# What to do when students answered more questions than instructed during an exam?

I am a 5th year grad student. This is the first time I am allowed to teach a higher level major course on my own. We just had our midterm today and I am confused as to how to proceed.

On the midterm that I created, the instructions were to "attempt only 5 problems" out of a total of 8. But I didn't specify on the exam what would happen if the students were to attempt more than 5 problems.

I noticed half of the class (11 of 20) did follow the instructions and only handed in 5 problems or clearly marked which one are to be graded. But there are those who did more than 5 and did not specify which ones I should grade, perhaps hoping that I would pick their highest 5 problems or they simplify forgot.

What should I do in a situation like this? I know it is "standard practice" to simply grade the first 5 problems in numerical order that they have attempted. Unfortunately it seems most if not all students have no clue how to do problem #2 and #3 (these were fair questions, but required students to be clever), therefore if I were to follow this standard procedure, the students who attempted more than 5 (which basically means they attempted all) will almost certainly get a failing grade, which seems a little cruel.

(I listed on the syllabus "rough" grade cutoffs, i.e. A = 90+, B = 80+, C = 70+, etc. with pluses and minuses. The grades of students in the class are basically clustered at the moment, with a bunch of students around 90-95%, then a couple around 70-80% and then some around 30-50%, with not many outliers.)

EDIT: I asked two faculty members they both told me to simply grade the first 5 attempted questions in numerical order, and the difficulty of each question shouldn't matter. They said the same policy is used on qualifying exams. Sorry that I was just overthinking. That's what I'm going to do.

– cag51
Commented Nov 2, 2021 at 1:00
• When I was a Senior undergrad, I took a course that was both undergraduate and graduate students. Most courses like this grade the two types on separate curves. This one didn't. For our (take-home) final there were 100 points, with 2 "extra credit" questions worth 5 points each. I scored a 93 which ended up being a B. Why? Because apparently, our professor didn't understand what "extra credit" meant. (I.e. you add it after the curve is determined.) And some overachieving grad student scored 115 points total out of the maximum 110. Which meant to get an A you had to score 95 points or higher. Commented Nov 11, 2021 at 18:51

My view is that we should make sure grades are good predictors of underlying ability. This answer reflects that. Perhaps it slightly overestimates a small number of students, but that is much better than vastly understimating/failing them (in my view, capriciously).

Option 1

Since the exam just happened, and with so few (~10) students, I would simply email them and state something like:

It's unclear to me which five questions you would like graded, please let me know by [some short deadline] or I will grade #1-5.

The short deadline - perhaps by the end of the next business day - is so they don't have too much time to game this system. In my view, if they are extremely likely to drop #2 and #3, any possible advantage they may have gained by discussing their answers and realizing which ones they did really wrong is well ameliorated by having them still have to pick five out of the remaining six and already having lost time working on more than five problems.

Option 2: Just grade the five most complete answers. This is probably what they want and what they meant to do.

If this still feels unfair to you after getting their preferred five questions, you could grade all students on their best four out of five. (This is what I'd do if this happened to me).

Finally, you could pick randomly out of the problems they started, but given these are upper-division courses, I feel giving them a little bit more benefit of the doubt feels more reasonable.

– cag51
Commented Nov 4, 2021 at 20:53

Mark the five best answers for each student. Presumably the fact that they completed more work than necessary means they spent less time on those answers: hence, they have already 'penalised' themselves for not following instructions.

Next time, make sure the instructions are clear on what happens if they don't follow instructions.

• I didn't downvote, but I guess the flip side would be: isn't this unfair to the students who actually followed the instructions but wanted to / would have benefitted from using the illegal strategy that they were told not to use? You claim it evens out....but I am skeptical, and the students who followed the directions may be as well.
– cag51
Commented Nov 2, 2021 at 2:42
• It could also be argued that you should grade the worst five asnwers to prevent students from throwing guesses at a wall to see what sticks.
– HAEM
Commented Nov 2, 2021 at 7:28
• @HAEM Come on, that's absurd. If your students can do well on your exam by 'throwing guesses at a wall' then you've got bigger problems than which answers to mark.
– avid
Commented Nov 2, 2021 at 8:02
• If I was a student, I would be infuriated if people who didn't follow the instructions got a preferential treatment (more opportunities to collect points) Commented Nov 2, 2021 at 9:51
• Not all exams have significant time pressure for all students. The notion that doing extra problems takes away time from the ones actually graded is likely false (otherwise you'd have many students who didn't even finish 5 problems). Doing extra problems has no drawback whatsoever for a student who finishes 5 problems with time remaining. Commented Nov 2, 2021 at 13:12

I would like to confirm the answer from Avid, with following thought experiment:

A student gets the eight questions and starts solving them, in the sequence from easiest to most difficult.
Once the student has finished five questions, he realises he still has some time left, and decides to solve the sixth one, and the seventh one, and finally the eighth one, which is the most difficult.

