How can I supervise a careless student?

Question

I am a postdoc in physics and was in an advisory role in a project with an undergraduate student majoring in math. It was my first time collaborating with someone junior to me. The collaboration was not extremely successful, and I think I need some advice on how to supervise students.

Background information: The project was my proposal but I offered several other options in the beginning and the student picked the current one. It was purely theoretical and I simplified the project into several math problems or calculations so that the student can easily start working on them without the need of advanced knowledge. The math tools required were only basic first-year ones, e.g., calculus and linear algebra. I knew from his CV that he has taken all required courses, so I indeed anticipated a better performance than the current one. He also mentioned explicitly he enjoyed doing these type of analysis.

Student's performance: I was initially confident because the student seemed to understand everything I said and was also highly motivated. He seldom had questions about my notes and was working long hours. However, every time the student wrote up some notes and claimed that he solved one problem, I could always find some obvious loopholes or wrong calculations in the proof. I tried to explain these mistakes and he always quickly absorbed my point. But then the same thing would repeat. He would claim that he solved the problem once again, and then I quickly found out a mistake in his proof. When I asked him to proofread some of his notes himself, he was also not able to spot any mistakes.

After a while, I decided to take the lead and did calculations myself, because maybe he was not well prepared to do calculations by himself. I would let him proofread my notes afterwards and raise questions when he had any. He always claimed that my notes were all correct. It was not a good sign, because sometimes I found out I made some mistakes in my own calculations, but he was never able to spot them.

In the end, I had to finish the project mostly by myself. It was okay, but the experience was kind of intimidating, because I didn't expect a student to act that way. I always imagine a student should either fail to make any calculations or successfully conduct them (like myself), instead of keeping writing notes without knowing they were wrong. It was extremely hard that I was not able to teach him anything because he always acted like he already knew what I said and the mistakes were only a result of carelessness. Still, I find it hard to understand why one can make so many mistakes without knowing.

Question: I was wondering, is there any good method I might adopt if I come across this type of student in the future?

Answer 1

I think that doing the calculations yourself and asking the student to proofread them may not have been the best approach. If he can't even spot his own mistakes, what are the chances he would spot mistakes by his supervisor? Maybe a better approach would have to have him do the calculations on a blackboard and challenge every step, possibly breaking everything down in small steps. This way you can maybe figure out why he makes these mistakes and how he can avoid them in the future.

Answer 2

In his Mathematical Foundations of Quantum Mechanics, von Neumann provided an incorrect proof of the impossibility of a local variable theory of QM that arguably put QM on the wrong track until John Bell decisively refuted it decades later. (This is the popular version, but others insist that von Neumann never intended his statements as a proof). I don't think anyone would call von Neumann a lazy mathematician. The point being that we all make mistakes, and beginners make a lot of mistakes.

You were working with an undergraduate. My point of view is that the primary goal in that situation should be helping the student become better at making sound mathematical arguments. If you get useful work out of the process that's gravy. My strategy would have been to circle the section containing the error, and ask the student to tell me why it might be problematic. Repeat as necessary. The goal of the exercise is to train the student on how to read and critique their own work.

Of course I recognize that I didn't see how egregious the errors were, and some students really are lazy. I'm assuming a good faith effort on the part of the student, who may simply be naive and inexperienced.

Answer 3

Your experiences are normal when supervising undergraduates, and do not represent any failing on your part.

Some thoughts, based on my experiences:

1. The comparative difference between you and the average undergraduate is much greater than you realise. As a Postdoc, your ability in your subject is much greater than the average student. You have got your degree, probably with good results, enjoyed the subject enough to want to pursue a PhD, got that PhD, and still been motivated enough and with a good enough record to land a Postdoc. Few students will go on to the second two of those. It will take a long time for you to understand the ways in which stuff which is easy for you is hard for people who are much less capable than you.
2. It is difficult to remember how hard stuff used to be. The stuff that undergraduates are doing now is already second nature to you. It is hard to accurately reflect on your own experiences of learning this stuff for the first time.
3. Undergraduates will frequently present as more confident and capable than they actually are. Not asking questions is usually not a sign of understanding and competence, but rather an indication that they either have not understood things well enough to ask questions or are worried about making themselves look foolish by asking "silly" questions. In my experience, the best approach is to get them to explain everything back to you once you've explained it.
4. The success or failure of an individual student is not a reflection on your own abilities. Yes, over a long period of time, your abilities will result in slightly more or slightly fewer students succeeding, but the variation in ability, motivation, etc. of each student is a much bigger factor than you are.

