Small class, seriously smart hard working ederly professor notorious for setting conjectures from whatever areas of interest he currently had as exam questions.
Failure was not even trying to answer, grading was scaled on how many you had a shot at and what kind of dent you made on them in the hour.
Fun times.
I have fond memories of nights at a local bar, working through a problem.
I remember one instructor who told us at the beginning of the course that he would be giving a "you are not expected to finish" exam. The problems wouldn't be difficult, as they were all variations on a theme, but there would be a large number of them. Having an expectation of what I would be facing, I "studied" by practicing my writing speed and mental arithmetic. Even with my writing speed being the bottleneck, I ended up finishing all of them ahead of time, and I still remember the look on his face as I handed it in. I'm pretty sure I didn't get them all correct, but apparently it was enough to severely skew the distribution of results. Later, I heard that he decided to make the exam twice as long in the next instance he taught.
That was a long time ago, before the use of computer-generated exams was common.
Fun times.
I generally try to think about a problem before actually, you know, writing stuff down. I can obviously think a lot faster than I can write, so writing down potential approaches when I can't quite see a way to advance from them - or for which I already know that they are wrong - is not really viable.
The only way I can see this working is in a "Give X potential approaches for this problem" kind of question. Giving exam questions for where there isn't a reasonably reachable answer derivable from the taught material is quite cruel. Keep that stuff contained to lectures so you can do a class-wide brainstorm session, that's a lot more productive and doesn't, you know, cause psychological harm.
> I generally try to think about a problem before actually, you know, writing stuff down. I can obviously think a lot faster than I can write, so writing down potential approaches when I can't quite see a way to advance from them - or for which I already know that they are wrong - is not really viable.
You are thinking about too simple of a problem.
Any moderatly complex problem won't fit in your head. The traditional approach is to find a path towards what you want to prove, highlight the main lemma and start working on them in order if you can but working backward is fine if you find that easier.
> Giving exam questions for where there isn't a reasonably reachable answer derivable from the taught material is quite cruel.
Life isn't fed to you piece by piece nor is it easy. Advanced questions are hard. That's the point.