As such, the student has proven:

• To be capable of solving all problems, even the most difficult ones.
• To have an ambitious work ethics.

I could not disagree more with the reaction of Cag51, as if the "skill" to follow instructions is more valuable than the proof of higher competence, especially in a school environment.

• Good answer and +1, but: I think the point here is that some of the students who followed the instructions may have equal or greater competence to some of the students who didn’t. This is a source of unfairness that the instructor must think carefully about eliminating (or reducing, since as I said in my answer, it seems impossible to completely eliminate). Commented Nov 2, 2021 at 13:49
• … In other words, the “skill” of following instructions (and similarly the instructor’s “skill” of writing an exam with clear instructions) is important because it facilitates the goal of assessing the students’ level of competence in a fair, level playing field. So @cag5 has a point… but so do you :-) Commented Nov 2, 2021 at 13:52
• Here's an alternative thought experiment: a middling student receives the eight questions and realizes that they're not 100% sure about the answers to most of them, so they'll have to guess and handwave and hope that they'll get enough points from their partial answers to pass. After doing so for five questions they notice that they still have some time left, so they write hasty guesses for the remaining three questions in the hope that they might guess right (or handwave convincingly) and that the grader will pick their five best (i.e. luckiest) answers. Commented Nov 2, 2021 at 14:37
• @Dominique: Perhaps more to the point, you seem to be assuming that a student who doesn't know the full correct answer has no chance of receiving even partial credit just by guessing about the parts they're not sure about. In my experience that's rare, especially for questions needing "a serious effort to solve and to formulate an answer". Indeed, whenever one isn't 100% sure how many points one's answers will get (either due to uncertainty on the subject matter or uncertainty about grading), being able to answer extra questions and have the best answers picked gives a statistical advantage. Commented Nov 2, 2021 at 16:09
• Or, a good student who knows the material does 5 questions (any 5, say they even work hardest to easiest) mostly correctly but makes some accidental error on one. However, they followed the instructions and stopped after doing 5. They thought the problems were interesting, though, so they went home and did the rest on their own time from memory, getting the rest of the questions all correct. Their neighbor did everything exactly the same, including making some accidental error, except they didn't follow instructions and finished all of the questions on the exam paper. Commented Nov 2, 2021 at 21:52

My most important advice is not to do that again. And, make sure students read and understand the rules. Not all will find them obvious, though with 20 it is easier.

There is no perfect solution, but there doesn't need to be. If you use coarse graduations, then it probably doesn't matter if you take simple actions. And if you don't grade competitively in any way then you can assure that it doesn't really matter at all. If your attitude is "I'm here to give points", rather than "I'm here to withhold points" then you have a solution. But since it is on you, then it means more work for you (another reason to avoid a repeat).

Do something like this:

Peruse the other students first, to get a sense of what is known and what is not - generally. Then look at the students who answered more than needed without indicating which were to be included and see if their knowledge generally matches that of the others. Look at everything they did, without throwing out questions arbitrarily. You can, judiciously sort them into the coarse categories without applying numbers.

It may turn out that the few students have really demonstrated mastery overall, so should get high marks. They may have done poorly on most questions - low marks. But if the graduations are sufficiently coarse (as is normally true in the US at the end of a course) then the sorting problem isn't as hard as you imagine.

But a distinction between 89 and 91 is probably (definitely) beyond the bounds of the possible.

And note that the Sorting Hat at Hogwarts only had to distinguish four categories.

Remember that you are grading individuals, not the class as a whole. Each student demonstrates a level of mastery or fails to do so. All you need is a rough measure, mixed with a bit of generosity. This works as long as being generous is applied generally over the course so that individuals aren't treated unfairly by the grading system itself.