And finally, and I think most importantly, you need to remember that is them that succeed or fail, not you. It is not up to you to ensure the project is a success, it is up to them. You should not complete a project for them.

Answer 4

Unfortunately I do not think any of the existing answers are good. I am pretty sure your analysis of what happened is wrong.

I was initially confident because the student seemed to understand everything I said and was also highly motivated.

He seemed, but did not understand.

He seldom had questions about my notes and were working for long hours.

People who do not understand do not necessarily ask questions. In fact, people who do understand the key concepts almost surely would ask a LOT of questions. Working for long hours implies nothing at all.

However, every time the student wrote up some notes and claimed that he solved one problem, I could always find some obvious loopholes/wrong calculations in the proof.

This is the evidence of incompetency, which you appear to want to overlook.

I tried to explain these mistakes and he always quickly absorbed my point.

He did not absorb anything.

But then the same thing would repeat. He would claim that he solved the problem once again, and then I quickly found out a mistake in his proof.

So of course the same thing repeats.

When I asked him to proofread some of his notes himself, he was also not able to spot any mistakes.

Of course he cannot spot any mistakes when he doesn't have any understanding.

After a while, I decided to take the lead and did calculations myself, because maybe he was not well prepared to do calculations by himself.

He was incapable to do it, not unprepared.

I would let him proofread my notes afterwards and raise questions when he had any. He always claimed that my notes were all correct.

This is exactly what some incompetent people do in order to try to get by.

It was not a good sign, because sometimes I found out I made some mistakes in my own calculations, but he was never able to spot them.

This is the other main piece of evidence that you seem to want to overlook.

In the end, I had to finish the project mostly by myself. It was okay, but the experience was kind of intimidating, because I didn't expect a student to act that way.

It was not okay, and if you continue to do this then you would simply allow more incompetent students to get by.

I always imagine a student should either fail to make any calculations or successfully conduct them (like myself), instead of keeping writing notes without knowing they were wrong.

You made a wrong assumption. Not every student is honest.

It was extremely hard that I was not able to teach him anything because he always acted like he already knew what I said and the mistakes were only a result of carelessness.

Of course incompetent people who are trying to hide their incompetency would give excuses for their mistakes. They will not admit that they do not know anything if they can get away with it.

Still, I find it hard to understand why one can make so many mistakes without knowing.

Already clearly explained.

I was wondering, is there any good method I might adopt if I come across this type of student in the future?

Grade fairly, instead of assuming that they are competent. You can teach an honest hardworking student. But don't assume that you can teach this kind of student that you have described. In almost all cases you would be wasting your time and reducing the amount of time and energy you can spend on your other more honest students.

Answer 5

I was initially confident because the student seemed to understand everything I said and was also highly motivated . . .

This is the problem in a nutshell.

You didn't probe the student's knowledge and understanding limits adequately to begin with. You just allowed them to make the right faces to feign understanding and mannerize their way through things as you told them what it was all about.

I know postdocs are time-pressed. But, where juniors are concerned, it's no use telling yourself that you shouldn't waste time on basic stuff: it's the flaws in the basics that trip people up, time and time again.

The age/experience/status gap is also a bit too much for most students in this sort of situation. This capability gap is often contradicted by the seemingly equitable way in which a postdoc adviser speaks to the undergrad. In their defense, postdocs are just usually striving to complete research work of their own, please current faculty and find a full-time position for themselves. Before the latter day comes, many academics don't give much thought to learning how to supervise properly let alone how to teach right.

