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In one of my classes, I had a student who generally understood stuff faster than the others. In tutorials, he would ask a lot of questions, mostly of the kind

"I tried this method instead of what you suggested, is it correct?"

Now, this probably sounds like the dream student, but I quickly realized that he was not really after my input, but rather seeking acknowledgement of his superiority (possibly showing off before his friends).

The exchange would often go like this. If what he suggested was correct, fine, I would say "great!" and move on. But quite often there would be flaws in his argument, which I would naturally point out. He would always assume that I misunderstood him and when I was (finally) able to show him that his argument did not stand, he would say something like

"Oh yeah, that's what I meant to say, but I phrased it wrong"

Note that this was an math class, so "phrasing it wrong" really means "failing to prove". When he asked a genuine question and I started providing an explanation, he would cut me off halfway through with something like

"Right, I get it, it's because this and that"

and convincing him there was actually more to it was yet another struggle.

I am concerned because I really feel he could be an amazing student if he would only accept that he does not know everything beforehand and therefore sometimes makes mistakes. Also, it seems like my time could be better used than in convincing a student that I'm worth listening to.

How can one explain this to such a student without humiliating him? Simple reasoning and proof by example (you'd think after the tenth time I pointed out his mistakes he would have learnt that he sometimes does them!) apparently just bounces off of him.

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Most students could be amazing students if they would stop doing the things that prevent them from being amazing students: not working enough, not paying enough attention, not being curious enough, not taking enough time to think, rejecting teacher's help, etc. Since we are on Ac.SE, I'm assuming that the student is at least at university level, and therefore an adult, overcoming this kind of limitations is also part of the personal development of the student. –  Charles Morisset Mar 6 at 13:59
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He needs a compiler. –  Trylks Mar 6 at 14:52
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Ahh... I wish I was still 18 and knew everything. Those were the days before reality hit like a ton of bricks. –  WernerCD Mar 6 at 16:26
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I remember taking a "Formal Languages and Automatons" course once, I loved it, and I was a lot like this student. Then I got a 2 on the exam, on a scale of 1 to 10. I had been way too superficial. Next time I had learned my lesson, and got a 9. Really useful experience. –  RemcoGerlich Mar 6 at 19:16
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Note: If the student's "contributions" are getting in the way of teaching everyone else, it's entirely appropriate to tell them "interesting question, I'll get to it later" or "talk to me after class". This is a tremendously useful technique for disruptions in ANY kind of presentation, actually; I've had to use it in business many times. Some interruptions are worth taking, some aren't; as the presenter you're entitled to decide whether and when you will take questions or comments from the audience. –  keshlam Mar 8 at 1:06

15 Answers 15

up vote 50 down vote accepted

I would suggest against [a deleted answer telling to put a lot of weight on simplest textbook examples] (I consider "ha! you missed the example from chapter 2" to be highly unpedagogical, as it is "appeal to authority" and "you should read and remember rather than think").

I think two things may help:

  • give him problems and require written solutions (it is harder to boast, or mask omissions, when one writes), solved "down to the last $\epsilon$", as you "want to see the proof, not just be convinced that he can prove it",
  • give more advanced problems (still, which are within his reach), for which answer cannot be hand-waved (e.g. "what is sum of", "give an example of set, such that...") OR don't tell the answer in advance (so instead of "prove X given Y" ask "decide whether X holds for all Y").

In both cases, I would tell him (in person) that he is very smart, and you give him more advanced problems because of that. (And that he still needs to learn to be precise enough for mathematics.)

Maybe he does want to show you that he is smart, and as you do not acknowledge it he, well, tries again.

In any case, I would not undermine his skills. In mathematics & theoretical physics I know a lot of people who underestimate their skills, but not many who overestimate for a longer time (such subject makes one humble, sooner or later).

