. Do make use of strategies for avoiding the confrontation of saying "it's time to go", but don't use only these strategies if that leaves times when you don't make someone leave. You have to change the way things work in order to set clear expectations. The moment you let even one student stay late, you set up expectations that are at variance with what you want, and that is truly an uphill battle. Students have to know you stinkin' mean business about ending at the right time, and the only way they know that (no matter what you tell them) is by actually doing it. Every time.
Demonstrate. One strategy that can help you is to use non-verbal signals. Get up and walk away when something is over. Even if you can't leave the room, can you get up from the study table and walk back to your desk? Can you take off your glasses, turn off a light, go into a different room, close up books and put them in packs? Get a neon light that you turn on when it's consultation time, then turn it off when it's over. Go open the door and stand there holding it, looking expectantly at them. Look obviously at your watch. Set a timer or alarm that rings (use a 15-minute warning if you like, too). Start talking about next time. Act as if you don't have to tell them they need to leave, act as if they already are in the process of leaving, and you'll find that they get the message. Physically break eye contact, turn your body away from them, and take a few steps. Leave the room and walk away, asking them to make sure the door closes when they leave. All these can be easier than having to say "it's time to go now." I promise they'll work for almost every student.
Be firm. By this, I mean precisely one thing: don't discuss it at leaving time. Discuss the new rules all you want, but never at leaving time. Leaving time is for leaving. Talk about  it next time you meet. Make an appointment. Send an email. Write a reminder note. But get them out the door.
Be oblivious. Use this as a last resort, but for any students who still have trouble leaving, and you truly still feel so uncomfortable repeatedly saying "see you at our next meeting" or "I really have some work to do" and really making them leave, then simply act as if they've left. Ignore them. Get busy with your own work. When they impinge on your awareness, act startled, and say "oh, are you still here? Office hours are over." Then go back to your work and ignore them. It will work. You don't even have to tell them to leave.
Give yourself a break. Recognize that you are the only one who can decide what you want, and you're the only one who can make what you want happen. If you don't choose to make what you want happen, you're the only one to blame for that (I guess you didn't really want it, enough, after all). So don't beat yourself up for not being Superman. You deserve to have the kind of life you want (within reason). It's clear you love your students, but it's not loving to them if you burn yourself out, or come to resent them over time.
Get real. You may not actually be helping your students all that much by being on call for them all the time. Will they ever learn how to study on their own? Are they learning the right habits that will help them in their future studies and careers? At some point, you have to stop flying your babies around and let them use their own wings.

Important note: I'm cognizant there is tension between be consistent and be firm on the one hand, and be oblivious (and possibly, demonstrate) on the other. However, realize that we're not dealing with a perfect world full of superhuman gods and goddesses—we've got a somewhat harried yet good-hearted T.A., a mere human, who struggles with setting firm limits on people he or she otherwise loves to serve, and who doesn't exactly relish confrontations that result in their disappointment. Since we're living in the real world, instead, I offered both what I think should happen (be firm and consistent) and also threw out a rescue line for situations where a particularly insistent or oblivious student makes things difficult. Think about it: once the lesson is learned (by the T.A.) on how to help people leave, and the experience is gained, even using the be oblivious "game" I suggested, change will occur within, and in time, this game won't be required. Consider: in utilizing these strategies, the O.P. will more likely be successful at the firm part, because in no case will he or she continue assisting the student past the requisite time, and that's the important part.
Don't assume others are exactly like you, and please recognize that sometimes, less-than-perfect coping strategies are necessary. For people who can stand to grow and are finding it difficult, they may need baby steps. Have some compassion!

re: 5. "see you next Tuesday". This is an unfortunate turn of phrase and should not be used in the UK.

@xddsg Is that better? I think it's really stupid that someone can't say that phrase innocently. Like, a car company can't trademark the word "sedan". Because then everyone else wouldn't be able to call their sedans sedans. How else do you say that you'll meet up with someone on the upcoming Tuesday? Ridiculous! :)

if the person is trying new things to get people to leave for the first time, and in fact might become flustered, it's sensible to avoid things that could be misinterpreted. Hustling them out of the door unexpectedly, being strict where you were previously relaxed and then shouting "see you next Tuesday!" as they leave would be pretty clear cut to me. Our TA does not want to see us again.

@xddsg My complaint wasn't really about you (you didn't invent the phrase), but about the world, where people are ready to assume the worst. All of my ideas should be taken in context, together. Note that idea #1 was to communicate clearly to everyone what the problem was and what will be done to resolve it, then there's little chance of misinterpretation. My example of "see you next Tuesday" was absolutely a hypothetical based on the idea of an actual next meeting time scheduled with that actual student. "next Monday" or "tomorrow" or "at our next meeting" would serve just as well.

@xddsg Note: to the pure, all things are pure.

Be oblivious. — No, don't play this game.  Be direct, be firm, and be honest.