And the big big lesson is that you are an educator, not a grader.

You'll get better at this, I suspect, but don't repeat old mistakes.

• Nice harry potter reference lol thanks for the advice! I appreciate it you taking your time writing this up! Commented Nov 1, 2021 at 21:57
• Less than book length, anyway. But once I get started.... Commented Nov 1, 2021 at 21:59
• +1 especially for "you are an educator, not a grader" (but good advice all around). Commented Nov 2, 2021 at 1:58

While I'd broadly agree with the advice in your edit, I would mark the first 5 in the answer booklet, rather than questions 1-5.

• What is the difference? Are questions not always in order? Commented Nov 2, 2021 at 12:58
• @Sofia: The questions are certainly in order, but the answers may not be, unless the students all solved them, or at least wrote them out, strictly in order (which would generally be a suboptimal test-taking strategy, as it's usually better to start with whichever question you find easiest). Of course, things would be different if the students were told to write answers in blanks on the question sheet itself, but I assume from the OP's phrasing that this is not that kind of an exam. Commented Nov 2, 2021 at 14:27
• aaah I see. I imagined a page with space for the answers but of course, if they are separate, they could be in a different order. Commented Nov 2, 2021 at 15:29

When this happens you generally have two possible options:

• Grade the first five problems.
• Grade all of them, and then take the final score as the sum of the best five problems.

It's obvious that the second option is better for the student, while the first is better for you (since it takes less work). Since the instructions clearly said "attempt only five problems", you should take the option that is better for you. You can't control what students do in exams, but you can stop them from abusing you as a grader.

Frankly I'm surprised this hasn't already been drilled into your students by their high school teachers. If you do take the second option, I would emphasize afterwards that it's a one-off act of mercy, and not to expect similar favours in the future.

• "Frankly I'm surprised this hasn't already been drilled into your students by their high school teachers." I'm not. Leaving aside the variations in quality of education at high school, I don't think I've ever heard of an exam being marked as "only attempt 5 questions out of 8". If you're writing up an exam, you typically want all of your students to attempt all of the questions, so that you can assess their capabilities in as broad an area as possible - and if you're okay with a narrower assessment, then why are you writing extra questions? Commented Nov 2, 2021 at 8:53
• The second approach in the answer is used for coursework sometimes - best 3 of 5 assignments was used in teaching labs. Those assessments were formative with detailed feedback so improvement could be expected, but it was possible for an occasional experiment to go so badly they'd fail to get a decent mark Commented Nov 2, 2021 at 10:08
• @nick012000 I've seen this since my A levels (UK school-leaving, over 20 years ago), through my own undergrad, and I've marked them for undergrad work in the last couple of years. This is quite a common approach and may be required or expected by the examination policy Commented Nov 2, 2021 at 10:10
• @nick012000: I've had final exams in college where I was instructed to only attempt some of the questions. However, this was typically an act of mercy to allow test-takers to select the questions they were best able to answer. If the instructor had later informed me, "some people answered more questions, so for them I picked their best answers" I would not have been unhappy: I knew which questions were my best 5, the lost opportunity to answer more questions was worthless. Commented Nov 2, 2021 at 13:16
• Pretty much all my high school (and undergraduate) exams had a choice between questions. That was some time back though so maybe it's less common now (non-exam based assessment was also very uncommon when I was at highschool but became more common after I left) Commented Nov 3, 2021 at 0:36

First, be transparent about what happened and how you are addressing the situation. Document your grading methodology and share enough details with the class so that no one will have reason to feel aggrieved.

Second, your goal is to maximize the fairness in your treatment of all students. Unfortunately your unclear instructions can leave some theoretical possibility for someone to feel (or claim to feel) like they are being treated unfairly no matter what you decide to do. But the scope of this theoretical unfairness is quite small, so if you proceed with common sense and good faith, I think you (and everyone else) will be fine.

Now, as for what to do, I think the following is a reasonable option:

1. For each exam, grade all the questions answered by the student. Use their top 5 question scores and as the basis for determining a tentative grade.

2. Review the grade distributions of the two groups of students (those who answered exactly 5 questions, and those who answered more). Do you see a sizable difference in the average scores across the two groups? I.e., something that gives you reason to believe the group of students who answered more questions than they were supposed to are enjoying an unfair advantage in the grading?

