Admit a teaching mistake without losing authority

Question

I made a small mistake while teaching a very simple concept. It was mainly a numerical mistake, the essential parts of the concept were well illustrated. I want to admit my mistake and even though most students will receive it well, I fear to lose my authority with some students, mainly the ones that think that they could teach the class.

Answer 1

As a student, I actually learned a lot from watching how professors handled mistakes. In a lecture, if you didn't intentionally make a mistake, this is an unscripted moment, and therefore a glimpse into how an experienced person deals with something unexpected. I came to respect professors who were able to make a mistake and fix it; it taught me how to think, and how to be honest.

By the same token, I lost respect for professors who were more concerned with the appearance of authority than just admitting to and fixing the mistake.

Addendum After reading some of the other responses here, I feel I should add that I'm a white male from the US, and didn't consider other cultures or underrepresented groups when writing this answer. I certainly see how perceived authority among students could become more of an issue if the cultural norm is that a teacher shouldn't be challenged, or if the teacher is working to overcome implicit bias. I still feel, on balance, that admitting to and fixing mistakes confidently is intellectually honest and will engender more confidence and trust than ignoring mistakes, and actually provides an opportunity for a positive learning experience. However, I am not an expert on these issues, so I wanted to highlight that as a caveat.

Answer 2

I think the genuinely legitimate authority of "the teacher" is that they have far more experience than their students. Not that they are perfect, etc. Yes, experience does tend to diminish mistakes, but does not eliminate them. In fact, part of "the lesson" can/should be about how to cope with inevitable errors! :) (as opposed to pretending that no errors will be made...) In particular, the teacher should not pretend to take up a "position" that requires "defense". :)

Answer 3

I make mistakes in class - not often, but more often than I'd like. I note them and correct them as soon as I see them (or a student points them out to me).

Sometimes I'm asked if I do that on purpose to see who in the class is awake. I reassure the class that there's no need since I err often enough by accident.

You may annoy the few troublemakers who think they can teach the class better than you, but you will earn the respect of the true learners.

Answer 4

Whoa, there is actually a lot to unpack in a post that short.

Presumably you're teaching in a university setting. What "authority figure" are you even talking about? If students look up to you, great! But it is not even remotely a part of your job to make sure you're "above" them in some imaginary hierarchy; your job is to teach them. Trying to enforce it in some way is usually unproductive both for the teaching and your "authority".

mainly the ones that think that they could teach the class

Do you actually feel contested? Why? If they want to teach the class, they are free to apply to the department asking to do so. If they don't, but feel like you're doing a poor job - why don't they serve as TAs helping other students? There are plenty of ways to handle this tension if it exists, and productive ones don't involve wrestling with the troublesome students.

Finally, when correcting mistakes, consider how impactful they were. If it is something silly like 2+2=5, either don't bother or mention it at the start of the next class briefly asking students to go over their notes since they didn't catch it earlier. If it is more impactful, dedicate some time to it. You have still delivered value to them, so chin up and try to see the situation through their eyes. No one wants to spend ten minutes on someone addressing insecurities more so than they do the actual content of the lesson. Stick to the point, and keep educating them: respect is earned by doing your job well. Your job is teaching, not some sort of power play.

Answer 5

The best policy as a teacher is to ensure the students know that you are human, just like they are, and can make mistakes. Let them know, also, that the best learners, and most knowledgeable people, are those who never close their minds but continue to learn. Those who think they know everything, besides being wrong, are destined to remain ignorant of many things they might have otherwise learned had they been willing to make corrections to their own preconceptions and mistakes.

Respect is earned, not commanded; unless you are teaching at the lower elementary school level (up through about the fourth grade). While you can always receive a certain level of respect by imposing it on the students, they will not have actual respect for you unless you have earned it.

In Asian societies, students would never dare to correct their teacher because it is taboo to cause one's superior to "lose face." But this, while maintaining a certain form of "respect," loses the advantage of teaching independent thinking. Students merely copy their teachers, generally finding little advantage to recognizing a teacher's potential errors in the absence of an acceptable way to disclose them. When an error is noticed, the student just stays quiet about it.

In Western societies the pendulum is at the other extreme: respect for teachers is secondary to one's own "right" to independent thinking--and correcting a teacher can become a matter of one's personal pride. I recall the story of a European boy whose family had moved to America. He was in primary school but was far advanced (a genius) in math. His father saw fit to enroll the nine-year-old in a math class at the local university. One day, the mathematics professor incorrectly worked a problem on the board, and the child corrected the professor--undoubtedly in the less mature manner of a child. The professor took umbrage at being corrected by one so young, and got very angry. The father ended up defending his son to the professor, and the professor had no defense because he had made a mistake. (Mathematics is somewhat more black-and-white than some subjects might be.) The professor had only made things worse for himself by attempting to hold himself up as infallible.