@JeffE In fact, I don't favor being oblivious either—I would be very direct. However, given that the OP's personal preference is to avoid stress-inducing directness, I think it is quite legitimate for him/her to use non-verbal communication when that is more comfortable. I promise you that psychologically speaking, non-verbal signals get past the ego much more easily, and in many ways are more effective. Basically, in the holistic approach to letting people know that the time is over, using these non-verbal methods in conjunction with clear communication (see point 1) will be more effective.

@JeffE I also don't think they will have to be employed very often. A particularly tenacious student who tries to stick around past all reasonableness can be very hard to deal with for someone who finds confrontation difficult. The "be oblivious" strategy is a last resort for a tough situation, and is far from a game--it's an effective coping mechanism to deal with a difficult person. I updated my post to make things a little clearer.

I'd say that in academia "defending your time" always needs to be priority #1. Requests and demands on your time can expand endlessly, and the work is frequently invisible to supervisors (not on a clock, frequently at home, including nights and weekends), so you must set boundaries for yourself. If you get burned out or overworked then you won't be able to help yourself or any future students. Presumably your institution has an idea of how much time you should spend on office hours (sounds like 2 hours per week; for me it's 3), so you should follow that guideline and not extend it.
Personally, I'm of the mind that students always coming to office hours is not a good thing. They should be able to pick up most of the material from the lectures, book, and study with other students; anything else is a sign of a system breakdown. Office hour time with faculty should be a last-stop emergency measure (most of my friends with bachelors' degrees never went to faculty office hours their whole college career).
For practical purposes, your #3 item is very solid (it's basically what I do). Consider also scheduling the office hour at the very start or end of the day, so that you have uninterrupted work time to mentally focus on other tasks. Possibly schedule it right before a lunch or dinner hour and commit to leaving for that when the time comes. Tell students when they arrive how long you can work for them (e.g., "We have until 5:20", or "Let's work for 10 minutes so the next student waiting can come in"); I find that students get better at focusing, prioritizing, and coming in with sharp questions when I do this.

Addendum via comment: Also, specifically request that students come with specific questions about specific exercises, what step they got stuck on, etc. (the same protocol as on math.stackexchange). Going over the whole lecture again should not be allowed; that just enables students to skip or not pay attention in class, at the cost of double your own time.

I'm also a TA, and I greatly enjoy working with my students during my office hours. When my two hours are up, I'm often in the middle of working with a student, and there are other students who want my help. Here's how I handle the situation:
Whenever a student comes up to me and asks me for help when my office hours are officially over, I turn them down. If they're a student from my class, I let them know they can schedule an appointment with me, and if they're from another class, I help them find a different TA instead. (In my department, TAs prioritize helping their own students but are expected to help students from any class.)
Then, I let the student I'm working with know that I can help for a while longer, usually 15 to 30 minutes, depending on how busy I am. Then, if I can help them resolve their problem by that time, great! I can leave knowing my work is done. Otherwise, I help them find another TA who can help them and leave.
My situation sounds a little different than yours because I can ask other TAs to cover me when my office hours are over. However, there are still a couple things I do that you can, too:

When a student comes in after your office hours are over, even if you're helping another student, tell them to set up an appointment with you or come back the following week.
When a student stays past the end of your office hours, give them a cut-off time 10-20 minutes in advance. If the student still needs more help after that, ask them to set up an appointment.

This is a common occurrence - a young, approachable instructor, one who seems more like his/her students than their other instructors, is a natural attraction to students - they believe you will understand them not just their problems in the course. Others here have offered good suggestions for you, but basically, you'll have to wend your way through this until you establish boundaries that are clear but sympathetic to the situation. For the following semesters, you can set the ground rules by explaining that while you are contractually required to hold only two office hours, you have on occasion allowed more time to a student's particularly difficult or complex problem, but that extra time is not usual, as your academic responsibilities extend beyond the course you teach. Suggest that  students talk to one another (peer learning is exceedingly positive), and if there is a common question, they should come as a group, not as individuals to maximize the time you do have available for them. Students can understand everything if it is explained to them. Mostly, they are kids looking for a kind word of support from someone they respect, trust, and who appears to be like them. Showing them that you care doesn't mean that you care to the exclusion of the rest of your life. They'll get it.

The most important is that you find the best way to help your students and yourself in the manner you deem fitting. Giving more time to students may not actually bring you closer to this goal if you think about it, nor may it be optimal even if it does.
What is not often emphasized is that students learn better when they have to explain what they think to other students, be it their questions or answers. In many cases simply getting them to write out their question in a clear and detailed manner for everyone to see can help them find their own answer in the process of thinking how to express themselves.
And even if they can't figure out the answer themselves, there are always other students who can help and would be glad to help, just like you. Collaboration in pedagogy is quite under-valued. Ultimately, you do not have to be the solitary teacher, and arguably should not be, since teaching other students does not only help their own learning process but should in fact be one of the most significant goals of education. Students cannot merely learn to solve problems but must learn to convey and discuss their ideas with others.
Your role is to facilitate this process, by checking what students tell one another and stepping in only when serious conceptual errors arise, but letting them be active participants in the teaching. After all, if you can impart your knowledge and your ability to teach to just 2 students, they in turn can teach 4 others...
All this is easiest if there is some common forum for students to participate in, where you would have to encourage them to post their questions.