3. If there is a sizable difference favoring the “rule-breaking” students, consider artificially raising the scores of the second group to compensate for that difference.

4. If there isn’t a sizable difference between the two groups, or there is a difference but it’s pointing in the other direction (the rule-abiding students being the ones who enjoy the advantage), consider not making any adjustments and declaring the tentative grades you calculated as the final grades.

5. As an intermediate solution, if there is some difference but you are not sure how relevant or significant it is, consider using the tentative grades as final grades, but announcing to the class that you are reserving the right to increase the grades of some or all of the students from the rule-abiding group later in the semester, if you feel that that makes sense. That leaves you an opening to be generous in some way that’s entirely at your discretion, for example if at the end of the semester there is a rule-abiding student whose score is very near one of the grade cutoff points and could benefit from a small extra push.

6. Any of the above options can be considered based on not just the statistical calculation I mentioned but also other information that you have that affects your perception about the extent of the unfairness.

If you follow these steps, I think the students will appreciate that there was a minor snafu in the exam instructions and you handled it reasonably and competently. Again, the key is: transparency, acting in good faith, and taking care that any grade adjustments you make are only in the direction of increasing the grades of some students, not in the direction of penalizing anyone.

• Re: 2. As a conjecture, students who are unable to follow instructions will perform worse on the exam. So it cannot be determined directly from the score distribution whether students who answered too many questions were given an unfair advantage. Commented Nov 2, 2021 at 15:03
• @FerventHippo it’s possible. In that case OP won’t have a dilemma as to what to do. But it’s also possible that some of the students you describe as “unable” to follow instructions are just unwilling to follow instructions, making an intentional gamble that this will pay off. I’m not so sure that such manipulative tendencies are correlated with lack of knowledge of the material. Commented Nov 2, 2021 at 18:59
• "In that case OP won’t have a dilemma as to what to do." Depends on the philosophy underpinning their concern. If the issue is to isolate the effect of answering additional questions, and to find as best as possible the scores that would have occurred in a hypothetical universe where they had answered according to instructions, the dilemma remains. Commented Nov 3, 2021 at 1:04

Grade all questions answered and then normalize it to out of five.

If all questions are worth the same, then it is simply score * 5/N where N = number of questions answered. Only do this if N > 5.

Also count a question that clearly abandoned early on as not answered- just ignore it.

Pros A student who does equally well on all questions will get the grade the would have gotten answering only five.

Although possible to get a better grade than they would have, it is unlikely. It would require that the student had no insight into which they did better.

Some or many will get a lower grade than they would have but it will not be as bad as just doing the first five- taking as true the OP statement about questions 2 and 3. It will soften the blow of those questions.

So bottom line is there is a negative effect for most who did not follow instructions, but it is smoothed out vs. just picking five to grade.

Cons

It is more work from you.

You will get complaints that you should have taken the top five. And some edge complaints about incomplete answers that the student will say was clearly abandoned.

• To avoid complaints about taking incomplete answers, you can sprinkle this strategy with guess that a student clearly would have picked 5 out of 6 questions they got to 50%+ and not those 2 questions at 20%, so you would average just those 6. Similarly, and if they got just 3 to 50%+ and 5 left at 10-30%, you could count 3 good ones + average of those 5 as the remaining 2 answers. Commented Nov 4, 2021 at 9:12

I find it highly unlikely that half your upper-level class failed to follow instructions unless we are not being told the whole story. Half the class doesn't do something like this unless something was at least somewhat unclear.

Did you announce your exam structure in the lecture before the exam? Is it described in the syllabus? Did you explicitly tell the students to mark the questions they want to be graded or rip out the pgs from the exam book they didn't want graded? Did you announce, verbally at the start of the exam, "remember attempt only 5 of 8 questions", or is it just in the written exam directions?

Written instructions are like the fine print of a 30 pg legal mumbo jumbo contract. No one reads them. They are taking a timed exam! Reading written instructions is a waste of time on basically any other exam. If you surprise your students with unusual rules in written instructions, you are effectively tricking some of your students. The only exception to this is if you allocate a minute or two at the start of the exam explicitly for reading instructions. "Now you will read the instructions on the first pg and not open the exam. Be sure to read the instructions carefully right now."

