I find it extremely time consuming to grade a homework in an undergraduate real analysis course without a rubric. Several instructors I worked with did not have a clear rubric in their mind at all. Instead, they usually just want "as much feedback (for the students) as possible".

Here are my questions:

1. What would be a reasonable amount of time (in terms of hours per week) for grading homework for a TA in graduate school? (How much time would be a sign of "too much"?)
2. For grading a homework in undergraduate level real analysis (or complex analysis), what would be a good rubric?

[P.S. I'm talking about universities in the US.]

The size of the class is around 25 people. A particular homework problem set is like the following

6.2.1, 6.2.2, 6.2.3, 6.3.3, 6.3.5, 6.4.2, 6.4.3 in Abbott's Understanding Analysis

• Your link to "Understand Analysis" gives no information about what you are citing to those who do not have access to MathSciNet. It would be more useful to link to the amazon.com or WorldCat page for the book. Feb 3 '16 at 16:54
• @DaveLRenfro: Thanks a lot. I edited it accordingly.
– user5897
Feb 3 '16 at 18:23

Many departments have a set of expectations for the amount of time a graduate student TA should be spending grading per week. It varies from place to place, but you should find out if your department has a clear set of guidelines and, if so, respectfully ask the instructor that he agree to follow them. I personally think 3 hours per week per course TAed is not unreasonable (and I've heard of higher), though I personally try to lessen my TAs grading responsibilities when possible.

There are arguments for and against a rubric, largely dependent on how much experience you have with grading. I personally do not think a predesigned rubric is optimal in such a course, but rather that you should make a rough plan of how you expect to grade each problem, and then make specific notes for how you handled specific errors as you go along (so you can deduct the same amount if the same or a very similar error appears in someone else's work).

One solution that your instructor might agree to is to come to a predetermined amount of time that you should spend each week grading problems, and have you grade as many different problems as you can within that time constraint, perhaps with some feedback as to which problems absolutely must be graded and/or which problems are relatively easily sacrificed.

In my department, homework graders are hired for a specific number of hours. I usually assign more homework than the grader can grade in the allotted time, so I give the grader a prioritized list of problems, from most important to least important. I tell the grader to begin grading with the most important problems and work down the list as far as his/her time allows.

In many (though not all) of my classes, I give relatively little weight to homework grades (compared to exams). For these classes, I ask the graders to grade on the basis of two points per problem (rather than the ten points that many people are used to). That way, the grader doesn't need to worry about detailed assignment of partial credit.

I write up detailed solutions to homework and exam questions, and (at least rough) breakdown of grade assignment. Solving the question helps convincing yourself that the problem is solvable within the allotted time, and helps keeping consistency when grading. Publishing solutions allows students to compare their work with a correct solution, and in theory learn from their mistakes (in practice, they only look if their grades are too low for passing, but there isn't much to be done about that).

Personally, I've found that writing a rubric a priori to be a nightmare once answers move into the realm of proofs and such--there always seems to be an incorrect answer that ticks off parts of the rubric it shouldn't really deserve. My preferred method is somewhat similar to how I was once taught to grade essays: sort the responses into stacks that correspond to the quality of the answer. For example, I might make stacks of

• Completely correct, good notation throughout
• Almost correct (perhaps a notation or arithmetic error)
• Correct approach, but some structural errors (failed to address a minor case, etc)
• General gist, but flawed argument
• Deeply flawed argument, wouldn't be correct without major revisions
• lost in the woods / no clue / can't follow

and then assign points / letter grades to each stack. Alternatively, I think of making stacks of A/B/C/D/F level work, without exactly quibbling about why something ended up in the specific stack (should have been 2$\epsilon$ instead of 3$\epsilon$ or whatever). Plus, it just makes me feel like Robert Pirsig in Zen and the Art of Motorcycle Maintenance. This approach also keeps me from getting stuck in sweating weather an answer deserves 7.6 or 7.595 points according to a rubric. If necessary, you also have all of the "A" level answers next to each other if you want to justify why one answer might be 10 points while another is 9.5 points if you want to further refine the grading.

I haven't taught real analysis, but I've taught plenty of proof-based courses, such as linear algebra, topology, differential geometry etc. After 10 years of teaching, I find that the simplest grading scheme is always the best. If everything is correct, then give the student the full score. If something is wrong, it should be 0. It's the only way to keep grading fair and consistent across a large class with many tutors.

I imagine that some students will no be happy if the grading scheme is so strict. There are two ways to work around it by giving them a room for an error: 1. Let's say that an assignment has 6 questions, each worth 10 points and let's say that G is the sum of scores for individual questions. Then the grade for the whole assignment is min(40, G) instead of G, i.e., students who solve 4 or more problems out of 6 completely get the full score for the assignment. 2. You let them resubmit if they made a mistake. Let's say that they have one chance to resubmit if it's a handwritten paper and unlimited attempts if it is a shared online document.