You can try to deal with this problem using email. You strictly enforce your office hours, but you tell the students that if they need extra help, they can email you. You can then deal with the questions of the students whenever it suits you best. Replies can be brief, you'll find it a lot easier to only give a few hints compared to a face to face meeting where it's difficult to not go into details.

Alternatively, I could lie about having meetings, other appointments, obligations, etc, but I would feel wrong doing so.

You don't need to "lie", because it's none of their business what other things you have to do, or even if you have no other things to do.
Simply allot x time for your meeting with the students, and when it is over, you simply tell them that time is up and they will have to look forward to the next session. And "goodbye". That is it. No justification, no excuses. The meeting is over.
This is not hard, and it is not specific to academia. It is basic, basic, basic human interaction. "Sorry, I have to go now" is a phrase you must surely know by now.

It might help if you limit each student that sees you to a set time interval--say, 10 or 15 minutes.  Or have a sign in sheet on your door that limits the number of students you will see on any particular day.  You seem to understand that YOU set the limits, the start and stop times.  But you also need to enforce those times and reschedule the overflow to a different day.
It may help for you to require the students that see you to post answers to the questions they have in a FAQ blog about the course.  Then you will not spend time with multiple students going over the same material.  Most quantitative courses have "lab" sessions with finite endpoints.  As a mathematician, I'm sure you appreciate that it is helpful to set clear limits on the set of all students you are teaching:)

Make the students reserve a slot of your time. Bonus if it is done using a web page (thus there's not a person who needs to turn them down). If they want to meet you in the morning, it's no problem, it gets debited anyway from your assigned weekly hours. If there are no hours left, they are showed an error message and will need to wait till next week (or maybe allow them to join another student… assuming you can handle both at the same time).
You could allow them to use up all your yearly office hours in the first month, but I would recommend not to allow them to expend so much office hours. At most for this month imho.
Finally, this also allows you to record the time spent helping students, both to students (see, I have been asked all these hours), to the department (if there's such demand maybe they should add more TAs?) and to yourself (it is easy not to realise how much time you really are dedicating).

Be honest. Then be strict. Value your time.
My suggestion:

1) At the beginning of office hours, genuinely express your thoughts and feelings to your students. You likely don't want to limit their learning. You like to teach them, yet you can only offer so much.
2) Define a strict stopping time. Write it on the board if needed. Make it clear that after the end of office hours, the office returns to be your office.
3) Live by your words. End on time.

You remind me of myself. I too tend to teach students on my off-hours. It's enjoyable, agreed. As long as you seem to understand that this is completely pro-bono work, and as long as you enjoy it, then I guess that's cool.
But you have to be reasonable. It seems like you're not respecting your own time, or perhaps, you have naively weighed how much time you have. Reflect on this. You can use that time in so many other ways. It's not just research time that you're likely losing.
Clearly announcing your intentions and feelings, as suggested, can alleviate any personal (and wholly irrational) guilt. Second, it serves as a catalyst to action; it'll make it harder to renege on your decision.
Speaking of which, I think I've spent more than my fair share of time on Stack Exchange today...

Point at the door.  Say "Out!"
Then, something like "Come back again at [office hours] if you'd like some more help."
Then, continue pointing and don't say anything else but "Out!" till they start collecting their stuff.
Have you heard of "Idiot Compassion"?
"It refers to something we all do a lot of and call it compassion. In some ways, it’s what’s called enabling. It’s the general tendency to give people what they want because you can't bear to see them suffering.

If you're just a pushover by nature, you may need to either find a different location to hold your office hours and additional appointments, or find a different location to do your own work.
Is the course too difficult for the students at their current level?
If not, just get the student unstuck about a particular question or stumbling block, then say, "I think you're well on your way now, off you go.  Have fun!" If the student is reluctant to leave, say, "I have full confidence in you.  You will be fine.  Let me know if you get stuck again."  Then walk out to the bathroom or the water fountain.
I love user21280's idea about fostering collaboration among students.  You can facilitate this by grouping two to four students at a time for particular questions, and after a little bit, suggesting they get together for regular study group meetings.  You can also take a page out of online teaching and get everybody into a google group talking to each other.

source: Stack Exchange

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

authors: Александр Левченко

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/

sort: votes


text:
What is the appropriate salutation for non-technical university staff in India?
There are issues in my living quarters provided by my university and I need to write a letter to the responding authority. The authority is a non-teaching staff.
As a research scholar, how should I salute them while sending an email or a letter.
I am confused between "Respected sir" and "Hello sir". Which one is appropriate among the both and is there any appropriate one other than these?

