I faced the following situation a few days back. I am doing my teaching assistance work under a professor.

I attended one of his classes as a TA during which he was teaching some technically wrong stuff, which he assumed as true. Since most of the class were students of the course, they do not know which statements are correct and hence are not in position to rectify the professor's mistakes.

There are more than five other TAs but no one pointed out the problem. I don't know whether the TAs know what is correct.

I stayed silent and observed whether anyone would point out the mistake but the class ended without anyone realizing the professor's mistake. The reason for my silence is this question.

Is it offensive to the professor to point out such mistakes? My question boils down to: Is it proper etiquette to point out mistakes that a professor makes during their lecture?

  • 51
    How you approach it makes all the difference. Professors are human -- they will react much better to a question ("did you mean to say..." or "I thought it was x, not y, can you clarify?"), or to a discussion in private later than to being called out in front of everyone ("Hey, that's wrong!!!")
    – Kathy
    Commented Aug 29, 2019 at 14:25
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    Unfortunately, every answer here can be right and every answer here can be wrong. It depends entirely on the personality of the professor and your relationship. I urge caution in your position.
    – Buffy
    Commented Aug 29, 2019 at 15:12
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    For what it's worth, although I try not to make mistakes, I'd always prefer that someone points it out as early as possible when I do. The worst thing that happens is I get a bit embarrassed, but that's so much better than students walking away with wrong information. I made a mistake once that was not caught and it ended up making one of my exam questions invalid Commented Aug 29, 2019 at 15:47
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    For best results, frame it in the form of a question. "Shouldn't the sign on the second term in the polynomial on the right hand side be negative?" is more polite than, "Hey, the equation you wrote is wrong," and acknowledges the possibility that you may have simply misunderstood something.
    – Matt
    Commented Aug 29, 2019 at 17:44
  • 4
    It might be helpful to elaborate on the nature of the mistake. There is a huge range of things that a 'mistake' might be and how you react is highly dependent on the specifics. For example, 'technically wrong' (or not completely 100% accurate) statements can be essential in many intro classes because getting bogged down in the minute details can be harmful for the overall understanding of the topic for the average student in the class. You don't want to be teaching intro calc and bring up a point that is only pertinent to people taking grad level analysis courses.
    – eps
    Commented Aug 29, 2019 at 20:31

17 Answers 17


It depends on the type of mistake. All mistakes must get fixed to make sure the students don't learn anything wrong. However, how to best fix the mistake depends on the situation.

If it is a small mistake that can be fixed easily (e.g. a missing minus sign) I would recommend bringing it up on the spot. The 'cost' to the teacher and impact on the lecture is minimal but the benefit is potentially significant.

For more serious problems in a derivation/ argument like the one you described I think the cost benefit analysis often comes down in favor of waiting until the end of the lecture and informing the professor then. Then the professor can prepar a correction lecture explaining clearly what the mistake was and what the fix is. Trying to fix a mistake like the one you described on the fly can easily end up in a very chaotic lecture in which nothing is clear anymore and the students get very confused.

In general, don't worry too much about politeness and etiquette but more about what's best for the students. Your job is to be the best teacher!

  • 53
    I like this answer and upvoted, but I think "inform the professor" could be phrased better. There's certainly a non-trivial chance here that OP was the one in the wrong, not the professor. Commented Aug 29, 2019 at 19:28
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    I was about to write something similar. Correcting an error in a sign is usually welcome as it is a mistake. Telling that the whole concept they are explaining is wrong requires caution: meet with him in private and ask this to be explained to you, this opens a good opportunity for discussion.
    – WoJ
    Commented Aug 30, 2019 at 12:06
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    @KamiKaze: Sorry, “non-trivial” is mathematician-speak. It means “moderately difficult” (in sentences like “that exercise is non-trivial”) or “moderately large” (in sentences like “there’s a non-trivial number of people who believe in ghosts”). In the latter setting it’s suggesting a larger number than “non-zero” would. Commented Aug 30, 2019 at 13:07
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    Since you're talking about the cost/benefit of waiting to bring a larger mistake to attention after class, I'd point out that the primary function of a course is the instruction of students. If the students learn something incorrectly, they will then begin studying it incorrectly. There could be a period of several days between the instruction and any possible 'correction lecture' during which the damage could be magnified.
    – Brian R
    Commented Aug 30, 2019 at 14:54
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    @Kami Kaze: This is the first time that I heard it is used for "moderatly large --- I've sometimes seen this usage, but I think both in math and elsewhere the most common meaning is "not trivial", where "trivial" means small enough that it can usually be ignored or it isn't worth worrying about. So rather than "moderately large", nontrivial more likely means being large enough that it probably shouldn't be ignored. That said, I think the stronger notion of being moderately large is much more common in math than elsewhere. Commented Aug 31, 2019 at 8:19

You know your professor better than we do, but I have only experienced professors who were thankful when their mistakes were pointed out (also by TAs).

