In a recent exam, I give student a true or false question asking them to decide if a statement is true. After the grades have been published, a student pointed out that I misread the statement and graded it mistakenly, as most of the students taking the exam did.
The problem counts for 1/40 of the total grades. So it’s not really a big deal. But I still wonder what should I do:
I would go with option 1, give everybody the points.
But also, for the students who actually got it right, I would give them +1/40 bonus points so as not to annoy/upset them either.
Basically, I don't think 1/40 of an exam is large enough a difference to offset any negative feelings that would be created by taking away points or making students who got it right feel like their achievement doesn't matter.
Edit: I originally started this answer with the following analogy, which has been absolutely beaten to death in the comments. It's not really that important.
Suppose that you're a cashier, and somebody buys $\$4.10$ worth of items, and you mistakenly charge them $\$4.00.$ They pay their bill, you hand them the receipt, and then just as they walk away you realize the bill should have been $\$4.10,$ not $\$4.00.$
Do you run after them and stop them? Probably not. The error is so miniscule that it's not worth annoying/upsetting them.
No matter how large or small the effect, if the mistake was caught by a student, I would never lower grades because of this. It would discourage students from pointing out mistakes.
Take out any deductions based on your mistake, for sure. But I'd leave it at that.
I think everybody who got the question "right" but was misgraded should have their score adjusted upwards. But everybody who got the question "wrong" should get the benefit of the doubt and leave their grades alone.
I would never, ever, downgrade a test score due to a grading error. I think you have to publicly own your mistake. That in itself is a teachable moment - it sends a powerful message that people in a position of power make mistakes, need to be held accountable.
I misread the statement and graded it mistakenly, as most of the students taking the exam did.
Why should you assert that a statement where you and the students agreed on the meaning of the statement is a "misreading"? Language is like that. Text is like that. Communication is the purpose of language and text.
Now you realize that there was another possible reading, and that other possible reading is correct on grammatical or technical grounds. Unless you are examining for "spot the badly formed question", why choose that reading? (A perfectly legitimate examination topic, but not, from your question, the purpose of this exam)
"Spot the badly written exam question" is something you are examined on, every time you write an exam. Clearly you lose marks for that, but that's not something the students lose marks for
You and your students agreed on the meaning of the statement as written, and you graded accordingly. Their marks stand.
One student spotted your mistake. Bonus credit for that, if the student spotted the mistake on technical grounds. If the student is spotting a typographical mistake which invalidates the question, that's cool, and you should be thankful, but you don't always award (for example) extra Math credit to students for being nice to you, or for having better English Language skills than you do.
Bonus credit you can arbitrarily assign as exam credit if that's the only avenue available to you.
Examination is a crude science. Did the minority of students who got the unusual answer, do so because they took the alternate meaning? Or because they took the standard reading and got it wrong? We never look at one question in isolation: if that one mark is going to make the difference between medical school and a career as a day-laborer, we make a judgement based on the whole of assessment. Fortunately, as in this case, that one mark seldom does make a difference, and, since exams have many purposes other than awarding marks, the "mark" may be completely irrelevant anyway.
I believe it is important to have a policy that grades are not adjusted downward for grading mistakes. I have experiences with two universities each with the opposite policy. In the first the grades can't be adjusted downwards when inspecting the exam. Here students were interested in checking the grading and explicitly seeing and understanding their mistakes and learning from them. In the other the students were so fearful of a grade adjustment downward that most didn't use the option to inspect their exam (even when this wasn't rational in cases where grades were more likely to go up). Thus in the second system the students missed out on both an opportunity to inspect the grading for mistakes and an opportunity to learn. Note that mistakes occurred very regularly in the system where checking was encouraged. In the other I don't know but I presume the rate of mistakes was the same but they remained uncovered.
The only argument in favor of the second system was from professors who didn't want to go through the work of offering an exam grading review. I don't think that this is really the right type of argument.
I would ask the students. If I make a mistake in grading, do you want the mistaken grade to stand - whether it is to your advantage or not, or do you want it to be corrected, whether it is to your advantage or not? Or do you want it to be corrected only when it is to your advantage, and are you happy for other students to gain unearned points over you when I make a mistake in their favour and not yours?
Academic integrity is one of the most important things we are supposed to teach, but it is usually not on any curriculum, and a lot of the time it is not addressed explicitly but taught only by example and by cultural diffusion. People make mistakes, and other people should not suffer for them. If people have been given the wrong information, and taken action on that basis that will cause harm to reverse, the person who made the mistake should take responsibility and make restitution. But truth is truth, and nobody should feel comfortable with points in their grade that they know they have not earned.
It's the same reason we don't tolerate plagiarism. You don't claim credit for work you haven't done and for ideas that you didn't invent. If you made a mistake, you correct it or you retract. You don't try to cover it up. You don't tolerate that attitude in your colleagues, either. Everybody hates the embarrassment of making a mistake, nobody with any empathy wants to put somebody through that feeling, and it is tempting to forgive others their trespasses so that they will forgive yours. But it ends up with the academic enterprise being corrupted, and eventually untrusted, because word will get around. If it becomes known that teachers are letting wrong grades stand because they don't want to upset the students by marking them down, the people using those grades in their future lives will adjust their trust in them accordingly.
The way round this is to invest your pride and feelings of self-worth in your integrity, not your infallibility. Everybody makes mistakes - teachers included - and everybody has erroneous beliefs. You can't prevent it or avoid it. We don't judge you morally for that. We judge you only on your response when you discover such an error.
We measure your ability to get the right answer, but it is for practical reasons (to guide your learning, to know how best to deploy you, and how much checking we need to do). It is not a judgement of your worth as a human being, only as a future cog in the machine. But I would much rather employ somebody who gets it right 90% of the time and put their hand up to all their errors than somebody who gets it right 99% of the time but tries to cover up or otherwise dodge the consequences of their mistakes.
So, to the question in hand, I think it's certainly arguable that a 2.5% error is probably lost in the noise, and not worth the hassle and upset of changing everybody's grades. I wouldn't have a problem if that was the reason. But I would want to tell the students - first, because some might be misled and their education sabotaged if the answer they thought was right is wrong or vice versa, and second, because it is an excellent lesson-by-example of putting your own hand up to a mistake, and seeking out the best way of correcting it. And I would want to get the student's buy-in to whatever is done, because it's their education, their grade, and their academic integrity at issue. They don't need to be told they've just lost a point (or not), they need to understand the reason why, and to agree with it. And if they understand why, and agree, and are taking more pride in their integrity and honesty than they are in getting high grades, then they won't mind losing the point, because it's fair and the truth. You will also be treating as adults, letting them make the choice, which is the best way to get them to act like adults.
That's just my view, though. And I'm well aware that my attitude has frequently put my job at risk and probably hurt my career. There are lots of businesses and bosses (and their legal departments) out there that do not appreciate forthright openness about errors and much prefer to forgive and forget and cover things up. They like people who fit in with the more usual social attitude. There is a price to be paid for academic integrity, and students should be aware of that too.