@hanugm Please edit responses to comments into your post rather than replying as a comment. Comments aren't meant to last and people might read your post without seeing the comments. The answer would be totally different in another place. In the US for example both of the options you gave would sound silly.

You can use Dear Sir.
I know students and research scholars use Respected Sir in case they address professors but Dear Sir will work in all cases.
Using Hello or Hi in a formal letter is frowned upon in an Indian university.

"Dear Sir will work in all cases"  What if the university staff is a woman?

If you don't know which staff member you are addressing, it is better to say "Dear Sir/Madam". In fact, most letters in India are addressed this way. The problem is the letter is copied to many people and sometimes it becomes difficult to determine who the author is addressing.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
How to react when encountering students who have previously failed my course?
Context: I am an assistant professor of mathematics at a small liberal-arts college in the US.
I did my graduate work at a large public university, and there I rarely encountered students who had previously taken a class from me, let alone ones who had failed one of my courses.  Now that I'm at a much smaller institution it happens somewhat frequently, and I've only finished one semester here!
At this time I have no idea how I should react to these encounters.  Generally former students and I exchange a pleasant greeting, but I find myself instinctively trying to avoid students who've failed because I'm afraid that they are still angry at me, I don't want them to feel bad, etc.
The title of my question says it all: How should I react when encountering students who have failed one of my courses?  I could simply treat them like any other student, but I'm concerned about reinforcing the stereotype of "the tone-deaf mathematician with poor social skills."
Perhaps this question is a better fit for the interpersonal stack exchange, but I figured I'd start here.

Please refrain from writing answers in the comment section; this conversation has been moved to chat.

believe that it is a 2-way street. If the student failed the instructor failed. When I get into math classes like intrinsic Math or Calculus I am a failure. I needed these classes for my computer science degree. These classes were consuming all of my time outside of worktime, When looking for help to understand these, I felt like I was on a deserted island. Some tried to tell me that this is the way computers work, but if that was true why are none of those function keys one a computer keyboard. I did graduate with 3.48, would have been hire with out Math. Continue to Nurture

TL;DR: be consistent
Speaking from the other side of this: I once struggled severely with one math class in particular and ended up taking it 3 times. I failed the first two times (the first try was a dud - I was a terrible student; the second time I gave it a good try but found the subject very difficult) then the third time with my studiousness greatly improved and my understanding of the subject finally sinking in, I aced the class. Here's where it's most relevant to your question: I had the same teacher all three times.
As other answers noted, the students really ought to be upset with themselves. Even bad teachers - and I had some qualms about this teacher - are rarely the sole reason for failure, as if so many students were failing the school would or at least could be urged to intervene. A large part of my failure was my own habits and then my own difficulties with the subject. How did the teacher handle that, and how would I have preferred them to have handled it? Thankfully, both those questions get the same answer; that teacher did a great job in my opinion.
The teacher was respectful, fair, and aware. It was a relatively small class at a huge school, so ultimately a pretty large class (~60 students). She acknowledged knowing me with simple eye contact, smile, nod that sort of thing and knowing my name (which is unusual in such a big class) but she did not make me feel uncomfortably highlighted at all, she respected my space and left it up to me to stand out or hide. She continued holding me to the same standard as before the 2nd and 3rd time I took her class, not wavering to have higher or lower expectations, which I appreciate. Lastly, she didn't ignore or emphasize the situation, but she did acknowledge it where appropriate: as I came to her for help one-on-one she'd gently give advice on where she thinks I need to focus efforts on or just general study tips, encouraging me to come to more office hours and work with TAs if I'm struggling, but then she'd leave it at that. No dwelling on past failures, no extreme pushing to get me through (I mean, she did fail me twice...err, or rather I failed her course twice). Even as I started to succeed (I eventually aced the class!) she maintained the qualities I described above, albeit more encouraging and "keep up the good work" rather than "I recommend you _____________". Her consistency with me, and also between me and other students, was an important part of the respectful relationship we maintained through it all (even despite my grumpiness through some of it, especially in my bad-student days where I'd try to put the blame on her when it laid most solely with me in that first attempt).

Thanks for posting the student perspective -- I think that's very valuable, here.

Repeating does not matter as long as you get there .I work with people who dropped in and out of college ,who started late and who have repeated stuff .

Yea it's no big deal in retrospect. At the time it is a sensitive situation, if only because there's a perceived need to pass the class, and likely also an emotionally/socially challenging issue for teacher or student. But life goes on, and better yet if one repeats and their perseverance pays off!

Wow you had a great teacher! In my 4 years at university only encountered 2 strict yet consistent and fair professors.

Yes, also in retrospect this professor was impressively good. At the time I disliked her, blaming my failing on her teaching style and thick foreign accent. Really she was a huge help and the sooner I recognized that the sooner I enabled myself to succeed.