Furthermore, did you define what an "attempt" is in your written instructions? Suppose you got the exam

1. several well-thought-out and presented paragraphs/calculations etc.
2. a few scribbles or sloppy scratch work
3. a few scribbles or sloppy scratch work
4. several well-thought-out and presented paragraphs/calculations etc.
5. several well-thought-out and presented paragraphs/calculations etc.
6. several well-thought-out and presented paragraphs/calculations etc.
7. several well-thought-out and presented paragraphs/calculations etc.
8. several well-thought-out and presented paragraphs/calculations etc.

I assume under your "grade the first 5 attempted problems" you'd grade 1,2,5,6,7? Correct? If you graded 2 and 3, and I was your student, and it meant I failed the exam, I'd try my best to get you in serious trouble with your University. I'd drown you in paperwork and proceedings for the next year. I'd rally half the class to complain with me. Don't be fooled, most Universities in the USA usually side with the students in borderline cases like this. The students are the customer and you screwed up by not specifying that there is a penalty for attempting more than 5 problems. I highly doubt that half the class was trying to get an advantage. It's much more likely that the students simply didn't understand, didn't know, or forgot your unusual exam specifications. Do you really want to fail a student who knows the material well because of this?

Rule nr. 1 for teachers is that students are always right in a collective sense. A single student can be wrong, but if there are more than a few who did something unexpected, then you are the one who is wrong, the students are right, however inconvenient that is for you.

In this case, this means that you should look at all the answered questions and grade the 5 best, no matter what the rules say. Now, one could argue that the students did in fact make a mistake, but that's a totally mistaken view to take.

The students are not at university to pass exams, they are there to learn and master particular subjects. They are paying for the services offered by the university, including the opportunity to sit exams to measure how well they've mastered the subjects they are studying.

If you are going to grade the first 5 questions leading to students who would otherwise have scored 100% to now fail the exam, you are not delivering a service to the students that they paid for. This is then grounds for appeal, which could even go to a court should the university uphold the decision to fail he students. With many thousands of dollars paid for tuition, no judge would rule that it would have been too much effort to correctly grade the students that would have avoided this absurd outcome.

• +1: I disagree with the first paragraph, but the last two are spot on! Commented Nov 3, 2021 at 13:05

You assert this is your first time teaching at this level. I noted carefully your statement (emphasis added)

Unfortunately it seems most if not all students have no clue how to do problem #2 and #3 (these were fair questions, but required students to be clever)

Since "most if not all" of the students did not successfully respond to the problems (honestly, did any succeed? your statement is vague on this point), it appears that you yourself have failed to either adequately teach the principles covered by the problems or in your expectations for the students to complete them. This calls their fairness into question. In every instance I have observed of this, the instructor owned their failing and eliminated such problem(s) from having a negative consequence on students' grades.

I appreciate that "clever" solutions are encouraged but when it requires such cleverness that the vast majority are likely to fail (per your own admission), the most ethical response is to remove said questions from consideration.

i.e. only grade 1,4,5,6,7. Students who did not complete the requisite 5 after eliminating 2 and 3 should be graded fairly on their attempts.

• It's fine to ask hard questions that very few students get. What's not ok is having some students count these questions, because they have a few scribbles on the pg, while other students get to count easier questions. Commented Nov 3, 2021 at 13:03

I ended up grading the first 5 attempted questions for each student i.e. if a student attempted #1,2,4,5,6,7 then I graded #1,2,4,5,6. For questions that require short responses almost anything other than a blank counted as an attempt. For questions that require long essay-like responses (proofs), anything that stated an assumption and claim counted.

I don't think it's reasonable to say students "forgot" to indicate which problems are up for grading. I think the students who submitted more than 5 questions for grading without indicating which ones they want me to grade, are simply trying to game the system or get an advantage over other students, and here's my reasoning:

1. I have repeated in class instructing them to indicate which questions for me to grade. In the exam students were given a "question sheet" which listed all the questions and were provided "unlimited" number of scratch paper, in which they will put their responses on. On top of that, I have verbally told the class in the beginning of the exam "to only submit or indicate 5 questions up for grading, not more," and also at the end of the exam to "make sure you choose which 5 are to be graded."
2. Some questions require only a very short response which could be totally correct or incorrect (for instance, find the kernal of some map, or, list all the subgroups of some group). I think some students aren't sure if they got these questions correct and don't want to risk losing points for the entire question(s), so they simply didn't choose which ones are to be graded, versus the rule-abiding students who had to choose whether to discard these "questionable" answers.