When an Asian student of mine corrected me in class one day, I was so surprised that I praised him! It is great for the learners if they are alert enough to catch a teacher's mistakes, and I preferred to have it corrected than to have inadvertently taught something which might be incorrect. I always invited my students to correct me--though it was often the case that I had, instead, opportunity to explain why their offered correction was mistaken. I would appreciate them for trying, and it was a teaching moment from which all of the class could benefit.

In Asian societies teachers are not supposed to appear fallible. They are not expected to admit any mistake. They are expected to maintain their superiority always. But, in my experience, the principle of earning respect in place of commanding it actually works very well with Asians, and being humble enough to accept one's own mistakes helps to earn their respect.

In the end, if your authority is based on the students' respect of you, you will maintain your authority best by putting the students' learning ahead of your own pride.

Answer 6

Back when I was in high school I remember situations where the teacher makes an obvious mistake - obvious enough that even students who haven't mastered the topic can spot it, such as a simple arithmetic mistake - and doesn't admit it. Some students joked about it privately afterwards, but the underlying reason for the jokes wasn't that the students think they understand the material better than the teacher. It was because suddenly everything the teacher says is suspect.

For example, suppose the teacher says X. The students think about a homework problem unsuccessfully, and guess that maybe X is wrong. But the teacher insists X is right. Can you trust that X is right if the teacher never admits they are wrong? Even worse: at this point, the teacher is definitely not an authority figure.

You're better off biting the bullet and admitting the error, especially since it was mainly a numerical mistake and the essential parts of the concept were well illustrated.

Answer 7

Frankly, you would lose respect from those capable students far more quickly by not admitting mistakes or worse still trying to cover them up. This is because they probably already know your mistakes, so their respect or disrespect would be based not on your mistake but rather on your honesty regarding mistakes. Students can often tell if you know you have made a mistake but try escaping without admitting.

Answer 8

You've received a lot of very good answers already. I'll just add that one more possible way to maintain authority and still correct the mistake is to make a joke about it. Which one depends on your sense of humor. When asked by a student why I wrote something that is wrong or misplaced or noticing that myself, I just say "because after 50 I have a brain-mouth-hand coordination problem, so occasionally I think one thing, say another, and write/do a third one". I usually add that "unfortunately, some younger people suffer from this disease too". It may look somewhat lame to you (or it may not), but usually it causes some laugh and smiles and if you can manage to make your audience smile at your will, you may be sure that you are still in full control. I also tell my students in the beginning of the class that "people usually look most stupid when they are afraid to appear stupid". The same applies to losing authority: one loses it most exactly when one acts of the fear to lose it.

Just my two cents.

Answer 9

I do a lot of live programming demos in my lectures (I'm about to do another one in about 10 mins* ;o). I make mistakes each time. It's no big deal, and it is why compilers give error messages. It gives me a chance to show how things are done that can't be adequately explained by conventional lectures, such as how to go about programming in such a way that you minimize errors and ensure that the ones you do make are found and corrected quickly and easily.

I had the same approach with my chalk and talk lectures back when I taught maths.

If you are not making mistakes as a learner you are too far inside your comfort zone to learn efficiently. As a teacher it possibly means you are too far ahead of the students to find their difficulties easy to anticipate.

In short, don't worry about mistakes, and try not to worry about authority. You have demonstrated that you have a good grasp of the subject by the fact you have been appointed to teach it.

Having said which, as a middle aged, white male marsupial, it is easy for me not to worry about authority, which is something that society needs to be working on. I suspect it is a lot less easy not to worry about authority if you don't automatically get the respect that your ability deserves because of qualities that have nothing to do with your ability to teach the material.

* I provided several "learning experiences" during the demonstration ;o)

Answer 10

You can flip it round, and use it as a teaching moment, which also takes the wind out of the sails for anyone who might act up.....

Instead of focusing on your mistake, focus on their learning. Id tackle it like this:

Before we carry on, i want to teach you one of the most important lessons in (subject).

How many of you, feel you've got a good grip on the material so far?

(pause)

Excellent!

So, how many of you spotted the mistake I made last time/last week?

(pause, some hands go up, some people look down)

Excellent!

At this point, you can either ask someone to explain what it was, or tell them yourself, followed by the punchline, where you ask why people didnt say something. They probably wont speak easily, its an awkward question but a really good one. If needed, pick one of your bright sparks who says they saw the error, and ask directly, why they didnt say something. Its a very valid, legitimate question.