So if I was you I'd do three things:

1. Before agreeing to advise any student, interview a few students in a probing way, a way that explores how they tackle questions, how they react to other perspectives suggested by you, how ready they are to adopt better ways of seeing things, etc. Give them plenty of scope to express themselves.

2. Always speak in a clear and formal way - do not try to equalize the nature of the working relationship: it's not equal between a postdoc and an undergrad.

3. When selecting an undergrad student collaborator, accord more weight to character traits - honesty about mistakes, effort to communicate clearly, willingness to share his/her ideas - than to traits of intelligence.

Answer 6

Normally people see their own failings as mistakes and failings in others as character flaws. It speaks well of you that you seemed to have done the opposite, trying to work with the student in correcting their errors, as opposed to just writing them off. Again, that's good of you. But at some point you also have to admit that other people don't care, can't get it, and are just not temperamentally suited for certain jobs. The old saying is that "you can take a donkey to the water, but you can't make him drink." The solution is then, next time, get a better student.

Answer 7

As an experienced IT person, I am not quite in your shoes, but I occasionally work with juniors that display similar behaviour or characterial traits as you describe. My advice thus is this:

• Focus on helping them help themselves. Maybe you can point out a specific chapter in some book they have access to, or name a specific technique they can google to help them. Even if they then just transfer the read knowledge unto the task, that will help them already.
• Don't be afraid to point out errors. As long as you do that objectively, it's fine. If you, at the moment, have no time (or nerves) for a deep explanation, it is fine to simply point to an error; give maybe a small hint of what it is about, and send them off.
• Them being "nice" or "understanding" or agreeing to all you say, or mirroring your sentences, and so on and forth, is neither her or there. It does not reflect in any way about what's going on inside their head when it's time to solve problems, which is the ultimate goal they have to achieve. Feel free to repeatedly remind them that unless they ask you about something, you don't know what to teach them. If you have a scheduled meeting, and they give you no "fodder" for anything to tell them, then the meeting will just be a short one. After 2 or 3 such events, they should be able to get the message.
• Remind yourself that they are adults being where they are willingly. They are not in school anymore, which arguably is forced on a good percentage of children against their will. This means that if at any point you get the feeling that they just don't care, it is a good point for you to stop caring as well. You will not make them better against their own will.
• Finally, if it's someone who usually is totally on the right track and just made an obvious, honest, error, you can simply correct it on the spot to save both of you some time. But regularly, do not do that. Nobody is helped by you providing the solution. If they cannot solve a task with the help mentioned above (i.e. you pointing out where they went wrong, and with some helpful pointers what to do instead, but not the whole solution), they might simply not be ready for the level of difficulty yet. They have to work on their skills; or maybe look for simpler tasks (which may or may not be in your scope to help them with).

Finally, you should yourself become clear whether you are in the role of a teacher, a coach or a mentor. It sounds to me that your role is that of a mentor. There are best practices and rules of engagement there - that Wikipedia page should give you some pointers for inspiration. The most important bit about the concept of mentorship (for me personally at least) is that the responsibility lies with the mentee, not the mentor. If the mentee does not pull, the mentor has no reason to push.

Answer 8

Do you and the student have the same cultural background? In some cultures you just say "Yes, Sir!" or "Yes, Ma'am!" enthusiastically because you don't question those who rank above you. If the student learns to operate in your culture, the math part might get easier.

Answer 9

I believe there is an emotional maturity piece here. It doesn't seem to me that the student is careless about this project if they're putting in the hours, it sounds like they simply don't yet have the "emotional maturity" (which is not a bad thing and normal for an undergrad) for this type of work. If this student's CV seems to be up to par and their technical knowledge is there, but from the inability to ask questions and admit mistakes, there seems to be an emotional aspect missing from this student's ability to perform.

In this case, it's your role (should you accept it, most people don't and just fail the student, which is fine) to provide a safe space for the student to ask questions and "scaffold" (this is a parenting term) the technical work at the student's pace, so you're kindly and supportively there to lead him through getting stuck or stumped.

This takes building a safe, personal, and informal relationship where the student can show up as themselves, rather than the "I know everything" robot that they think you expect them to be.