• You should edit the question to add more context to it rather than putting it in an answer. The only part of this answer that should be in the answer is the first paragraph. Commented Nov 5, 2021 at 20:52
• This is both an answer and a clarification. The part which is an answer should stay — thank you for coming back and telling us what you did, we encourage that! — but feel free to edit your original question to add your two reasons at the bottom. Commented Nov 8, 2021 at 20:48
• +1: Given the clarification under (1), I think this isn't unfair, but the situation is very unusual. You must have a strange group of students. I do think you should mark on your spreadsheet which students got heavily punished for this rules violation. Allow students to learn from their mistakes and redeem themself on the final. Penalizing them is OK, but causing them to fail the course for this if they know the material is not OK in my opinion. Punishments should fit the crime (this is a minor crime, so the punishment needs to be minor too) Commented Nov 9, 2021 at 23:39

Your institution should have a rule for how to grade exams in this circumstance. If so, find out what the rule is, and follow it. (It appears from the update to the question that this is what you did and it resolved the issue.)

If the institution's rule is one you disagree with, follow it anyway; it would be unfair to apply a different rule, because students who took the exam may have known the rule, and may have submitted answers according to their understanding that the rule would be followed.

If your institution doesn't have a rule to deal with this happening, I personally believe the fairest and most sensible way to deal with it is to mark every answer and then take the best 5. The reason I think this is the fairest rule is because it doesn't penalise a student for starting a question, realising they can't answer it, and then choosing a different question. If a student wrote one or two lines on some question and then gave up, it would be absurd to treat that as one of their five questions when they have written 5 full answers to other questions. That student could lose up to 20% of their mark just because they put pen to paper before realising that they could do better on a different question. (Or if they were supposed to cross it out to indicate that they didn't want it to be marked, then they could lose up to 20% of their mark simply for not putting a line through something they thought would be ignored anyway.)

There are some other answerers and commenters who believe taking the best 5 answers would be unfair on students who only attempted 5 questions. I disagree; suppose the exam is 80 minutes long. Then if a student "followed the rules", then their mark is based on work which they had 80 minutes to do. A student who answers all 8 questions will receive a mark based on work they only had ~50 minutes to do. My own experience (from marking exams where the best k answers count, and students are told so) is that students who attempt too many questions tend to have rushed and made mistakes in most of their answers.

Also, if your institution doesn't have a rule to deal with this happening, then make sure that someone higher-up knows that they need to make one so this won't be a problem in the future.

• "Your institution should have a rule for how to grade exams in this circumstance" In what country do you refer? US institutions do not regulate exams nearly this tightly. Commented Nov 3, 2021 at 0:12
• @AzorAhai-him- If there isn't a policy at the institution level, there may be one at the department or course level. My experience is from setting and marking exams at two UK universities, but unless this is the first time an "answer k of n" exam has been set, then it's likely some students have answered more than k questions in the past, and a decision about what to do will have been made then; so that would be the policy. That said, by "should", I meant either there's a policy already, or there should be one; it is better for students to know how their exams will be marked. Commented Nov 3, 2021 at 2:20
• Interesting. I would find that pretty unlikely in the US, instructors have a lot of flexibility in how they set their courses. Commented Nov 3, 2021 at 3:00
• @AzorAhai-him- Then I will defer to your experience. Commented Nov 3, 2021 at 3:27
• @AzorAhai-him- If this institution gives instructors flexibility in how they do this, then that just means it is the instructor's responsibility to decide in advance what to do if students answer more questions, and make this known to students. An exam rubric which says "attempt at most five questions" without specifying what happens if you attempt six is simply not fit for purpose. Commented Nov 4, 2021 at 7:45

I have just been in this situation. I solved it by grading all of the problems and calculating the expected value of randomly selecting five problems. In my case, a complaining student actually admitted that he was trying to game the system.

I give choice because sometimes people have difficulties understanding a problem as posed and because sometimes people draw a blank on a particular problem.

Picking the worst answers is the "standard practice" where i live and most fair to the students that did follow the rules. Picking 5 of the best answers is giving an advantage to the people who didn't read the rules. I think what the student has proven by solving multiple questions is irrelevant. Rules are rules and who is to say that people who only solved 5 questions couldn't solve all 8? It is after all, the smart thing to do.

