I sometimes assign open problems as extra credit problems. Some thoughts:
1) Do you tell the students the problems are open?
YES- it would be unfair for a student to work on something they almost surely won't get.
NO- Some Open Problems are open because people are scared to work on them. Having said that, I think P vs NP is beyond the one smart person phase or even the if they don't know it's hard maybe they can solve it phase.
NO- See Page 301 of this interview with George Dantzig where he talks about his mistaking an open problem for a homework and ... solving it.
CAVEAT---There are OPEN PROBLEMS!!! and there are open problems??? If I make up a problem, think about it for 30 minutes, and can't solve it, it's open but might not be hard. See next point.
I tell the students:
This is a problem I made up but could not solve. It may be that I am missing just one idea or combination of ideas so it is quite possible you will solve it even though I could not. Of course, it could be that it really is hard.
A friend of mine who is not in academia thought that telling the students that I came up with a problem I could not solve, but maybe they can, is a terrible idea. He said that if a student solves it, they will think worse of me. I think he's clearly wrong. If I am enthused about their solution and give NO indication that I was close to solving it (even if I was) then there is no way they would think less of me.
Is there any reason why telling the students I could not solve it but they might be able to is a bad idea?
2) Should Extra Credit count towards the grade? (We ignore that there are far more serious problems with grades with whatever seems to make them obsolete: Calculators, Cliff notes, Cheating, Encyclopedias, Wikipedia, the Internet, ChatGPT, other AI, your plastic pal who's fun to be with.)
No- if they count towards the grade then they are not extra credit.
I tell the students they DO NOT count for the grade but they DO count for a letter I may write them.
What do you do?
"Is there any reason why telling the students I could not solve it but they might be able to is a bad idea?"
ReplyDeleteYou are their teacher and they might feel you should have more abilities and skills than them since you are grading them.
As a teacher, I'd be happy if my students were better than me. I hope the students would be happy too, as long as I was helping them progress.
DeleteIt is fine for extra credit to count for the grade as long as it can only increase the grade and the students could still get A's without doing the extra credit.
ReplyDeleteIf it doesn’t count towards the grade, it’s not “extra credit”. It’s just extra.
ReplyDeleteYou helped me at a rough time when I was going through a lot in my PhD by giving me an open problem and telling me it was open.
ReplyDeleteIf you come up with an "open problem", ask a bunch of people about it, and one or more of them solve it, I don't think you should be embarassed. (If it were me, I might be embarassed anyway -- but I don't think I should be. Unless, like, it turns out that it was an easy problem.)
ReplyDeleteI think there's enough variety in how things might be proved, and luck (in terms of what methods a given person has seen), that it's hard to predict who can prove what. (Maybe something similar applies to AIs?)
If I were a student, I'd prefer that open problems be marked as such. If a prof assigned a problem and said "I can't solve this", I would not think less of them if I happened to solve it. (See above re luck etc.)
If "assigning a problem that you can't solve" is an issue: presumably you've thought about it enough to maybe have a partial approach? In that case, you could assign steps of that as sub-problems. (Assuming that you've worked out some of the steps.)
Your letter of recommendation is important, but the student's grades are also important; the two are not mutually exclusive. Both count.
ReplyDeleteI think you should include it in their grade. A grade is meant to indicate mastery over the material. Are you really going to write that letter for someone who got a D? Or give them a D if they solve an unsolved problem? Is that showing their true mastery of the material?
ReplyDeleteGive them the problem as extra, but be explicit that it is difficult and research level and open ended.
ReplyDeleteThe worst thing here is not setting the expectations and students spending a lot of time on it, students have limited time and your course is not the only one they take.
If they solve it in their extra time, that is fine, but they should not drop the critical stuff they need to do to get a reasonably good GPA overall.
I do give research level problems, but I tell that this is optional and it is extra credit, and they can get an A+ without it.
I try to make it more than solving a problem, I like to make it a way for them to learn new things and skills and get a bit of research experience, and challenge themselves. Typically less than 10% of the class do it, but those who do, enjoy doing it. I have a lost of them.
Razbarov also had a good list. Adobe of them are hard enough that even if Razbarov himself spends a few months he might not be able to make much progress on them, despite being one of the smartest folks in complexity their. Some of them are things that he can most likely shove them off he puts a few weeks of his time dedicated to them. The better kind are the later kind where it is publishable but also most likely solvable by me if I put a few weeks into it.