How to deal with a professor who grades assignments and exams incorrectly I currently have a (graduate) professor who clearly does not understand the material she teaches at the level required by the course. This normally would not be a problem - I'm fine with educating myself via textbook - but unfortunately her inaccurate knowledge also extends to grading. I have no problem with studying hard for a difficult class, but I can't possibly know how to predict the exact incorrect ideas that the professor has and incorporate them into my work.

My first response was to very, verrrrry diplomatically approach the professor and talk to her about the questions - but she immediately became angry. I then talked to my advisor, who said that this isn't the first time she's heard of problems with this teacher. My advisor said that her only idea is for me to go to the head of the department, but I'd really prefer not to do this for two reasons:


Relatively small department; it's likely that this professor has
a good relationship with the department head, and I would look bad
It seems like a "nuclear option" and I would prefer to avoid it
(if possible)


This is my last semester of graduate coursework in molecular biology, and I have never had a problem like this before. I feel like my only option is to drop the course - without it, I would still have all my coursework requirements fulfilled - but I don't want to have a W on my transcript. 

I have been unable to come up with a satisfactory way to resolve the problem.

Possibly helpful additional information


I have talked to other students in the class; all (of the six I have talked to about the issue) have experienced similar problems in grading
I have confirmation from other teachers that my answers are correct, but they don't want to confront a colleague (and I can't fault them for this)
I don't dislike the teacher; she seems like a relatively OK person. I just wish she understood the content better
The teacher can't possibly have a grudge against me, since I had never met her before the class
I'm  very interested in what this class covers, which is why I took it despite not needing to
I have taught some of this material at the undergraduate and graduate level; I understand it's difficult stuff. It's more the teacher's attitude towards grading that is the problem.
Not a definitive answer, since I’m a postdoc with comparatively limited experience of such conflict situations, but I do have a few suggestions.  They aim to:


maximise the chance of getting better grading without ruffling too many feathers;
give you solid documentation if you do end up escalating the complaint;
minimise the embarrassment in case it turns out that you’re misunderstanding something and your lecturer’s grading is defensible after all.  


If you confront the teacher again, do so by email rather than in person.  This has several advantages.  Firstly, it allows you to look over what you’ve written and make sure you’re phrasing everything as tactfully as possible.  Secondly, it gives her time to (hopefully) get over any initial anger/embarrassment and give a considered response.  Confronted on a sensitive topic in person, it’s easy to get flustered and defensive, and entrenched in a position it’s difficult to climb down from later.  Finally, if she doesn’t respond constructively, you have the exchange in writing, so are on firmer ground for escalating the issue to the department head.

If possible, phrase the question/request so that your desired outcome is also palatable for her.  If you argue that she’s fundamentally misunderstanding the course material, she’s pretty unlikely to accept that — admitting that one’s wrong about something is already difficult, admitting one’s incompetent is a whole lot harder again. Instead, you could say that (e.g.) you have learned some of the material previously, and so know it with a different viewpoint from hers (and maybe give a couple of examples here, ideally with sources in well-established literature) and you would like to check that this angle will also be acceptable for work on the course.  I’m not saying you should say exactly that — but look for something that allows her to concede that your understanding is correct, without having to admit (to you or herself) that hers is wrong; and down the line this makes it easier for her to improve her understanding of the subject, rather than remaining antagonistic towards your suggestions.  On the other hand, if she does defend her current approach, this gives her a chance to lay out her case more clearly and carefully.

If you do this and she still doesn’t engage constructively, you’re now on very solid ground to escalate the complaint.  You have a written record of your good-faith effort to sort this out tactfully.  You have specific examples where she has doubled down on her misunderstanding of the material.  (I’d suggest double-checking these with your advisor or another faculty member to be absolutely sure you’re right about them.)  Even if the head of department supports this teacher in general, it will be comparatively difficult for them to dismiss the complaint or paint you as a troublemaker.