I tried to copy/paste the plain text of your answer into Word to confirm that I think the amount of bold sentences in your third paragraph is distracting. I think it reads much better with no emphasis added.

@Therkel I added all that emphasis to make it easier for people skimming to get the main points.

I'm surprised at the premise of this question. You're assuming failure is bad.
As educators, there's a responsibility to teach a subject matter, but also an implied responsibility to teach a culture and skillset that prepares students for life. If you teach your students that failure is something to be embarrassed about to the extent that it makes you avoid simple interactions with people who are aware you failed, then you're missing the opportunity to teach them that failure is a learning opportunity. By avoiding students, you're playing into the negative stigma, which is the real way you're "failing" these students.
Some others above have suggested not avoiding the students, which I agree with, but I really feel you need to take this a step further and incorporate a "don't be afraid of failure" attitude into the class itself, versus just after the fact. Help students prepare themselves for failure. Even if they don't fail your class, they're going to fail something at some point in their lives, and you have an opportunity to prepare them for that.

I must admit this is one of the best First Posts I have reviewed.

That students failed your course should not mean that you should avoid them.
I think lecturers should accept (and most do) that there is always the chance that a number of students will not pass their course. (Sometimes there might be good reasons. Sometimes your course just happened to be the one where a student learned a life lesson — e.g. "laziness doesn't help you pass your exams", or even "mathematics wasn't my destiny after all").
But that shouldn't mean that these students should no longer be part of usual human interaction, such as greeting people you know.
Actually, I would say avoiding certain students would be awkward and actually would contribute more to reinforcing the stereotype of "the tone-deaf mathematician with poor social skills."

Showing up as not remembering what actually happened may actually help.

@erfink downvoting an answer for words that were never used in the answer is inappropriate. Nobody but you even mentioned genetic ability.

@erfink I meant that someone who failed a mathematics course might have come to realize that mathematics is not for them — it's a personal decision and also should not affect the usual human interaction with the lecturer of the course.

I joined to answer from a student's perspective.
I failed a 3rd level calculus course. Briefly, I had taken Calculus 1 from a professor and wanted to continue with her - she was demanding, but a very good and fair instructor. In order to schedule Calculus 3 under her, I took Calculus 2 in an accelerated summer course. I wasn't well prepared and failed the Calculus 3 course. My feelings toward the professor were never negative. I still believed that she was a good instructor and my failing grade was my responsibility.
Several students advised me to retake Cal 3 under a different, more lenient professor. Instead, I retook the course under the original professor. She never treated me as a sub-par student, and I never treated her as if my failure was her fault.
My point - treat your student as a former student that you have met before, but not as one who has animosity toward you. It's very possible that they learned from you and still hold you in high regard in spite of the failure.

In public, you should treat them as any other student. Being able to play the tone-deaf one is actually an advantage here! If the situation arises, you may acknowledge casually you have met before (without specifying when and where). The worst thing for them would be being singled out in front of their fellow students (like in "...advancing to the next problem. X, you should already know how to handle that... that is, if you have been revising since...").
If you want to improve the local culture: when you have opportunity to take them aside very discreetly for a moment, you might offer to them something like this:

If you want to know what went wrong the last time, or want some pointers of what exactly the goal that you will have to meet is, just drop in at my consultation hours - and I'll explain.

I have taught many calculus classes, and students failing my classes is not at all unusual. Sometimes on the first day of Calculus 2, I might make an offhand remark like "Some of you look familiar, I may have had you for Calculus 1" even if I in fact recognize some of them as having previously failed Calculus 2. I hope this causes some students to have a feeling of relief: "The professor remembers me from somewhere, but he doesn't remember me specifically as a student who failed."

Currently this is the only answer that suggests mentioning it to them and offering it as a learning opportunity which would be my reaction as well, upvoted. I wouldn't take them aside though but would instead just mention it as part of the announcement @idmercer has suggested "Some...familiar...may have..Calculus 1; for those who find themselves repeating the course I am honoured you are taking it a 2nd time round and would be happy to offer some additional pointers on where things may have went wrong last time."

One lecturer pointed at me and said that some people like my course so much that they keep returning .Other students burst out laughing .I just said Bloody Students because I was technicaly a staff member because I had a part time research position .I thought it was a big joke but I am a rough diamond .I guess that really sensitive people could get upset.

Honestly? As a student I'd find it more awkward if you were. Just smile and say hi like you would with anyone else. I always find if a professor is friendly and approachable then it's more reassuring.

