Dtyjlui

At U.S. top schools, recommendation letters are more important than grades.

If your professor knows you well and has a truly positive opinion of you, this will come out in the recommendation letter. The best thing you can do for yourself cultivate a real relationship with the professor (e.g. by visiting office hours, talking about ideas beyond the syllabus of your class etc). If you can talk about your goals for doing original research, so much the better.

As an aside, perfect grades aren't a very strong signal for who will be a good PhD researcher, so I really wouldn't worry about the grades very much anyway. A person who is curious and pushes themselves beyond their comfort zone -- even at the risk of getting some bad grades -- is a much better PhD admit than someone who has always gotten perfect grades.

If you asked me for the points and the letter, i would give you the points and reflect my irritation with you in your letter.

Here is my two-part opinion.

First, it would be a breach of professional ethics if a professor let the quality of their letter of recommendation depend upon whether students questioned their grading judgments. (I know for a fact that I have made grading mistakes, and I have come to terms with the fact that I need to receive all requests for reconsideration, even though the majority of them are misguided, to allow the students to have my back on the not infrequent occasions they are correct.) I know this is a statement of ideals, while you are asking about what happens in practice; for that I would guess that your cordial interactions will be remembered far more than the content of your query.

Second, I still think you should let the issue go, for the following reason that is unrelated to the letter of recommendation. You had an opportunity to present an argument about how the grading scheme was applied to your work; you did so; and the grade was confirmed. Perhaps this is a learning experience that one should take the time to formulate the best argument possible the first time around, if you think you didn't do so. But the fact that you now think you could have presented a better argument is, in my opinion, not relevant: you had a chance, and you did the best you could—none of us are perfect.

As a professor, I encourage you to reframe your thoughts: you didn't "miss just enough points to change [your] grade from an A+ to an A"; rather, you earned enough points to rise to an A but not quite enough to rise to an A+. It's amazing how this one detail can result in a huge shift in perspective.

--- Comment by Greg Martin

This comment by Greg Martin
is so good, and so important here, that I want to highlight it here as an answer, and make some broader points about this type of situation. This is somewhat tangential to your specific question, but I will come around to the connection with your question at the end; so please bear with me.

In university-level teaching, it is very common to encounter intelligent ambitious students who have got high grades throughout their schooling and are used to performing at a very high level. Some unfortunately adopt an annoying way of framing their work, where they speak in a way that sets 100% success as the implicit default position, and any derogation from this constitutes "missing out" on points. This is a somewhat natural way that elite students come to speak of these things, since they have always obtained high grades throughout their schooling, and they are sufficiently talented to realistically shoot for 100% on a piece of assessment. In these cases it is somewhat natural for these elite students to frame things as "missing out" on this mark or that mark, since their focus is in weeding out remaining errors in otherwise high-level work. Unfortunately, over time, these students get sloppy with the way they talk about learning, and their language reflects the implicit view that perfect knowledge is the default position for them, and anything less than perfect performance constitutes some aberration, often in need of arguments over grades.

The other thing that is common to encounter in elite students is an implicit reversal of the relationship between learning and grades --- the elite student often considers the formal grade to be of paramount importance, and the learning as a method to increase grades. In reality, learning is of primary importance, and formal grades are merely an imperfect tool to assess the degree of success in that learning. In extreme cases, one occasionally encounters intelligent students who are so concerned with their grades that they allow opportunities for self-reflection and learning to bypass them entirely. Most university lecturers have had at least some experience of a situation where they attempt to impart some broad lesson to the student during a discussion over grades (e.g., pointing out some broad deficiency in their work that is a "soft-skill", which is not easy to quantify), where the student shows no interest in learning from that situation, but is only interested in arguing for a higher mark.

These kinds of attitudes constitute deficiencies in understanding the process of education and assessment; they reverses the true nature of what is going on. For ambitious and intelligent students this generally do not hamper learning too much so long as that learning is done in the confines of a formal course with a fixed scope and assessment structure, and with formal assessment of grades. However, once you come out of that environment, into situations without formal grading, these attitudes tend to stunt learning.

Most PhD programs are focussed primarily on training a student to be able to conduct independent scholarly research. They require students that are proactive in learning, and are hungry for knowledge and improvement outside of their formal courses. Some PhD programs have courses in the early years and others don't have any courses. If coursework is required then you're expected to get good grades in these, but they are merely considered as preparatory work for the real meat of the program --- the main focus of the program is on your ability to learn outside your courses, and to be able to advance your research work under supervision, without getting marks as feedback. Hence, when writing a letter of recommendation for a PhD program, a professor will assess your subject-matter knowledge, as reflected in your grades, but he will also try to assess your ability and willingness to learn independently beyond your formal coursework. If your focus is on making arguments to advance your own grades, to the detriment of self-reflection on your own performance, and opportunities for broader learning, this bodes poorly for your ability to succeed in a graduate research environment, where grades in courses are secondary, and self-driven learning is primary.

I mention these things because they are the background to assessments of a student's ability to engage in self-learning in graduate school. I'm certainly not saying that you have these deficiencies, but please bear in mind that your professor has probably encountered some students with these deficiencies before, and he is trying to figure out if you possess any of these problems yourself. You say in your question that you already made the case for a higher grade and you received an explanation for your marks. Ideally, that would assist you to reflect on how you can improve your work --- not improve your grades, but your work. Anything that reflects a willingness to self-reflect and improve your own work is going to reflect well on you in a letter of recommendation. Anything that reflects an attitude of focus only on formal grades, and a resistance to self-reflection will come out poorly.

I personally would let it go. Most of the time people (this does mainly depend on personality) think they're right and if you attack (i.e. challenge their views) them they get extremely defensive and unresponsive. If you are going to argue in favor of those extra points make the professor himself admit they are wrong; without you outright saying it. Perhaps explain the benefits of those extra points to him? Anyways that's my 2 cents.

There should be an appeal process, that bypasses / escalates beyond the professor's purview. If you successfully make the appeal, you may be able to get a recommendation letter from one of the board members rather than the professor whose judgment (or that of his TA) was found wanting.

Alternatively, you could take the course again with a different professor or opt for a different elective.

You are obviously between a rock and a hard place. Write your own assessment of the professor in ratemyprofessors.com to allow other students to decide whether they want to risk their careers by taking a class given by that professor, eat your losses, and then move on.