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Whether to tell this student that he is "very smart" I'm not sure I agree with, but the two bulleted suggestions are excellent. Overall this question resonates with me more than most on this site, and I would like to try to take the time to leave a careful answer...when I have it! –  Pete L. Clark Mar 6 at 17:05
    
@PeteL.Clark If OP thinks that the student is "very smart" (or put here another positive remark about his skill) I think that telling him that won't hurt (especially if followed with "but..."). At least it is how I dealt with all (as I call it) "smart but reckless" (more than often it was some kind of attention-seeking and trying to prove that one is smart; or a typical "the first sip of knowledge" behaviour). But, anyway, a full disclosure: I used to be "reckless" (as used above). –  Piotr Migdal Mar 6 at 17:20
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+1 for "subject makes one humble, sooner or later." The best way for an instructor to help a student gain humility is to expose him to more of the subject, as you suggest, not by pointing out what he did wrong with the primary aim of humbling (rather than correcting) him. –  ff524 Mar 7 at 6:41
    
About your last paragraph, this is actually a well known phenomenon: Dunning-Kruger effect. It's more about human nature than some specific subject though. –  Voo Mar 7 at 12:06
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Also telling a student they are very smart can backfire (evidence from social sciences) instead tell the student that you are confident that they can solve the problems if they put in the effort. Effort is something which we all have control over, but we consider intelligence to be innate... –  daaxix Mar 9 at 6:13

I feel that generally your focus is misplaced. It appears to me that by focusing on how to deal with this one student, the learning environment of the other students is somewhat compromised.

First, I would strongly suggest that you need to put this dude into his place. Let's not ask "How can one explain this to such a student without humiliating him?" Let's think "How can one explain this to such a student through humbling him?" There are numerous indications that what he does is disruptive:

Example 1: In tutorials, he would ask a lot of questions, mostly of the kind "I tried this method instead of what you suggested, is it correct?"

If the tutorial is about A and he decided to use K method to solve it. Wonderful, but were the actual materials covered? If he seeks this kind of "Look at me! I am awesome!" feeling, I will deter that gratification by allocating the last 10 minutes to discuss alternative approaches on solving the problem set. Don't feed the troll, make him wait and train on his patience.

Example 2: "Oh yeah, that's what I meant to say, but I phrased it wrong". Note that this was an math class, so "phrasing it wrong" really means "failing to prove".

Did you actually tell him this thought? You do not need to say "You are wrong." You can, however, say that a certain attitude or a certain pattern is wrong: "While your attempt is well intended, I wish to stress that in mathematics, one wrong phrasing can buy you the direct ticket to failure."

Example 3: When he asked a genuine question and I started providing an explaination, he would cut me halfway "Right, I get it, it's because this and that"

That's an unprofessional behavior and you should have slapped him right there. Simply smile, slowly raise your palm to signal a stop, and calmly say "Please hold on and let me finish, there is more to it, and I want to present a full picture."

Overall, I think this student needs circumstantial challenges (in other words, come to feel how the world actually runs) and he should turn out fine. I am more concerned for the rest of the class; If I were one of the students, seeing this alpha male's obnoxious behaviors go unchallenged, I would seriously doubt why I should be here, and should I even ask a question.

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All these are relevant remarks and I did do those things. I just want to make one thing more precise: during tutorials, there are times when I let the students solve the exercises by themselves and move around the class, answering individual questions and giving pointers when needed, so those dialogs would take place when the other students are working on their own. –  Ri49 Mar 6 at 15:30
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+1 for "While your attempt is well intended, I wish to stress that in mathematics, one wrong phrasing can buy you the direct ticket to failure." and "Please hold on and let me finish, there is more to it, and I want to present a full picture." Very good suggestions. –  starsplusplus Mar 7 at 10:19

I also think that he seeks recognition, from you and maybe from his peers. I also think giving him more advanced questions might humble him, but I think this wouldn't be the most effective way, because it wouldn't give him the recognition he seeks from his peers.

The following is how I have dealt with these kind of students, and how my teachers dealt with a much younger version of me :) And it proved to be very effective.

Whenever he offers his new version of a solution, don't argue with him, but tell him "this sounds like an interesting approach, I think you should share it with other students". And ask him to come and write his solution on the board and explain it to the other students. You should also go and stand or sit in the far end of the class, so basically you temporarily switch roles. This has three effects:

1- He will ask fewer questions: Even though he wants to show off his superiority he doesn't want to stand in front of all students and explain a solution EVERY TIME. Even if he likes to, his fellow students will be fed up with him, and they will communicate it in their own way, in or out of the class.

2- It humbles him When writing and explaining to other fellow students, they are going to ask him questions and point out his mistakes. If they don't, you can ask them to ask him questions if they have any, or to point out the mistakes. If they manage to do so, he will feel that he is not that smarter than his fellows after all. If they don't, you should give them hints to find his mistakes. Also, since this is in written form, and in front of many people whom he communicates with on a daily basis (much more than you), it is much difficult for him to hide his lack of understanding.