It's not bad etiquette:

  • it helps everyone involved to learn something new.
  • you point out the mistake in a friendly and factual manner, so they can save their face.

Everyone makes mistakes and can err, even a professor. It's not embarrassing, but a wrong reaction might be. But my respect for someone being glad about their mistakes being corrected always just grew. This especially shows that they care about teaching their students.

  • I asked in general because I can be a ta for a professor with whom I'm not familiar...
    – hanugm
    Commented Aug 29, 2019 at 13:38
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    I like this, but it is a best-case scenario. Unfortunately, not all instrucors feel this way.
    – Ben Bolker
    Commented Aug 29, 2019 at 19:35
  • I'd say it depends on both the lecturer and the mistake. In some circumstances it could possibly come off as the TA trying to look smarter than the lecturer, which would not be advisable. Telling the lecturer afterwards generally will have the effect of giving the lecturer a chance to rectify his mistake the next lecture without losing face. But, as I said, it depends on circumstances. A relaxed, senior lecturer may welcome the mistake being pointed out in lecture, but they will probably say as much if told about it after the lecture (or they may say: thanks for not saying anything till now!)
    – Stumbler
    Commented Aug 31, 2019 at 15:12

I spotted an error with a professor's example and, having checked and confirmed my work over the weekend. I went to his office the next week with the example and showed him. He was happy with the correct example.

My surprise was that he presented the corrected example clearly stating I had sorted it to the whole class - nearly fell off my chair!

So, go for it and be polite. Any good professor will be pleased.


Check with the professor outside of class time; find out what their preferences are. They may want all corrections publicly and immediately, or all corrections privately and later, or they may ask you to make a judgement call as in @user2705196's answer ("how important is this correction? can it easily be fixed on the fly?"). Make sure to be diplomatic, qualifying your comments by saying that you might be mistaken (even if you're pretty sure you're right).

  • you might actually be mistaken (consider double-checking your concerns with some of the other TAs before going to the instructor)
  • this might be a low-level course where the instructor has decided to sacrifice some technical correctness for the sake of clarity
  • maybe the instructor would rather not interrupt the flow of class/would rather correct mistakes later or in a different venue (e.g. posting corrections on the class web site); this presents obvious problems with students spending more time being confused, or absorbing incorrect material before seeing the corrections, but it's the instructor's decision about how to run the class.
  • maybe the instructor is an insecure jerk and doesn't want to be corrected at all, unlike many of the site members who have commented or answered here saying they'd always want to be corrected. In that case you should do whatever you can to fix the problems in a separate channel (e.g. in lab or tutorial sections); you can even (quietly!) organize your fellow TAs so that you're all presenting the corrections (as in @mkennedy's answer). You should still be diplomatic (and make sure that you don't mess the students up, e.g. make sure that they know what the "correct" answers will be for testing purposes)

Yes, it’s usually good to point it out, but be polite and careful about how you do so.

Some good ways to point something out:

  • “Should that f(x) in the last equation be f(y)?”
  • “For the third step, should we be assuming that the marginal cost is positive?” [when your suspected mistake is a missing assumption]
  • “I’m confused; you said that ZFC is a complete theory, but I thought that because of Gödel’s incompleteness theorem we believe it’s not complete. Am I misunderstanding something?”

Some important general principles to bear in mind:

  • Make sure you don’t embarrass the lecturer. So, phrase it as to suggest the mistake was more like a typo or oversight, or your own possible misunderstanding, not their stupidity or ignorance.
  • Make sure you don’t embarrass yourself, if it turns out you’re wrong. So always phrase it with some uncertainty/questioning, never as a bald un-hedged statement.
  • If the lecturer doesn’t agree about the mistake, leave further discussion until after the class. Arguing it out in class will embarrass at least one of you, and waste everyone’s time.
  • Minimise the disruption to the lecture. Try to phrase it clearly and concisely, and give it at a good moment — soon enough that it’s still fresh in everyone’s mind, but wait a little for a “paragraph break” if necessary rather than interrupting the flow.
  • If you’ve previously corrected mistakes and the lecturer accepted them but seemed annoyed, check with them before doing so further. They may feel that e.g. you’re nitpicking unnecessarily about unimportant details, in a way that’s not worth the time or disruption. Whether they’re right or wrong, that’s a pedagogical judgement call that you should probably respect.