Background:  I was a student at a small science and engineering school (which has since reclassified as a liberal arts college), and I failed my first semester freshman math class (calculus).  I made up the class by taking a comparable class at an adjacent school.  In my sophomore year, it became clear that being a semester behind in math was going to make all my science and engineering classes that much harder.  I wasn't sure about the best way to catch up, so I sought advice from the only math professor I knew at my school:  the one whose class I had failed.
I dropped in during his office hours and explained that I was looking for advice on how to catch up.
How I wish the conversation had gone:  Prof:  "Good question.  What options have you considered?"  Me:  "Doubling up on math classes next semester or taking a differential equations class at a community college over the summer."  And then we'd weigh the pros and cons or maybe he'd suggest a third approach.
How the conversation actually went:  Prof:  "You failed my class?  I don't remember that."  Me:  "Well, yeah, water under the bridge.  What I need now is--"  Prof pulls out grade book and tallies up all my homework and exam scores (twice) and compares it to the curve for that semester and repeatedly apologizes because it was "really close."  I didn't need or want to hear that.  The effect was that this completely derailed the conversation and made the whole thing an uncomfortable visit to a past failure.
Takeaways:  Students fail classes.  They may blame themselves or you or external circumstances.  Regardless of the actual (or perceived) reasons, at a small school, they're likely to need your help in the future.  They may even end up in another one of your classes.  If they're still at the school, working toward a degree, focus on now and not on the past.  Treat them like all the other students.  The ones who blame you and hate your guts will avoid you.  If you avoid the others because you think it's the polite thing to do, that might embarrass/intimidate them from seeking your guidance or signing up for another class that might actually benefit them.

If they're angry with you, they shouldn't be.
They failed your course, you didn't fail them.  If anything, their attitude should be one of apology and yours should be, I expect you to try harder this time.
A little bit of indifference on your part is not too much.  They have to prove themselves to you, after all.  Once you see they are making an effort and that they are likely to pass this time, you can lighten up.

You should not avoid the repeats. They do not feel bad in general. Remember that if somebody is doing your course again, he or she may have done really well in other areas. Failing the odd course here and there is normal at a credible tertiary institution where they do not give degrees away and hence the degree still holds value. Remember that final exams have multiple candidate numbers       and you did not specifically fail that person because there were no names on the scripts .
When I repeated control systems in 1986, the lecturer was very surprised to see me back because he thought that I was good in class when it came to asking questions. I get on with him fine. If you have a sense of humour, you can crack jokes about your repeats. Some students deliberately fail the odd thing to prolong a nice social life anyway. They will pull finger and pass when they feel like it.
At university everyone is clever enough to pass with a C or better because otherwise they would not have passed the entry exams .The dean said this in 1979   . If somebody fails it is because they are lazy. The only stuff I failed had early morning lectures and I through being lazy got myself in the internal assessment boat where I needed more than 50% in the final to pass where others could pass on say 38%. So none of this is your fault so the repeats can’t feel bad about you.
I am very thankful that my department made me repeat. It was borderline repeat material but I needed the year to grow up. Instead of working on the door, I got a part-time research position. At the time I was the only undergrad to have one; so I realised that it was a privilege and pulled finger and made something of it. So some repeats have nothing to be angry about at all.

I tried to give your answer some structure, but it is still very tedious to read because you are jumping between different lines of thoughts. If you can, please [edit] it to be more coherent.

Though there are many good answer, felt to add a few lines. Failure and success is a part of the game. Don't underestimate the students who have failed your course and that does not make you an inefficient teacher provided you have given your best.
Treat them as other student but give them more attention and try to understand why they have failed in your course. Talk to them friendly and try to know the root cause of the problem so that with the due course of time they can over come that challenge and gain success next time.
"Actions speak louder than words", give a good gesture to the students and encourage the students who have failed so that they would try their level best to come as successful candidates next time.

You should always remember you are judging the performance of the student, not the student himself/herself.
It maybe this person has to work outside school hours to make ends meet, needs to take care of someone at home, has boyfriend/girlfriend trouble, has medical issue etc, - a thousand circumstances none of which are of your business to know - so she or he could not devote enough time to your class.
Failing (or doing poorly) should never make you loose sight that you are teaching real people with real and sometimes complicated lives.  Thus, treat him/her like you’d treat any other student, irrespective of score in your course.

I suppose failing does happen, but perhaps the answer here is to best as possible prevent students from doing so.  Have you considered during the term trying to reach out to underperforming students to discuss their progress in the course?  Many of them may be too embarrassed to reach out when they are struggling with the material, and it may be best also if their grade is at a point where they can't turn it around to advise withdrawal from the course rather than fail [this could be a particular institutional quirk - but in the universities I attended it was considered better to withdraw for no grade than fail and receive a 0].
This pre-loads the awkwardness to during the semester, but intervention can help some students bring it around, or at the least feel that their difficulties are acknowledged - and will help ensure a continued professional and respectful relationship.

At this time I have no idea how I should react to these encounters. Generally former students and I exchange a pleasant greeting, but I find myself instinctively trying to avoid students who've failed because I'm afraid that they are still angry at me, I don't want them to feel bad, etc.

