# How to deal with very motivated students having “off-topic” interests?

There are some very motivated students who are very interested in math (in general), where the interest takes over most of their time. The problem is that they don't put enough time in the lecture they are attending, which leads to bad grades or even them failing the course (which is not fair for them and often leads to discouragement). [E.g. there was a student in a basic course about numerics who was understanding the basic concepts and who was always asking me questions about the axiom of choice. He lacked a deeper understanding in the course and did not perform very well at the exam]

How can I encourage to such students to concentrate on their (exam-related) study without discouraging them?

• I've seen many such students, unfortunately. Some doing very well in my more challenging courses, going well beyond what is seen in classes in general, while failing time and again in the standard courses. The only advise is to convince them to focus on their current courses, and handle their other interests as a hobby (for now at least). I'd be thrilled it I knew how to do it reliably... – vonbrand Mar 14 '14 at 12:06
• This is really an issue with the course, not the student. Long term it might be worth seeing how you can restructure your programme to accommodate this style of learning. – Nico Burns Mar 14 '14 at 21:24
• @NicoBurns I disagree. If many of the students were failing the class due to similar problems, I would think it could be the course, but in this case it sounds as if the student is simply not putting enough time into studying. – David G Mar 15 '14 at 6:56
• Hmm... I think that is certainly a possibility. But that's only an issue because they are expected to learn particular knowledge. If the student is putting a lot of time into learning other things which are more advanced (and succeeding at doing so), then really it should be possible to credit them for this. What they are learning is probably more useful in the real world than what everyone else is learning... – Nico Burns Mar 15 '14 at 15:48
• @NicoBurns I agree with you that this should somehow be credited. But the problem is that students have to pass certain lectures in different fields and if the university/the state says that the have to pass a particular lecture, you cannot credit the person to something else. In the answers, there are some methods to credit the student or keep the motivation high level, but there are some contraints set up by the univerversity/the state. – Markus Klein Mar 15 '14 at 20:51

Some possible approaches:

• Challenge the student. A possible reason why the student is having "off-topic" interests is that the student doesn't find the "on-topic" things interesting (he "thinks" it is too easy) or that the student doesn't see the point of the topic (he lacks a vision of the big picture). So the thing to do would be to divert the student's interest into your course. Tell him about some of the big unresolved problems related (even tangentially) to the content your course. Give him a difficult nugget to think about.

I don't know enough about numerics to give a suggestion of a topic. But were the course basic real analysis, an old chestnut is to ask the student about the existence of "a function $f$ of two variables $x,y$, such that for each fixed $y$, $f(\cdot,y)$ is a continuous function of $x$, and vice versa, but such that $f$ is nowhere continuous as a function of two variables".

• Mentor the student. Rather than having the student wander here and there somewhat randomly in his musings, wouldn't it be better to make his interest more focused and organised? Offer to mentor the student in a reading class on the subject he is exploring on his own (and maybe even get departmental approval for it to be graded). Set out precise expectations for the reading class and establish a regimented schedule (you meet with him every week, for week 1 he should have read so and so). The trick is to set up the reading class in a way that his "off-topic" interests are sufficiently sated, while leaving him enough "down time" for him to work out the assignments for the class in his official curriculum.

• Have a talk with the student. Life is not always fair, and we don't always get what we want. (Say what? I have to take time out of research to apply for a grant?) Explain to the student that to be successful in life, some "unpleasantries" necessarily intrude. Ask him to read the part of Littlewood's Miscellany where he talks about his undergraduate exam preparation at Cambridge. Show him clear evidence that at the rate he is going, he will likely fail the class. Tell him that he needs to put some effort into the class. Your student will hopefully be an adult about it and change his attitude. And if he doesn't... well, it's a life lesson.

• I agree with every point in your answer! – dtldarek Mar 14 '14 at 20:16

I strongly agree with @WillieWong, just wanted to add one more solution.

Sometimes you don't have enough time to deal with such a student (e.g. mentor him). On the other hand, there are those who have more time, for example, you might be able to find a PhD student who would happily take care of this guy (esp. if their interests are aligned). Such arrangement is beneficial to each side, since:

• The guy might find a friend that shares similar interests/passion.
• A slightly older friend might have a better influence than seasoned professor.
• The PhD student might interest the guy in his/her research project, perhaps gain a collaborator or someone to continue the work.
• The PhD student will also gain an experience as a mentor, it is low-impact now, but will be useful later and failure doesn't cost much.
• You have dealt with your problem.

I hope this helps $\ddot\smile$

• I have a PhD candidate friend who is my random-maths-thoughts guy. It's super handy to have someone who will share interesting things he's learning about measure theory and then listen to me ramble about the philosophy of logic (which is in no way related to any of my classes, though I wish it were). – David G Mar 15 '14 at 6:59

For some such students, the problem is that they don't understand the "why" of the more elementary steps. It may help to point out an interesting application from middle or end of the course and explain that to get there, they need to master the intermediate stuff, and to get there, they need to go through the "easy" stuff first. Maybe a sports analogy can help. Even natural athletes don't win marathons or go to the Olympics unless they train, and the "easy" stuff is their training.

• Sorry, but I don't think that this is the point here. These is normally talented and highly motivated students who are in some sense "distracted" by the beauty of mathematics and want to dig deeper on some historical or weird issues (like axiom of choice). They pay attention to their courses, but not with the passion they share with their "hobby" interest in mathematics. – Markus Klein Mar 15 '14 at 6:44