(Note: in Germany, tutorials are exercise sessions, typically weekly and mandatory, which accompany a lecture. They are held in groups of 5-30 students and are lead by a more advanced student whom I call the instructor.)

There is an interesting pattern I noticed during math lectures and tutorials at my university. It sometimes occurs when a student has an objection to something the instructor wrote or said. If the objection is about something simple like a missing sign, it's usually handled quickly and without problems. But whenever the socially acceptable time to respond is shorter than the time needed to understand what the objection actually is, the instructor usually doesn't even attempt to understand it. Instead, he does a quick sort of pattern matching of what the objection roughly sounds like, makes a guess as to which thing the student most likely misunderstood, and then attempts to explain that particular thing again.

Quite often – probably over half the time – this guess is accurate on the first try, and the response makes sense. If it's not, often the student replies and the instructor figures out what the objection is in a quick back-and-forth, and gives her a sensible reply that's a bit delayed.

But where it gets most interesting is if the student's grasp on the current problem is actually better than that of the instructor, and the objection she raised is correct. What happens then is that the instructor gives a bunch of explanations of stuff the student already knows, which all totally miss the point; the student might try to rephrase her problem, but this can at best lead to renewed pattern-matching based guesses from the instructor. The more convinced the instructor is that he is actually correct from the start, the longer this can go on without him realizing that he isn't. If the issue is dropped before it's resolved, sometimes it's revisited after the end of the tutorial. Because of the change of context, where now the pressure to respond quickly is gone, this might be the first time that the instructor actually tries to understand what the objection was.

I've observed this pattern many times with striking accuracy (the most extreme example is back from high school), and I've even observed myself doing it. The environment is highly competitive, because understanding math stuff is so closely correlated to IQ, that caring primarily about signaling strikes me as the norm, and anything else as fairly unusual.

A weakly related observation relates to the behavior of different students when they present their solutions during tutorials (or seminars). The primary motivation for doing this – certainly the thing that those students care while doing it – is to signal competence, i.e. show off. Unfortunately, the strength of this signal and the quality of the presentation can come apart: you will seem even smarter and more skilled if it looks like the things you are presenting are simple to you. The upshot is that some people will deliberately try to present the material with a dismissive attitude, sometimes going as far as to signal their own boredom or lack of interest. There seems to be an almost qualitative difference between students who want to show off honestly on the one hand, and students who just want to show off on the other, with the former usually doing a much better job at presenting their solution to the respective problem.

This is also something I've observed myself doing: I distinctly remember an occasion where I was being deliberately casual about a relatively hard problem I was presenting, even though I wasn't nearly as far above the level of the course as I was letting on. These days, I am presenting solutions fairly regularly and enjoy doing so, but am careful not to downplay their difficulty. I don't consider showing off to be the problem; on the contrary, if it makes people do a better job presenting, it's a good thing. But dishonesty seems to be obviously bad.