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I'm a high-school student in the United States, and from time to time a teacher makes a mistake while writing on the board in front of the class. Usually, the mistakes are minor, such as forgotten punctuation, but sometimes there are more major mistakes.

To give an example of the latter, I took an informal math class during the summer. The teacher, only a few years older than me, was working through a problem on the board, which we were expected to copy down as he wrote. It was fairly convoluted, and most of the class didn't seem to be paying attention.

At one point, the teacher made what I was 90% sure was a mistake in logic. As far as I could tell, one step of the process would work for some numbers but not others, although he claimed it'd work for all numbers. I noticed the mistake early on, but I was hesitant to point it out because a) I wasn't entirely sure it was a mistake, and b) I couldn't figure out how to correct him without being rude and setting myself up as better than him. (In the eyes of the rest of the class, too — I'd previously gained an arrogant reputation, and given that he was a math major at a prestigious university, I definitely didn't know more about the subject than him.) On the other hand, the flaw in logic might confuse other students.

Finally, seeing that no one else was going to see/point out the mistake, I politely asked him to explain his reasoning. He used an example number, which turned out to be one of the numbers that worked. I asked for him to work another example, this time suggesting one of the numbers that I thought wouldn't work. Seeming slightly thrown by my forcefulness, he tried the number — and it didn't work. He then realized his mistake in logic and corrected himself.

I didn't feel right about the way I'd handled it, and afterwards, when I described the situation to others, they said I'd wasted everyone's time and would've been better off directly pointing out the mistake rather than asking him to explain it.

So my questions are:

  1. Is it even worth correcting a teacher's minor mistake in situations like this, or does it just make them look bad?

    • Related to that, does it depend on how minor the mistake is? And if so, how can I tell what kind of mistake is worth ignoring?
  2. If it's worth it, how do I do it politely?

59

I think your approach was actually pretty good. I think what you should attempt in the future is to ask a specific question that you think/know will not work. Also, definitely avoid accusing him of being wrong. You should address it from a stance of attempting to better understand the concept.

So, rather than giving him the chance to try it with an example that does work, say something like:

Could you help me understand, I'm trying to get this to work with 525,600 and I can't get the intended result. Can you help me figure out where I'm going wrong?

This is deferential and non-confrontational. It's completely appropriate for you to ask for clarification, particularly if you can't get the concept to work properly. It's really important to help your fellow (less attentive) students learn the concept appropriately so that they can do well on their homework/exams later.

In math classes I've taken in the past (at the college level) all of the professors I've had have been happy to have errors pointed out to them because it helps them do their job better. Not all professors/teachers will feel this way - and someone new to it like you had in this class may take it with less grace than a more experienced professor. So, until you get a bead on how they will react to being corrected, it is a good idea to go about it in an indirect way.


If it's a minor error (such as writing down the wrong number or getting the sign on a number wrong), this is still something that is good to correct as part of working through the problem in class is to practice working through it and minor errors will give the incorrect result, which will make "checking" the answer fail.


Please don't wait until after class to address this. If you do, your fellow students will not have the benefit of the correction and may think the logic will work when it does not. At that point, you have to rely on the teacher remembering to correct themselves in class the next time it meets, which often doesn't happen.

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Is it even worth correcting a teacher's minor mistake in situations like this, or does it just make them look bad

You are taking it from the wrong end. More precisely, your are not prioritizing the problematics correctly here.

The purpose of teacher isn't to look good. I'm perfectly aware that in interpersonal situations, ego can be an issue, especially when there is a status of authority, as it is the case regarding teachers.

But a teacher is there to teach. And since they are humans as well, they happen to make mistakes. Either it's mindless errors or them being wrong on something - we expect them to have a good grasp of their field, not to know and understand by heart whatever is included or related to it. Each time it happens and isn't corrected, the teaching is flawed by it and the students learn false things.

Whenever you spot an error your teacher makes, you have the opportunity to fix that flaw. While the teacher is indirectly responsible from it, you have the ability to fix the situation, by preventing the teacher to fail at doing their job. By pointing out the mistake you make the teacher to notice, which give them the opportunity to correct themselves and therefore correct whatever rubbish the students were going to learn as something correct.

Taking that into account, the issue of having the teacher teaching things is more important than having everybody involved to look good. In your example, the teacher already did a mistake, that's done and they didn't needed you for that. What you can do on the other hand is to give them the opportunity to correct it for everyone to know.

From my college years through the people who taught me and the classes I gave myself, I know that 'I don't know' is among the hardest sentences to say, especially when you are in aposition of knowledge or technical authority, but those who truly have the wellbeing of their students at hearth and will value it more than their ego will say it in a blink rather than answering rubbish to a question they don't know or understand the answer.