3- He will think more about a solution before jumping in and offering a wrong one Because he is explaining it to many people, and not only you. Thus, the cost of making mistakes will be higher, and he will think his new solution through before proposing it.

Now these effects will not happen over night, but after 2-3 class sessions I expect him to improve his attitude enormously.

Let us know if this, or any other suggested solution, helped.

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I like writing it on the board. It's a really good idea and deals nicely with the "I phrased it wrong" situation. –  starsplusplus Mar 7 at 10:21

I am going to write an answer based on the student's perspective. I'm graduating college now, but I feel like I was almost just like this kid in Freshman year of college / Senior in High School.

You mentioned the kid is smart, and quite talented. Too much for his own good. I hated mathematics and still got A on it while not even paying attention to the teacher. The kid needs to be challenged but not at the expense of the class. I later figured out I like challenges the most, and more hands on things than math even though I was super quick to learn it. I sat in the back, solved a rubik's cube, and waved the teacher off because I didn't need to do my homework. The previous week I corrected a question on the midterm exam and got extra credit because no one else saw the flaw.

Here is what my genius math teacher did to me that worked wonders looking back.

A) Instead of just numbers on the sheet, take what he is excited about learning and have him a problem on that. For me it was programming so he said can you graph this on a computer where it shows and calculates the area under the curve? Hah! I didn't even know what I was getting into. Yeah! sure no problem. By trying to do it in a way that made sense to me I willingly did more various types of problems than we would have in class because I was trying to graph areas under all sorts of various curves. He tricked me, and I liked it.

Just use what he likes, and find a real world problem :D. Even if it were surfing or something crazy ask him to calculate how high and fast he could go on a wave given a certain value.

B) Group project that is required to participate in and peers give a portion of your grade based on rating. I didn't really care about my grade honestly because I knew I could pass any test. I cared more about what others thought of my abilities. When we did the group project and some of it was extra credit we all got a's because I wanted to solve the extra credit and I let my group do the other 2 regular problems. It's a way of allowing your student to satisfy his show off ability and still learn. we did not always do group projects, only a couple in the semester.

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I recognize this student's desperate need for approval. If you are going to try to work on him, try to nudge him in the direction of deriving satisfaction from the math itself, rather than impressing others with his abilities. You might try this line of approach--"I knew a guy once [Hi, my name is Mike, I'm the guy, btw, just so you don't have to feel you are being deceptive.] who had a light turn on in his head at one point that changed his life. He realized that he got much more out of loving the math itself than loving the attention he got from being good at math. He had a lot of raw talent, but he realized he was wasting effort trying to impress people when he could have spent that effort getting better at, and more out of, the math."

This is a really delicate thing for you to approach, however, because that need for approval is probably due to some severe self esteem issue which you don't know the source of (and possibly the student doesn't either). Seeking approval from other people is like an addiction--you can't change it over night, and you find yourself returning to it again and again even when you wish you could stop. [Eventually, you post on message boards all over the internet seeking upvotes... :) ]

Another approach you could take would be to be much more indirect about his psychological issue, but possibly accomplish something in the same direction, while overtly focusing only on the math.

"I think you know that you are better at this than the other students. But I think you're aiming too low--you can really learn to excel at this. Do you want to do that?"

If he answers in the affirmative, tell him what you think he needs to do. A critical skill in academia is learning from other people, so he needs to not cut people off in the middle of an explanation. A critical skill in mathematics in particular is precision. He needs to learn that "I meant to say x" is not going to cut it in math. If he meant it, he should have said it, otherwise, it's wrong. Tell him that up to now you have not wanted to be too hard on him, but if he wants to be really good, you're going to quit pulling your punches and not let him weasel out of a failure to make a complete argument.

Basically, ask him if he wants a coach, or a coddler. If he wants a coach, you're going to judge every statement like a mathematician reviewing a submitted paper would. If he doesn't want that, then it's his choice; you tried. At that point you have done what you can for him, and all that's left to decide is whether he's enough of a distraction in class that you need to address that aspect for the good of the other students.

