# What is the best way to assign letter grades in a math class?

Here's the most common way that I've seen letter grades assigned in undergrad math courses. At the end of the semester, the professor: 1) computes the raw score (based on homework, quizzes, and tests) for each student; 2) writes down all the raw scores in order; 3) somewhat arbitrarily clusters the scores into groups corresponding to grades of A, B, C, etc.

There are a few problems with this approach though. One might object that the assignment of letter grades is too arbitrary. Students also might object that they don't know in advance what grade they are likely to get in the course.

On the other hand, it's difficult to assign letter grades in a less arbitrary manner. For example, if we declare in advance that a score of 80-90 on an exam corresponds to a B, we might find that the exam was too difficult and that scores on the exam were lower than expected.

What do you think is the best approach to assigning letter grades in an undergraduate math course?

• This may be more appropriate for SE Academia. Search there for "grade scale" and you'll find numerous prior questions on the topic (almost all of them motivated by math courses). – Daniel R. Collins Aug 16 '18 at 15:09
• The answer may depend on what you are using the grades for. Are you using grades to signal mastery (or progress towards same), or are you merely using grades to order students into a curve? – shoover Aug 16 '18 at 21:46
• I think that grading on a curve is a bad practice that shows that a teacher does not have a specific criteria for passing. If the exam was too difficult, this should be the students' fault, not the teacher's, who might have been clueless enough to administer a test from a higher-level course and now covers his butt with a curve. Know what you teach, know what you consider a sufficient amount of knowledge and skills to pass, and grade accordingly. If all fail, all get F. If all succeed, all get A. Curve fosters animosity between the students, because one's success depends of others' failure. – Rusty Core Aug 20 '18 at 16:50
• This question assumes the US context, and that should be indicated. The grading scheme described in the post would be against the rules (possibly even legally actionable) where I work (Spain) because the rules require publishing, before the course begins, a scheme (approved by the department) for determining the grade of a student. The professor is expected to evaluate students in a way that conforms with the scheme. Exams that are "too hard" or "too easy" are understood as a failure by the professor to write an appropriate exam. – Dan Fox Aug 21 '18 at 8:15
• I am also required (in the U.S.) to state my grading criteria in my syllabus at the beginning of the semester. – Sue VanHattum Aug 22 '18 at 2:58

What I do is a blend of the two methods that you describe. At the beginning of the course I give students the strictest grading scale that I might possibly use (a standard 90-80-70 scale). At the end of the term, I reserve the right to lower the scale as needed. In this way, any deviations from the stated scale are in the student's favor but I can account for overall difficulty of the class.

As @shoover hints at in their comment, the question assumes that you've already answered the question of why you are assigning letter grades at all. Assuming the answer to that is something along the lines of "because I have no choice" or "that's just how it's done", here's how I approach it. (Perhaps useful info: my college has a brief description of what letter grades should mean across disciplines. For example, a B is an indicator that the student is ready---and encouraged---to pursue further studies in the discipline.)

I don't use numbers at all any more, and grade assignments like (I assume) my colleagues in the humanities do. Does the work demonstrate mastery of the material? Put an A on it. Is it littered with errors, both small and large, but with evidence of a reasonable amount of understanding of the basics? C. Of course, there's written feedback on individual errors/questions and the assignment/exam as a whole as well. This written feedback should, and usually does, correlate with the grade.

Course grades are then compiled from these individual grades in some somewhat arbitrary but pre-defined and known way. (Best 6 assignments from 8 count 60% and the final exam counts 40%, or whatever.) I also reserve the right to move a student's grade up or down by upto one letter based on promptness of submission and class participation and whatever other sundries pop up during the semester. (This is much more often a boon for doing something not explicitly assigned credit rather than a dock.)

In my experience, this bypasses a lot of the concerns that seem to have driven the question.

[Bonus anecdote; related but not strictly part of an answer: I studied and then taught a little in the UK in places where 70ish earned an A and a passing mark was around 40. I moved to the US and started teaching without knowing about the usual US system. In my first Calc 1 assignment my students did well with some tough (in context) questions and most scored between 60 and 80 (so, I thought, at least a B- and some really strong As). They were not happy. This is part of what prompted the switch to my current system, but I like it regardless of its origin.]

• Why didn't you learn what typical US practice was before your first test? (I think a lot of the high IQ crowd here has a blind spot when in new situations. Assuming that "what I did" is what everone does. Hear it all the time in the Q&A.) – guest Aug 18 '18 at 16:45
• <shrug> I moved from a big research uni to a tiny liberal arts college and this was in the first week of teaching (my second in the country). I did plenty of prep to cover the change but this slipped through the cracks. One little mistake like this is not bad going, I'd say. (Not that I'm claiming to have got everything else right.) – Matt Ollis Aug 18 '18 at 17:14
• OK. Glad you did some general prep. [Keep a curious attitude and don't assume you have it all, based on previous background...can make gaps pedagogically.] – guest Aug 18 '18 at 17:40
• I'm glad you're glad, anonymous internet person. Thanks for the fortune cookie. – Matt Ollis Aug 18 '18 at 19:20
• You could have been more ready, but you had a blind spot because you were too quick to assume your limited personal experience was universal. – guest Aug 18 '18 at 23:46

60 D 70 C 80 B 90 A

IF you are familiar with the course, you should be able to set appropriate difficulty tests. If you are less familiar, than sneak in easy test (or hard one) if you think you need to correct a little for scores being out of whack halfway through. but even then try to have some personal guess on if the issue is your previous testing being off or just student performance being different.

Nothing is perfect. So don't sweat it so much.