The other option is picking random questions, but that doesn't feel very professional to me.

• Not sure how picking the worst 5 helps anyone. Seems like this would lead to absurdities: suppose a student began attempting some question, then quickly realised they couldn't answer it so they moved on to a different question. This student likely scores 0 for their partial attempt at that one question, plus their four worst other answers. But a student who did the same thing and also crossed out their failed attempt to indicate that they don't mean for that answer to be marked, could do 20% better on the exam. I can't see any justification for a 20% penalty on a rules technicality. Commented Nov 2, 2021 at 18:40
• Students may know that it is their worst five answers which will count, but they may think their quickly-abandoned attempt at a question is obviously not an answer and obviously not supposed to be marked as if it's an answer. I've marked exams where students wrote the question number and then just one or two mathematical symbols or words and moved onto the next question, where a full answer would typically take up an A4 page. Where do you draw the line? I would find it absurd to mark a student down by 20% for doing that, and I think the student would too, at best. Commented Nov 3, 2021 at 6:53
• More fundamentally, an exam is meant to test a student's learning of the relevant course material, not their understanding of the rules of the exam. If 20% of someone's mark depends on them crossing out a non-answer, then whether or not you think they "deserve" to lose those marks because it's their own fault, it makes the exam mark less of a valid metric for what it's supposed to measure. Commented Nov 3, 2021 at 6:56
• @kaya3 I think you've seen students scribble on answer boxes, because their worst questions are not picked. You wouldn't care to clear your answer if it didn't matter, but it does, so you do clear it. Where the line is drawn is not important, as long as it's the same for everybody. You do make a fair point about testing the students, but you can't please everybody here. I still think this is the best option in this lose-lose situation. Commented Nov 3, 2021 at 7:14
• For a concrete example, it obviously matters for a student to write their name or whatever other identifying information is required on the front of their answer booklet - and we announce before and after the exam to remind them to do this - yet I've had one or two intelligent students forget to do this, so that I ended up with an exam script with nothing on it to say who to award the marks to. Would it be reasonable or fair to have a rule saying those students just get 0 marks? I don't think so, even if the students know the rule. Commented Nov 3, 2021 at 7:34

Simple. Given there are 40 students who answered more questions than allowed, generate 40 arrays with the numbers 1-8 in a random order. In Python,

``````from random import shuffle
a=[1,2,3,4,5,6,7,8]
for s in range(40):
shuffle(a)
print(s,a)
``````

This will give something like

``````0 [4, 2, 5, 7, 6, 3, 1, 8]
1 [4, 7, 2, 3, 5, 8, 1, 6]
2 [5, 1, 6, 7, 2, 8, 3, 4]
3 [6, 1, 3, 8, 4, 5, 2, 7]
...
``````

Then you only consider the first 5 questions numbers that the student answered. For example, if student 0 answered questions `1 3 4 5 6 8` then you would only consider questions `4 5 6 3 1`.

This is very fair because the questions considered are randomly selected. So there is no gaming the system.

• Fairness is not just randomness or not being able to game the system. Would it be fair to just generate a random grade for each student? That's random, and can't be gamed either. Commented Nov 2, 2021 at 15:39
• This strikes me as more work for an unfair solution. Two students, with 8 identical answers to the same 8 questions could get different grades depending on which questions got graded for each student. Commented Nov 2, 2021 at 16:15
• @Justin, of course it wouldn't be fair to generate a random grade for each student. My suggestion only applies students who have broken the rules, as I say in the 1st paragraph. Commented Nov 2, 2021 at 16:34
• @Beska, that would admittedly be an unfortunate outcome, but the disbalance in this unlikely scenario would only apply to those who have broken the rules. Those who break the rules should be satisfied with anything that is better than "your grade is the sum of your 5 worst answers". In other words: If you agree to play a roulette game under the same rules as your opponent, you can't complain if your outcome turns out to be worse than your opponent's. Commented Nov 2, 2021 at 16:37
• Setting aside what people "should be satisfied with", potentially giving different grades to people with identical answers just sounds like trouble (if not a lawsuit). It would surprise me if the school sanctioned this method (but I have admittedly been surprised many times in my life.) Commented Nov 2, 2021 at 16:46