  • In the end, remember that the buck stops with the lecturer, not with you. A good lecturer should gracefully and gratefully accept useful corrections. If they don’t, and mistakes recur, then you won’t be able to single-handedly rescue their lecture course, and trying will probably make things more confusing for students, not better. So accept that you can’t fix this course, file it away as a useful lesson for your own future teaching, and (if the mistakes are really serious) discuss it with some other experienced faculty member(s) to see if it’s possibly worth reporting.

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    This is amazing: "Arguing it out in class will embarrass at least one of you, and waste everyone’s time."
    – user102072
    Commented Aug 30, 2019 at 9:17

This so depends on the personality of the professor and is not really abpout etiquette but rather about personal relations.

At one postgraduate pure mathematics class I attended in Cambridge, the lecturer wrote down a theorem and one of the students immediately said out loud 'that theorem cannot be true: consider the counter-example of...'. To most of us, it seemed he had a good point.

That lecturer, a Fellow of the Royal Society, and noted for self-possession, was able to explain kindly why the supposed counter-example was not relevant - something that was far from obvious. But I can readily imagine that a less self-confident professor, not good at thinking on their feet, would have been thrown by such an intervention. Not all professors have complete mastery of the subjects that they are teaching.

  • 1
    I think it is generally more allowable for students than TAs, though it depends on whether the class was set up as a lecture or a seminar.
    – Weckar E.
    Commented Aug 30, 2019 at 14:15
  • 1
    The fact that the lecturer took it in stride does not mean the remark was not rude. However, as someone who's attended a lot of math classes, I would more likely put my money on Asperger's than rudeness on the part of the student. Commented Aug 31, 2019 at 19:12
  • @MatthewLeingang Were you there? You must have been! That is precisely the correct diagnosis. Nevertheless, I know some lecturers who could not have coped with such an intervention.
    – JeremyC
    Commented Aug 31, 2019 at 21:36
  • @JeremyC Like I said, I've been in the research math world a long time and have witnessed a lot of students such as you describe. Commented Aug 31, 2019 at 22:48

Ask a non-assertive question rather than pointing out errors

I agree with user2705196's answer, but will refine it a bit:

When relevant Instead of saying something like

Professor, I think you were wrong to state that X, it's actually Y because Z.


Professor, can you elaborate a bit on how X agrees with Z?

this way - if you got it wrong, they'll explain it (and it would still help other students, who might have the same misconception as you); and if you got it right, there's a good chance the response would be "Oh, Z? It should be Y, sorry" - and then the Professor has corrected his/herself.


My practice was to always point out a mistake (politely) and I prefer my TA or students to call me out. I am only human.

However, I know some faculty could take that the wrong way. If you are working with a professor who you think might not react well to being called out in front of the class, then try pointing out an error or outdated information after class (in private).

  • 2
    Good point. For any professors out there, I recommend mentioning to the TAs something to the effect of "If I make a mistake, go ahead and bring it up right then" if you'd like that to occur; if not, say you've got a system you prefer, obviously don't do that, but my point is that communication is key for this kind of thing, and you want your subordinates to know exactly how to handle such a discrepancy, rather than, say, post a thread about you on Academia.SE :)
    – user45266
    Commented Aug 30, 2019 at 4:19

Step 1: Do not assume that you are correct. Approach the situation with humility, not assertiveness.

First, review the lecture and notes and try your hardest to figure out why the professor presented what they did. Ask other TAs to better explain the misunderstood portion. Do not claim that the professor said something wrong but rather present your confusion.

IF you cannot justify the professor's explanation then approach the professor and ask them to lead you through the explanation according to your notes. The hope is that they see their mistake and will say "Are you sure I said that during lecture?" to which you can reply "Yes, I am certain but I did not want to detract from the lesson at hand."


Indeed an embarrassing situation and public rectification must be avoided, at least in environments where discussion is not a part of the game. This is my experience.