It's the same here : asking about a mistake allowes the teacher to explain both the correct thing and eventually to warn the students if the mistake is particularly easy to commit.

Regarding the way to do it, you are right to not want to do it pedantly, even if the teacher is still fine with your move, the students may not like you from that and/or respect the teacher less. In your case, you tried to work around it by 'tricking' the teacher with a value that would break is formula and apparently the other students weren't on board because it takes time. Moreover, it can seem even more pedantic and arrogant, since driving the teacher's moves towards an anticipated failure seems infantilizing.

A good compromise I use in these cases is to inject doubt in your sentence, doubt is the mark of the sciences which let everyone make progress without taking their own ego and beliefs into account :

Excuse me, but I'm confused by <whatever> part of the formula, it seems to me that it doesn't work for all cases. I'm afraid I could have missed something.

  • The teacher will focus of what you think is a mistake in the particular context in which it may be wrong.
  • By not assuming that it is a mistake, you are giving to the teacher the opportunity to do it, saving their face in front of immature people who might see it as weakness.
  • By not assuming it's a weakness, you save your face in case the mistake was on you, which can somtimes happen if you are used to point out mistakes.

Nobody's feelings are hurt, the mistake is corrected and it doesn't waste time.

3

To answer this question, perhaps the best approach is to ask a few other questions.

Firstly, I'd ask, What am I here for? It seems rather banal, perhaps, but if you're just in the class because you have to be, it might really not matter. Your approach toward the teacher may turn out (whether you want it to or not) somewhat snobbish or smart.

On the other hand, if you honestly there to learn (which it sounds like from the reading of your post), if you ask a question to the teacher politely, your attitude can come across as an interested student who honestly wants to learn from the teacher.

Secondly, I'd ask, What kind of teacher is this? I've been in classes where you can feel that the teacher likes nothing even close to a challenge. Fielding questions in a group setting is difficult, makes them nervous, and even brings them to the point where they make more mistakes.

On the other hand, there are some teachers who love the material they are teaching and know it like the back of their hand. They want to share what they have learned with others, and are glad for questions.

That said, my preferred approach would be to raise my hand (provided a fairly small class setting), and say something along the lines of,

Say, you said that xyz works with any numbers. How is that, since plunking in the numbers {6, 28.8} yields 42?

I'd also mention, if things start going amuck, just nod and accept what your teacher says: don't argue over it.

1

One of the things that was encouraged by my lecturers was self confidence. They WANTED students to point out their mistakes as it happened, because if they wrote something wrong down then it would be replicated 100+ times.

If you correct the mistake, you demonstrate 2 things. 1. you're concentrating on the lesson 2. your understanding

Neither of these 2 things are something that a teacher will complain about. As such, a raise of a hand and a simple comment of 'I don't think that XXX will work for YYY' is perfectly polite and acceptable. If you're wrong, well, clearly your understanding of the problem is wrong and needs to be corrected; which is why the teacher is there.

Bear in mind, that if this happens several times a lession, it isn't a reflection on you; it's a reflection on the teacher.

Don't be scared of them - they're only human.

0

If it was a real mistake you would have been 100%(!) sure thats what it is. You should simply point it out1 and if there is no agreement leave it, you know it better, that should be enough.

But its rarely one can be 100% sure about a mistake a teacher made.

So for any other situation, let me tell you how I usually approached:

The facts are, something your teacher is explaining comes over odd for you, not to say straight out wrong. But isn't that the usual classroom flair?

One thinks that what the teacher is saying makes not really much sense, until you have more insight and you get it.

So you simply could describe your problem from the point what you don't understand, instead of explaining him what is wrong in his example.

I mean you don't even have to pretend that you don't understand what he is explaining, its a fact, leaving the cause aside.

So I would simply ask about the problem, and let him explain the relation to your problem, or why the problem is in no relation. If you still don't see why he is right, do what students (should) do. Ask him for clarifying it so you can understand it.

If he is right for the 10% of your uncertainty, you learned something and he noticed that you are paying attention.

If he is wrong, he will catch it by himself without loosing his face, and he still will notice that you understand the matter well enough, to get confused by his mistake, what is a positive note, too.


1Not like showing him up, but politely asking if it is a mistake and in case of disagreement showing something up you are 100% sure about shouldn't be a problem.

