# Grading problems that nobody solved

Once in a while an exam happens where nobody correctly solves (i.e. there might be partial solutions) that trivial problem of yours (and I'm not talking about intentionally hard and impossible tasks used, for example, in "testing waters").

First of all, it is my fault (i.e. when I wanted them to solve it and nobody did; it's another matter when I let students surprise me for bonus points). There are a lot of possible causes, e.g. an especially good day (like when everything seems simple), non-standard intuition, sometimes a missing dependency, like a formula from another course they should have known, but didn't (and I should have checked they do).

Question: However, after it happened, how one should grade such task? In particular, should the "maximum" be kept as intended, or maybe moved to progress point of the best solution?

Example: The task might be about throwing a fair coin some number of times, and bounding the number of obtained heads from below with given confidence. The basic solution could use the Chebyshev's inequality, but you can obtain a better bound with, for example, Chernoff bound.

• A partial answer, or an answer that isn't as sharp as it could be, would get partial credit from me. "Nobody answered as I expected" isn't the same as "only blank answers"... Mar 18, 2014 at 19:39

I doubt there can be a general rule for this case. If it is my mistake in asking something they couldn't possibly answer (or even if a few answered because by some chance they knew about the topic), I'd just take the question off the grade (probably keeping the points of those who did answer as bonus).

If they should have been able to answer, I'd try to find out what happened, but would probably keep grades as-is.

• I've added an example to clarify my question. Mar 18, 2014 at 19:34

As long as the question was formulated in a non-confusing way and the students were provided with the right theorems to solve the questions, I don't see any urge to change grading or even remove the questions from grades.

Why? In an exam you want to find out if the students have learned a significantly enough. IF all fail in this, they haven't learned it and should not get better grades then (exept when the needed theorem was not covered).

In an extreme situation, maybe almost all students would answer most questions only to a certain level and then stop which would maybe proof that fulfill the requirements of your course but did learn nothing in addition from your course. Would you let them pass the exam then? (I hope not).

However, you can grade more merciful (especially when you have the feeling that something went wrong during the lecture or the kind of asking was maybe to sloppy).

You can also include in grading other factors seeking for adjustment to this decision how to grade that particular question: Was the exam maybe too long? How was the overall performance? etc.

Regarding your example: I depends heavily on how you asked. If the questions was "Derive the best lower bound for ..." and they used one method which was not the best, I would keep the grades how they are, but maybe give almost all points (but not all) if someone did so. If the word best would be missing, a student would think, he/she has finished since there was a (not so bad) lower bound derived. It that case, you can think about giving away all points.

• On your example: You can prevent such situation if your question reads like "Show that ... is a lower bound for the following quantity: ..." (But the exam becomes easier by this since the students know the "solution") Mar 18, 2014 at 22:09
• "Derive the best lower bound for X" is a terrible kind of question when there is no closed form for X! May 10, 2020 at 2:31