I'm not a professor, so take this for what it is.  The reason you're asking already establishes that you care, which is a great thing.  You care for your success in being a teacher as well as the success of your pupil.
If it were me, I would ask the student if they would mind meeting with you after class.  There, I would have a conversation.  Acknowledge that they were previously enrolled in your course and were not able to perform to the satisfaction that you think they are capable of — it's important to express you think they are capable of succeeding (otherwise you would be having a different conversation) because it communicates to them that they have potential and you aren't discouraged by their past performance.
Over the course of the conversation I wouldn't focus on their inability to perform, but express that you would like them to succeed.  In order to do so, you would like to identify what did and did not work for them last time (perhaps it had little to do with your course and there were external factors affecting their performance) and determine if there are any steps you both could take to ensure success.  Perhaps leading to a plan for them (or possibly you) to follow through on.
In any case, don't act like you have never met the student or their previous time in your course did not happen.  Don't shy from events that occurred or let them influence your behavior.  You formed a student/teacher relationship last time, this time will be building on it.


text:
How to withdraw a published paper when former boss seems to be raising ethical and data integrity issues with the editor?
Recently our group published a paper in an important open-access publication. During my work, I was subordinated to a person who left the research center six months before I finish the study, but during two and a half years this person evaluated the work, and suggested some analysis and modification in both pictures and graphs (I have all this personal communication). Specifically, this person had knowledge about the way how the data were generated and about local ethics statements, formally approved by a scientific committee. Since he left the research center, we did not talk about the manuscript with each other and I remained working in both figures and analysis to be incorporated in the submitted version; obviously it seemed clear to me that we had no obligation to show the final version to someone who was not part of the group anymore (this person was not listed as author in any time during the execution of the study because he asked this). In addition, our group performed some additional adjustments in the manuscript following indications of two experts during the process of review. The new boss was informed about the manuscript to be finalized, submitted and later, accepted. The contribution of the former one was properly acknowledged in the final version of the paper.
The former boss sent us a letter where he states he did not know about our work (i.e., that, supposedly, we made our study without his agreement and knowledge - misconduct, so). It seems that he had some kind of personal problem with someone in the research center before he left, so I believe he wants to prejudice the group, and myself in particular, since I am the first author of the study.
Some days ago I was surprised by a communication from the Editor-in-Chief of the journal where the paper was published, asking about the raw data of our work and if we have proofs concerning the ethic statements related to our study after a message sent by the former boss to the publisher.
While I have at least a dozen of emails attesting that the former boss knew about the study,  I don't know if I can show them to the publisher. Thus, I would like to withdraw the manuscript in order to avoid any future trouble with this former boss. I am very, very disapointed with this (this is a serious questioning about my conduct), and I would like to withdraw the manuscript from this jornal. I would like to know how to do this. Any suggestion?

I deeply appreciated all replies, thank you all. I've contacted the Editor in chief of the journal where we published the paper and explained all the situations in a clear and open manner, and he understood the point. The paper remained published without further action since our arguments were truthful. Concerning the person who attacked us, I decided to just ignore him. Silence is the best answer for mediocre persons.

Can you please clarify what exactly have you been accused of?  I can't tell whether it's an accusation about authorship or about scientific fraud.

Thanks for your reply jakebeal. The former boss sent us a letter where he states he did not know about our work (i.e., that, supposedly, we made our study without his agreement and knowledge - misconduct, so). It seems that he had some kind of personal problem with someone in the research center before he left, so I believe he wants to prejudice the group, and myself in particular, since I am the first author of the study.

I have at least a dozen of emails attesting he knew the study, but I dont know if I can show them to publisher. My decision is to withdraw the manuscript in order to avoid any future trouble with this person.

you say that below that you had a friendly relationship with him, pick up the phone and call him. Ask him what he's upset about it.

edited question to incorporate comments

I understand you as saying that your former boss does not want to have you to use his name in conjunction with the study, but then he does not want the data he collected to be used either. Is that, in summary, what you are saying?

Thanks for your reply Daniel Hatton. This is a very important point. Maybe in Chile, where the former boss came from, they have other kind of conducts...

The publisher is unlikely to let you withdraw the paper unless you convince them there is an extremely serious problem with it (misconduct or an unfixable mistake).  They have an ethical obligation to make the paper available to the research community, regardless of whether you regret publishing it, and it takes a powerful argument to overcome that obligation.
In particular, if you ask to withdraw the paper, then the publisher will assume that the accusations against you are true.  If you succeed in withdrawing it, then the entire community will assume there was something terribly wrong with the paper (and, if you don't publicly identify errors in the paper, they will assume it was an ethical problem).
In other words, withdrawing the paper is tantamount to admitting guilt.

I have at least a dozen of emails attesting he knew the study, but I don't know if I can show them to publisher.

Yes, you should certainly make use of any evidence you have that the accusations are not correct.
There should be no problem with the ethics statements.  Presumably you have proof of approval by the appropriate review boards (or, in the worse case scenario, they can confirm their approval).  If you don't have proof, then maybe there really is a problem.
As for the other accusations, hopefully the e-mails from your former boss will help clarify the situation for the editor.