Do this in a cordial, supportive way. So they don't feel picked out for bad reasons.

Then, draw the lesson from it. People in authority will make mistakes at times, whether in academia or commerce or other areas. And often, nobody will say a thing. This will happen periodically throughout their entire lives. "I want you to think about that, and decide, what you feel should happen, in situations like this." Or whatever else you feel is the lesson you want as a take-away.

In this way, you flip it round. You maintain authority and initiative. The people most likely to feel they know it all, are in the position of "well, why didn't you say something?", which deflates them and reduces scope for issues.

And moat importantly, everyone learns a really important point, in the best way possible - seeing it taught, by their teacher.

Answer 11

You really should admit to the mistake. As others have pointed out, the absolute worst thing for a teacher's reputation is to make mistakes that students can see, and not admit them; or even worse that that, to argue with, deflect, or browbeat the students who point them out.

That said: Time is of the essence. The quicker you can fix the error, the better. Within seconds, by yourself, is ideal. If a student points it out in a few minutes, or anytime in the one class session, then that's perfectly fine; usually easy to go back and fix it.

But if it's outside the class session that the half-life on how useful this is starts to tick down. The particular numbers may not matter a whole lot if the essential concept or process was shown correctly. It becomes more of a burden if you need to recreate all of the work (board work lost, etc.) from scratch. If days have gone by and no student noticed, I'd be prone to let it slide for time-efficiency purposes; if a student does point it out or it's really crushing my conscience, then I've written up a handout document showing the correct solution. (Although Krantz in How to Teach Mathematics argues against even that, specifically.)

When I do make a mistake in class, and a student catches it instead of me, then my standard framing response is like this:

Thank you so much! I usually make about one mistake a day, and there it is. That's why we need to do the hard stuff in teams, and I'm depending on you to watch what I'm doing for mistakes like that. I'm so glad we're doing this together!

Answer 12

Admitting and owning up your mistakes actually is how you get authority and respect in the first place. Not admitting your mistakes and hiding them instead will make you lose authority and respect because, believe me or not, students actually notice those things. They may not have the syllabus knowledge or experience to exactly put a finger on it and specifically name the mistakes, but all you need is just one person from the whole class at a given time to notice each instance to unravel the deception. And keep in mind that some students are retaking their courses for a second or a third time. Such behavior of a lecturer will quickly establish an impression that the thing you care about the most is manufacturing and maintaining an artificial image of yourself being infallible, not giving your students the highest quality lectures. Nobody is infallible and you are not expected to be infallible; you are expected to be a decent teacher, and that includes being honest and admitting to your mistakes.

And I also think that the issue with admitting to your mistakes could be a red herring in this case. The actual, real problem could be your proficiency in lecturing. If we get to the point where your mistakes are so frequent that it starts affecting the quality of lectures, then maybe it is the time to take it as constructive criticism and improve. Putting more time and effort practicing the material being taught and repeating various examples over and over again will help you catch and filter the mistakes you are the most prone of making, and will improve the experience for both you and your students. On the other hand, investing your time and effort on developing and practicing mistake-concealing techniques is not going to solve the main problem.

However, please don't get too fixated on practicing. Have in mind that the serious problem is not having a lecturer who makes frequent mistakes, the serious problem is having a lecturer who thinks it is a good idea to deceive their students and hiding their mistakes. It is about having the healthy mindset.

I am sorry but on the few occasions I have witnessed a student or a small group of students laughing or otherwise trying to undermine lecturer's authority in response to their mistake: if the lecturer was honest and eager to admit and own up their mistakes, I have NEVER seen such students not being totally hushed and shamed by the majority of the class who is actually interested in learning.

Answer 13

Just so it's said, authority is a function of attitude, not a function of action. One person can do everything perfectly and still be unable to command authority; another can goof left and right and maintain it. The key is to be calm and assertive. Don't question yourself or your capabilities, and students will naturally fall into line.

With respect to the specific problem, my approach has always been to turn it into part of the lesson. Walk into class the next day and lead with: "How many of you noticed the mistake I made in last lecture?" Get a show of hands so you have an idea of how many people actually did notice (which won't be as many as you think); explain and correct the mistake; move on. There's no need for you to 'admit' you goofed — treat that as a mere obvious fact — and no need to explain anything beyond the basic issue and correction. You on't have to 'make it up' to the students, you just have to fix it. Hold in your mind the fact that you are an expert on the material and the goof is inconsequential; the force of your own self-assertion will move people past it.

Yeah, I know it's a lot harder in practice than it sounds, but it does work.