I vividly remember doing research as an undergrad and thinking I need to put on my armor to make myself seem smarter or more legit around the grad students, post docs, and especially the professor at the expense of vulnerability and true learning. The emotional immaturity makes us believe we MUST to show up as more capable than we really are to be accepted, supported, and respected. It's intimidating to be the new (little) guy amongst giants.

Answer 10

Here is my opinion as a student of this type.

Let's take, for instance, something as simple as F=ma. This is something which can be introduced to high school students, and they may say they understand it, but if you give some random questions, then they may not know how to start, or have a lot of misconceptions of be able to use the law, but incorrectly.

The main issue stems of a feeling that the person feels that they understand the main text completely, but when trying to apply in another context realizes that the main text actually said something different than they thought, and that the issue is more complicated than initially thought. This is a fundamental problem that pedagogy has to tackle. Related question on Philosophy SE by me, also tangentially related Veritasium video

I believe, this fundamentally stems from a conceptual gap in understanding the material, and if the student were to somehow have an introduction to the material which tries to give the concepts which the technical details try so hard to capture, then they would be able to make all the calculations up to arithmetic errors.

For example, I'd imagine it'd be the same type of difficulty one has if one tries to paint Mona Lisa from a description of it, without ever seeing it. It seems clear to me that a person who has actually seen it, or has active sight of Mona Lisa would be able to pain it easier than a descriptive person.

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Incidentally, I found a certain fix to dealing with these kind of issues when I started doing powerlifting. In videos where they instruct on how to do the motion that you'd typically find on YouTube, there'd be an end section where they discuss how the exercise commonly go wrong. So, perhaps you could try giving probing with questions of common misunderstandings to check if he understood the material/ kick him out of the Dunning–Kruger state.

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In my personal opinion, very few number of people can understand the text in the intended meaning by author in first go. And everyone suffers from these issues to some degree. For some people, on the outside you feel they don't have the problem, because they try work themself their problems in private or ask on SE :)

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Since you said physics, maybe you could ask them to read Penrose's books?

Answer 11

An "undergraduate student" is someone that started his university studies and will end up with a 3 years diploma (at least this is how I understand it - this is how it works in most of Europe).

You therefore have the whole zoo of students: the ones that arrived there by mistake because there was some light on, the ones who wanted to do A and realized that this is not for them, the ones that wanted to do A but are not good enough to do it, the ones that are in the right place, the ones ...

You got an average student who is nice enough to show enthusiasm but was maybe not that interested in the topic. He maybe wants to go through it to put a checkmark and go ahead. From my experience, this is 76% of students.

I studied physics which I loved. I also had math which I saw as a useful toolbox and that's all (I also have screwdrivers and I am not that interested in all the love that was put into their engineering). Calculus was great, algebra was a walking nightmare. I smiled my way through algebra and was happy to close that chapter of my life.

is there any good method I might adopt if I come across this type of student in the future?

With time you will get better at choosing the students to have the ones that are actually interested.

In the meantime, well, you will not change the world and will end up with students like me. I would have loved my teacher to just give up. She did not, which I appreciate as a human, because she loved her topic and I am a rather nice guy so I smiled and tried my best to do pretend work.

I also had economics during my PhD and I forgot to take part in any of the courses (which I now regret). I realized that a bit late (when I read that we had to get a mark for that) and crawled miserably into her office. She said that she prefers to have students that are interested and she also realizes that economics is like any topic - someone may not like it (she said she hated physics at school). Gave me a top mark (it did not matter the slightest, just bureaucracy) and we were done.

Answer 12

According to the book The Peter Principle, your student has reached his level of incompetency, and therefore, is not capable of figuring out the mistakes all by himself.

I am a software tech lead, and I'm facing exactly the same issue. When doing code reviews with junior developers, I can easily point out the mistakes while they were having hard time to identify them.

Albert Einstein once said:

You cannot solve a problem with the same mind that created it.

So, with that said, I think we're down with 2 options. First one would be continue to help the student to raise his level of competency, and second option would be to find a replacement, if necessary.