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I am writing from a student's perspective, and I've got this to say:

Why try to humble this student? To me it seems that this student has his own pace at which he learns mathematics, and his pace and yours just don't happen to be perfectly synchronized. There are hard lessons in his future, to be sure, eventually something won't come as easily and will require deep and concentrated thinking on his part. But I think lessons like these are things that should be experienced with the body. Nothing teaches better than failure (or equivalently for well-motivated students, anything less than shining success), and these lessons you wish to impart to him will probably only be truly appreciated when he comes across his first real obstacle.

I am more concerned about the potential to hurt your student's youthful self-confidence. Let his energy drive him! Definitely press (as my professors have) the need for practice and getting your hands dirty! But it would be a great crime to him to shoot him down just because you see him as overconfident - if he is, then he'll have to pay for it eventually, but that lesson is well earned and well learned and should really be experienced for oneself.

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Your student was probably smarter than all of his teachers in high school, and has never experienced academic failure --I think a lot of college freshmen start out that way.

I would sit him down, and tell him plainly:" You aren't getting your money's worth from this class, because you aren't taking advantage of my teaching."

Chances are, nothing will get through to him but a F on his report card (maybe not in your class, but it will happen sooner or later). However, you will have done your best. If he doesn't respond, I would limit the amount of time you spend on him, and focus instead on students who might have less raw talent, but who are more open to learning.

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"Chances are, nothing will get through to him but a F on his report card (maybe not in your class, but it will happen sooner or later)" Wait, what? Being very bright and overconfident is a recipe for a future A- when you could have gotten an A. I have taught maybe a thousand students over the years and I can't think of a single very-bright-but-overconfident student who failed the course. (Like the OP, I teach mathematics.) –  Pete L. Clark Mar 6 at 16:56
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Also it seems like a rather uncharitable take on the student in question (or almost any student, really) that he is not "open to learning". I do acknowledge that one must have concern for the other students in the tutorial as well. –  Pete L. Clark Mar 6 at 17:08
    
@PeteL.Clark I wasn't intending to be uncharitable. I was largely basing my comments on my own experiences as a bright-yet-overconfident college freshman many years ago. And in defense of taking the tough love approach, I think the OP's descriptions make it clear that, at the least, this student isn't currently open to the learning available to him through his professor. It seems like Ri49 has already made any number of good faith efforts to help his student get past his ego. –  Chris Sunami Mar 6 at 18:13
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I take your point. Ri49 has, through no fault of her own, not yet gotten through to this bright, interested -- but problematic -- student. She hasn't given up, hence the question. I see that you write this only in case the student doesn't respond. That should be hard to argue with...but I still don't like thinking in terms of writing off this student. I hope you see where I am coming from: it's a strong thing as an instructor to classify a student as "not open to learning". To me, it sounds like this student is open to learning...but is doing something else wrong. –  Pete L. Clark Mar 6 at 18:26
    
@PeteL.Clark I definitely agree with you no teacher should "write off" a student. However, my advice was rather meant as presenting the student with a clear choice --to either take advantage of what the teacher has to offer, or to not take advantage of it. You can't force someone to learn, and the original post indicates that arguing with this student is taking time away from other tasks --perhaps working with students who are more receptive. –  Chris Sunami Mar 6 at 20:00

I am currently taking part of an 8 week software development hack school. The class has about 14 students with varying levels of experience and knowledge. The informal format has been the best learning experience I've ever had for a couple reasons..

  • The teachers meet each student where they are at. Each student is encouraged to excel at their own pace. This is great because it doesn't slow down the students with more development experience... This is HUGE! Fast learners shouldn't be forced to learn at a slow pace.
  • All assignments are project based (typically created small apps) and are generally "graded" on effort and not getting the correct or best solution.
  • Varying levels of experience creates a highly collaborative environment. I'm somewhere in the middle of the class and am not afraid to ask the more experienced students for help and they are not afraid to share their advice.

I don't believe it's a teacher's job to tell a student they have a lot to learn. Life generally teaches us all how much we have to learn :-)

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I don't believe it's a teacher's job to tell a student they have a lot to learn. — I agree. It's a teacher's job to show students that they have a lot to learn, and then give them the tools and excitement to start. –  JeffE Mar 9 at 14:27

Sometimes people are so un-selfaware that subtlety won't work. You may have to just directly tell him how he's coming off. It's possible to tell someone in a way that it's clear that you're at least trying to give blunt but helpful criticism rather than just putting that person down. It's definitely possible that the student will still feel humiliated if you choose to do this, but I think it's also an important life skill to be able to maturely deal with valid (or even invalid for that matter) criticism that you don't like.