  • You 'might know it better' - but what about the blissfully ignorant rest of the class? It's not fair for them to be fed misinformation, surely? – Tim Aug 24 '17 at 8:26
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    @Tim I once had a teacher who had not much knowledge about the matter he was teaching. And it happened a handfull of times over the courses I had with him that he explained things that had been plain out wrong. Arguing with him, even demonstrating why his statement can't be true, had not been accepted. Those who cared came after the class to me and discussed the matter with me. And the blissfully ignorant... Well, how they benefit from a discussion? I didn't wanted to express one shouldn't try, but biased by before mentioned experience I wanted to clarify, one shouldn't insist on it. – dhein Aug 24 '17 at 8:35
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I think what you did was probably the best course of action.

Look at it from the teacher's point of view: your authority comes from the myth that you're an infallible source of knowledge and wisdom, but the truth is that you're only human and you make mistakes. Even the most knowledgeable teachers mess up sometimes! So... the kindest thing to do (unless you really hate your teacher) is to not try to undermine the teacher's authority by directly pointing out their gaff, but to ask a question that will force the teacher (if they are any good) to spot and correct their own error. It's a way of fixing things without the teacher losing too much face in front of the class.

Teachers–even good ones–will make mistakes. But it's kinder to give them a chance to spot and correct their errors, before you embarrass them by pointing them out. (And, of course, you very well might be the one embarrassed if it turns out the error you point out is actually yours and not your teacher's!)

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I realize this was asked 7 months ago but I was searching for similar solution. My stats professor corrected a problem on Confidence intervals (C.I.) incorrectly.

It was an explanation for when 2 fixed samples (same n) are taken from a normal distribution with unknown mean M and a known standard deviation and a 90% C.I. for M is constructed with the 1st sample and 95% C.I. for M is constructed for the 2nd sample, will the 95% C.I. be longer than the 90% C.I.? I wrote based on our textbook that yes and when n is fixed and normally distributed, decreasing the C.I. decreases the margin of error (E) which in turn increases the C.I. estimate. This didn't need to be stated for the problem at hand but she crossed out decreases E in this statement and wrote increases. I had no choice but to bring this up to her because it went against our text and if our textbook is wrong, why did she assign it? It was an error that would have led to confusion in future problems.

So, I politely asked her in an email, "could you please clarify the H.W. question pertaining to the 90% and 95% C.I.?" I pointed out that what I wrote was exactly in the textbook, word for word and provided the page #, then asked if I was misunderstanding the text. She replied that it was correct and that she mistakenly corrected my statement. I don't like correcting anyone, especially a professor, but it was too confusing to fail to do so. Yes, I'm not going to be a statistician (I only need the class for nursing degree but if I were a professor and made a mistake that would ultimately lead to error down the road in class, I'd prefer correction).

  • 1
    You might consider removing all of the technical details of the specific problem that you corrected your professor on from this post. They aren't particularly relevant to the interpersonal situation at hand and might steer people who don't understand them away from an otherwise helpful answer. – Rainbacon Apr 9 '18 at 2:12
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When I was a lecturer I encountered this situation plenty of times. In particular at the beginning, when you are new to the task, it is easy to get overwhelmed between the explanation, the need to keep the class focused, the attempt to make complicated subjects understandable to the slower students, and so forth. Errors will just pop like flowers in a spring field, and stick out in their wonderful colours.

I usually did not like when, otherwise good, students pretended not to have understood and asked me to re-explain the whole thing just to make me aware of some error. This detracts time from the lecture, it makes the lecturer rewind their thoughts, with an obvious overhead in catching up once the error is clarified.

So, you spotted a mistake?

  1. raise your hand, or catch the lecturer's attention by voice
  2. state the issue, briefly and concisely, e.g.

I think there is a typo (or an error) in that statement (formula). It says XX on the board, it should be YY instead.

  1. if the lecturer's insist that they are right, provide a working example

As stated, if I use ZZZ number, it does not work.

Done. Everyone happy, no one harmed. Knowledge has been restored to its holy correctness. Do not worry about being direct with your remarks: they are the lecturer, and if they feel threatened by your correction, then they ought not to be in such position.


I notice now that you mention that your lecturer is only a few years older than you. They may look insecure. Treating them as adults, i.e. telling them things straight and concisely, will boost their confidence. To them it communicates that the concepts were clearly conveyed to the point that students can identify the wrong statements in the reasoning and correct them.

Treating them as idiots, i.e. having them re-do the exercise with a number of your choice because you are pretending you did not understand, while it is obvious you did, undermines their authority in front of the rest of the class, who may now think that it is a dumb-and-dumber game; it also makes them feel insecure, as it conveys the message that their error has made the entire lecture less clear despite their efforts.

This should be less of a problem with older, more experienced, lecturers.

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