[chongli]

They're absolutely fair if you're given plenty of practice at them. If the only synthesis problem you see all year is on the final exam then you have a point. However, if you're doing novel (to you) proofs on assignments every week throughout the course, you should be used to the novelty by the time you reach the exam.

Expecting a final exam consisting only of calculation and memorization type questions is wholly inappropriate in a mathematics course full of proofs.

[prerok]

I think you are both right and it really depends on the leap that has to be done during the time constraints of the exam and how much practise was included in the curriculum.

Off-topic, I know, but I always disliked the time pressure of exams. All the bad scores I got were down to not feeling quite right at the time of the exam: maybe I didn't sleep well, the food I ate did not quite sit with me, had a fever, etc. None of these things actually impair too badly but if the time is short, there is an impact.

I suppose it's similar to sports where you have to, at least somewhat, adapt on the go. Many teams botch a game here and there. But... your final exam? Botch it and you're screwed. It just does not feel right.

[hashmap]

it depends on what you mean by fair, i think. is the purpose of the test to gauge how well a person performs on tests? the difficult problems i encounter in the real world involve collecting a bunch of context on it, sitting with it for a bit, then putting it down and going for a walk. when i come up with something to try it's usually when i am outside and looking at trees.

maybe this is good for weeding out students who would not be a good fit for high stakes speed math.

[chongli]

It's really not high speed math. You'll have 2.5 hours to solve maybe 5 problems on the exam. A math grad student who TAs the course can typically complete the exam in 45 minutes or less, without any preparation whatsoever. An undergraduate student who can't solve the exam in 2.5 hours (without external aid) is not going to solve it in 10 or even 20 hours. They simply do not know what they're doing at that point.

It's really no different from a software dev interviewee who can't solve basic programming questions without being handheld and coached through the entire process.

[knollimar]

I think if TA no prep completion time to total time ratio is above 2.5 it's not the time pressure based exams I'm referring to.

I didn't get those exams in math courses. Engineering courses I did get those where some of the point of the test is the speed of your pattern matching ability (did you use design skills to reason about it or did you brute force a solution).

Math you're already extrapolating theory and you need ample time for that.

[menaerus]

I hope you don't interview people because what you laid out is full of false assumptions.

[hashmap]

Pointing to the interview process works against that argument rather than for it, and for the same reasons. Have you never been stuck on a problem at night and woken up with the answer? A good number of the really interesting problems I've solved got solved that way. Many of them felt like they either didn't have an answer or there's no way I was going to get it. Good thing there isn't a 2.5 hour timer following me around!

[chongli]

I have been stuck on problems that I figured out the next day. Many times. But that was when I was new to the topic, at the beginning of the course. By the time I reached the exam, I knew the tricks and how things fit together, and I could quickly solve lots of different proofs based on that same material.

That’s what the exam is testing for. If you need unlimited time to write the proof, then you haven’t studied the material yet, and should be expected to perform poorly on the exam.

It’s like the difference between someone who has never touched React before the interview, and someone who has been programming with React for several months. You expect the person with several months of experience to know how to solve problems with React several times faster than the person who doesn’t know it at all. If you’re hiring and looking for someone with a minimum of 1 year of React experience then you shouldn’t expect the person to take a full day to do basic tasks with React (especially if you the interviewer or anyone else on your team can do those tasks in just a few minutes).

[hashmap]

> I have been stuck on problems that I figured out the next day. Many times. But that was when I was new to the topic, at the beginning of the course.

Maybe it has been a while since you have worked on something difficult, then? Difficult for you, I mean. Maybe the difficult things are now easy.

> If you need unlimited time to write the proof, then you haven’t studied the material yet, and should be expected to perform poorly on the exam.

I mean, maybe. I remember some classes and exams where I had simply never seen the topic before, and the problem relied on having picked up on metapatterns that weren't explicitly taught during the class and applying them in novel ways on the spot. Though my guess was that at least some of those problems were markers for "if you can one-shot this, we want to know".

> If you’re hiring and looking for someone with a minimum of 1 year of React experience then you shouldn’t expect the person to take a full day to do basic tasks with React.

If you're talking about the basics, then yeah I would agree. I guess I don't really know what counts as a synthesis problem in this context, and if we were looking at specific examples it would be more obvious why one might be fair and another might not be. I've heard that line about TAs being touted as being able to solve the tests in just a few minutes, yet somehow unsolvable problems fell through the cracks to the students in the same class more than once in mine.

[chongli]

If you're talking about the basics, then yeah I would agree.

That's the crux of it, really. For a lot of students, the kind of proofs we do in undergrad pure math courses are very difficult. For a math professor? They're extremely basic.

There are levels to this. If a typical high school math student is at level 2 or level 3 (of math ability), a 3rd year pure math course may be at level 10, but the professor teaching the course is at level 100. Okay, so these are made up numbers, but I hope they help to illustrate.

For someone who has never tried to write a computer program in their life, writing Fizzbuzz may be quite difficult. For a working lead developer with 10 years of experience? Quite basic.