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Note that this was an math class, so "phrasing it wrong" really means "failing to prove".

That's something important to learn in a math class. If some of your students don't get it, it might be worth to spend half an hour of your next class to explain the context so that everyone gets it.

I think teachers way to often spend to much time on trying to teach techniques while not teaching fundamentals of their subjects like this idea.

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You should not take this as an affront against you, but rather as a strange way of learning, and then work with the student to allow him to improve.

It seems like your student has a psychological need to be "right" and feels mental pain from being "wrong". As these things tend to be irrational, it doesn't need to make any sense to you or even himself. You can take this into account and instead of trying to prove him wrong, you teach him to take his mistakes not as failure but as key-points for tasks to improve.

Phrases that could help your relationship:

  • "I see that in its core your explanation is correct, but some words could be misleading to a reader, so it might for example be better to use this instead of that."

Concept: Accept that he got 60% right, help him on the other 40%.

  • "I see that you are a very eager student. How about you formulate your findings into an essay so that the others can benefit from your knowledge as well? I will of course give you a bonus for it."

Concept: Accept that he has a strong need to improve outside the bounds of the class, give him the opportunity to do so, and a reward if he does right.

  • "That is a great answer, but have you taken into account that this?"

Concept: Reward him from being a good student, then encourage him to optimize the details without explicitly calling them wrong.

“Problems are Only Opportunities in Work Clothes.”
- Henry J. Kaiser

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I think you should feed his curiosity and let the rest of your class benefit from his way of thinking alternate solutions to the problems. One way could be where you have already established there is a flaw in his solution; but, are having a tough time getting through explaining that to him and/or for him to accept it, share a portion of the board with him during class while you continue to teach the next concept to demonstrate that while his questions are encouraged, they are taking up too much of yours and other student's time just to level set with him. This will force him to think twice before defending a wrong solution. Who knows, he might also teach you something.

Another suggestion is to have different levels of homework based on your lectures over a span of a day or a week and increasing levels of difficulty for extra credit. The ability to do the more complex should exempt the students from doing the lower level. Finally, share the solution at the end of the deadline for submission and dedicate a 15 minute Q&A session over the complex solutions. 1. To demonstrate understanding of concepts 2. To use the concept in a real-life problem 3. To partially use multiple concepts over the span of the lectures or the level of understanding you expect your students to have at the point in the semester.

Note: The use of him implies him/her.

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I had a very similar situation. And my first thoughts were: "Great! I have a smart active student". However, soon other students started to complain that he is confusing them, and they lose focus when I explain material outside of lecture material to him. Therefore, I stopped answering his complicated, though good questions. Ans said something along the lines off: "This is a very good point; however, it is beyond of the scope of this lecture, but I would be happy to discuss it after class." We had some great discussions after class.

My main point: Your active student might be confusing others by bringing up new concepts.

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Possibly he is more comfortable processing problems in written format, but a little bit tongue-tied in verbal expression? It seems quite a common combination - to be talented at abstract thought but less confident in oral communication. I've definitely had that experience, of being frustrated and impatient with stumbling over concepts in speech, when they are perfectly clear in my head. The fuzzy verbal arguments and the early interrupting could be signals "I'm embarrassed / not comfortable in this mode of communication". Maybe you could meet one of his non-standard solutions by saying "can you write it down step by step and I'll check it over to see if it's correct".

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I was a lot like this student. For me, it took depression that robbed me of my mental speed to stop this (although I usually provided a satisfactory proof!) I think one thing you could do is limit his (and anybody else's) participation in class to a certain level. This is most important for keeping control of your class.

As far as potential, be careful about projecting your values. He might just want to coast through life on his smarts, and finds finding these solutions fun or a way to pass the time while he's at class. Also remember if he's good at math, he probably also is good at other things: I remember faculty outside my major encouraging me to switch or do more work in their area when I wasn't even doing all the reading for them. You could give him something hard to work on if he wants to (especially to present, because he likes attention), but if he doesn't you have to treat him like every other student. As far as his arguments go, you could say something like "I see. Why don't you fill in the details and get back to me?" and if he gives you something wrong point it out and have him fix it (or end the line of conversation).

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