Even if there is a serious problem, I doubt they would let you withdraw it, making it disappear completely; this is typically not possible after publication. They would instead retract it: they'd print a notice in the journal's next issue explaining the problem and alerting readers that they no longer stand behind the paper. People looking for the paper online will instead see the retraction notice (the original paper might also still be available, with the word "RETRACTED" stamped over out). This also usually makes it impossible to publish the paper elsewhere.

The main problem is that I suspect that probably the former boss will keep attacking, even though I prove that there is nothing wrong with my study. His goal is to tarnish my reputation. It seems to be a personal problem, actually.

When you say that his goal is to tarnish your reputation, specifically, are you implying that he had a problem with you (rather than just "someone in the research center"?

I say 'my reputation' specifically because I was the first author of the manuscript. I always had a friendly relationship with him, so I simply can't understanding why this person is doing this. That's no make any sense to me.

It must be confusing, yes. But I agree that given the evidence you have, you should be fine.

@Worried: If you say you have had a friendly relationship with him, maybe you should do what Mark Joshi suggested and just contact him directly (and politely, as much as possible). From what you're describing it does sound like he's acting erratically, but maybe you can come to understanding nonetheless, if you actually have some civil communication. When people ``communicate'' by accusing one another through a third party (like a court or an editor), the conflict will almost inevitably escalate, to no-one's benefit, so it's better to avoid it, when possible.

Hi @tomasz, I have sent a couple of emails to the accuser, but I never received any reply. I definitely guess that, if you have some doubt about anything regarding a publication, you should, first of all, to contact the authors instead of send a letter to publisher, especially when a lot of people know that you were part of the group that you are accusing.

In addition, I recently discovered that this person now is engaged in posting anonymous criticism against some works in blogs. Obviously, even if you prove that you are not guilty, your reputation may be compromised.

I found your actual problem difficult to understand. Independently of the - hypothesised - agenda of your former boss (which you do not really know unless you talk to him), what does he claim? That ethics approvals have not been obtained? That experimental data are somehow flawed? Could you be more specific as about the accusation?

I believe you can show the emails you mentioned to the publisher as a proof regarding ethics statements etc., since they were sent by the same person that is accusing you of misconduct now.
If there was no actual misconduct, I see no reason why you should withdraw the paper. Withdrawing should be your last resort, such a retraction would probably taint your CV quite a lot.
It seems the previous coordinator has an axe to grind.

I see no reason to withdraw the paper simply because you are "offended". Someone is checking on the appropriate records -- provide whatever records you have and that you think clearly demonstrate that the results shown are legitimate, then go on with life.
It makes no sense if everytime someone steps on your foot you tell the world that "this place clearly does not respect me; I'm going to leave this town right now and will never return".

It seems that he had some kind of personal problem with someone in the research center before he left, so I believe he wants to prejudice the group, and myself in particular, since I am the first author of the study.

Time to talk to a lawyer or two!  There's the legal department for your institution (go through your department chair), and you may also need your own lawyer.  Start with the institution lawyer.
Slander and defamation of character are immoral and illegal.

Outside of North America, a lot of human interactions can happen without a lawyer. OP should simply answer the questions from the editor and move on.

Yeah, I'd avoid lawyers.  It will both complicate things and look defensive/guilty at this stage.  (And in the U.S. the bar would be very high to have a case for defamation here.  Publishing a paper makes you a public figure for issues related to this paper, and public figures can't win a defamation case unless they can prove actual malice.)

I can only speak to how things work in the US, in case that's helpful....  Talking to a lawyer can be helpful in two ways.  One is to get information.  The other is to outline an assertive letter or two for the OP to send directly.  The conversation with the lawyer can be had without the former boss or the Editor-in-Chief being apprised.


text:
Is there a Ronin alternative in Europe? How to be an independent scientist in the EU?
I am a senior postdoc in a theoretical/computational field and for various reasons I am quite tired of jumping from one postdoc to another (have to switch cities/continents every few years, and many post-doc funders contractually require a maximum academic age). I am not eager to work in industry either though. I found out that some people become "independent researchers". Sometimes it means essentially doing freelance R&D for various for-profit companies, but sometimes they actually perform normal academic research, but their funding is channeled not through universities with their unwieldy bureaucracies.
In particular in the US there is an organization called Ronin institute, which helps independent researchers to apply for funding and receive it. My question is: is there anything comparable in (continental) Europe?

Some clarifications have been edited into the post, and a discussion about normal academic career progression has been moved to chat.

RI scholars are not limited to US, they’re located in countries throughout the world: http://ronininstitute.org/research-scholars/research-scholar-map/

IGDORE is based in Sweden and registered as a non-profit. From what they say the latter makes them eligible for certain Swedish and EU grants.

It is exactly what I was looking for!