I'll try to keep this as short as possible, but feel free to ask any questions that would help paint a better picture of the situation. I'll be a bit vague with specifics, so bear with me.

Last week, I got a grade back on an exam I felt OK about. I knew I had screwed one problem up & was really fuzzy on another, but was expecting somewhere in the mid 70s. I got the exam back...and it was a 50, ouch.

After reviewing the questions, I missed the one I knew I missed entirely & a few mistakes on other problems. All of these mistakes would've put me at a 66. Definitely wasn't happy about that, but they were entirely due to my error.

That leaves 16 points (2 letter grades worth in this class). Where did this come from? One problem, we were asked to show a graphical comparison of two concepts & specify which was the better process. I (correctly) specified the process & (correctly) drew a graph straight from the book that illustrated this comparison. I only got 4/10 points due to not having a textual explanation, along with the graphical one. The problem statement literally only said "Graphically explain your answer".

The second one where I got 10/20 points, I had the question correctly answered & a large portion of the work shown. However, I didn't write down a few steps because: 1) It was an extremely simple equation to remember, literally just 3 terms & 2) It was 3 short steps that could be (and were in my case) done in your head. I got half the credit taken from the problem because I did not show these simple steps, when I clearly demonstrated I knew the concept the question was asking about, wrote out nearly every step, & got the correct answer.

~`~

So, I went & spoke to her today about these issues. She completely disagreed with me (and the dictionary) about what a "graphical explanation" is. Her argument was, "Have you ever seen a published paper that only had a graph without an accompanying text-based explanation?" Well, for one, I have, but that's not really the point. A single question on a long exam can't exactly be held up to "publishing standards". My issue with that answer was that whether or not she wanted a further explanation, she didn't ask for one. I wasn't going to spend 5 of the 55 minutes writing out a 2 paragraph explanation if it wasn't explicitly asked for. The only explanation asked for was a graphical one, which was readily provided.

For the second question, she said she won't give credit for not showing all of the steps. So, even though it was extremely apparent I knew what I was doing, because I didn't write out each of those small steps, half of the credit was taken. Basically, out of a 14 step problem, I wrote out steps 1-5, did 5-7 in my head, then started back writing at 8. I would understand taking off a large part of the credit if I made a massive leap from 1 to 8 to 14, but 2 steps that were very basic math that is easily done in your head should not account for half of the credit.

But the two biggest things that irked me: When I pulled out my exam & asked her about the first problem, she compared it to her answer key, said "Huh, I should've given you more points for that"....then didn't mention that fact again. The second thing is that on the second problem, she said not showing the work was only part of the reason I got so many points deducted. The other part was I started with the complete wrong equation. She then went into trying to show me why it was wrong by doing a unit analysis & deriving it from another equation. It started to get jumbled on her paper to the point I couldn't follow along. I told her I thought I had got that equation from her notes, but I must have remembered it wrong.

Turns out I got it 100% right. It's the exact equation from her notes, sign for sign, variable for variable. I didn't understand how I could have got the correct answers if I had started with the wrong equation from the start. I'm really starting to think she simply has it out for me after all of this & I have no idea what to do. Any suggestions would be very much appreciated. As a side note, I have this whole conversation recorded. So I'm not mis-remembering certain things she said, I just re-listened to the entire thing.

TL;DR: Professor takes multiple points off of exam unfairly. Admits she should have given me more after comparing it to her answer key. Tells me I missed points because I used the wrong equation (when I didn't). Took off points for not answering part of a question she didn't ask.... What do I do at this point?