Talk to the teacher and s/he will fix that.


I've had both. In one case I proposed a 3rd option that was within the rules he put forth and it worked, and in one case I approached after the class and discussed my confusion/questions.

In the former even though I had proof of something (I'd worked it out because, you know, thinking outside of the box) I was unable to get him to acknowledge it. It was unfortunate, because mine was creative AND 'cheaper' to implement.

In the latter, the professor listened, stared at the drawing, laughed, and said "In the 15 years I've been teaching this class, no one has pointed that out. You're right- it's wrong".


I would never consider pointing out something in class as there may have been liberties taken with the example/material to make it simpler to present. An after class discussion is most useful. And showing that you have strong interest in the topic for further diving, assuming said Prof is devotee of the material, will lessen any negative impacts of 'nit-picking'.

However you may still have a Prof that is a complete and utter .... pr*ck. It happens. In that case, just let it go. And you may have to determine what you want to do on an examination where the correct answer is what you know and the correct answer is what he knows... and they don't agree. .... but you didn't ask that ;P


I recommend not pointing out the error during class time. I would follow up with the professor in the privacy of their office. No one wants to look stupid but everyone makes mistakes. I would have all of your supporting evidence in hand and then ask about it in a private situation. If the instructor was indeed mistaken this will allow them to offer a retraction and correction in the next class period.

  • 1
    I would +1 you if you dropped the last sentence. I mean, you would gain the Professor's favor, but that's not the appropriate motivation IMO.
    – einpoklum
    Commented Aug 30, 2019 at 17:44

I was a TA for class being given by a respected visiting professor. I attended the lectures because it was my first time being a TA for this class and I'd only gotten a B when I'd taken it the previous year!

He made mistakes, generally a few each lecture. Sometimes I would ask a question about it and he would fix it. Sometimes I would get a friend of mine to ask. I kept very complete notes and would hand out errata/corrections in lab every week.


As a student, when I believe the professor has made a mistake (big or small) I always frame it as a question. Like if I see the professor accidentally left out a minus sign, I will just politely ask why the minus sign went away from that term.

Often times the professor did make a mistake, but often times they didn't as well and I accidentally missed a step that they did. This saves the potential embarrassment of trying to correct the professor and being wrong, as well as being a learning opportunity if I missed something.

Keep in mind the possibility that the professor was not wrong and that you missed something.

I imagine you could do the same as a TA. Since it's after the fact now, I would ask during office hours.


In my classes, there was a culture of "don't cause the professors embarrassment". The best way to avoid this was to, after class or in an e-mail, ask the professor:

"Hey, so the you were talking about x being y way, but I read somewhere else that x was z-way. Could you please clarify this with me?"

Since you're a TA, that should mean that you have ample time, even face-to-face, to talk to your professor about that.

Asking in the middle of class interrupts the flow of the class, however asking the professor separately, then them correcting it at the beginning of their next class allows them to let it flow a little bit better.


The TA shouldn't correct the instructor during the lecture. It undermines the instructor's authority and distracts the students.

Write down the mistakes and let the instructor know afterwards. The instructor can then choose to remedy this by sending an email to the class, correcting himself in the next lecture, etc. He will also have the option of asking you to correct him during the lecture next time, if he is fine with that. On the other hand, from his tone you may discover that he is uninterested in the corrections to begin with - a discovery better made in private than in front of a class.

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    "Undermining authority" is a poor argument for being silent about mistakes.
    – einpoklum
    Commented Aug 30, 2019 at 17:43
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    @einpoklum I think more careful reading of my answer will reveal that I do not advocate being silent about mistakes, but rather taking care in when and how the mistakes are discussed.
    – Trusly
    Commented Sep 2, 2019 at 18:10
  • 1
    Ok. Well, "undermining authority" is a poor argument also for being temporarily silent about mistakes.
    – einpoklum
    Commented Sep 2, 2019 at 18:13

Tell him after class. There will be some profs that don't care but others who would be annoyed with an in class interjection. This is a simple safe default.

And it's not just about putting the prof on the spot but that lecture is a sort of participatory conversation between the students and lecturing prof. You are interjecting yourself into that dynamic. Again, some won't care...but a few would prefer that students either rise to correct (or not). In addition, in the case that you're mistaken, it will definitely be derailing for the class in a way that a mistaken correction by a student (the real participant/recipient of the lecture) would not.

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