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This fall, I'll be a reader (i.e. homework grader) for the first time, and the course is a second-level linear algebra course, which is likely the first proof-based course most of the students will experience. Most students will be in a math major (more applied than pure) but some will be from other STEM areas. Points will be awarded based on rubrics, but I feel like additional feedback is especially important and formative for a first proof course.

Unlike grading as a TA, I won't be able to communicate with students outside of writing notes on their solutions, and students will not be allowed to contact me directly (they must go through the TA to ask for regrade requests, etc.). If I could talk the students, I'd be able to get their feedback and adjust as I go, but this will not be possible for me as a reader. What are some general best practices for grading and giving feedback in a way that lets students have a good experience?

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    $\begingroup$ Since this is during covid, I assume the process will be electronic. Is there any kind of software setup that your school is using? $\endgroup$ – Ben Crowell Aug 29 at 12:37
  • $\begingroup$ We are using Gradescope currently. But when classes return in-person (in a year or whenever), I expect to continue doing this, and students will hand in homework by paper then. So, general advice is appreciated. $\endgroup$ – yadec Aug 29 at 14:32
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    $\begingroup$ As a first thought (I just read your question a few moments ago), I know some students dislike things like "vague" or "incomplete" written (and not much else) along with $-3$ or $-5$ points taken off. On the other hand, providing even moderately detailed justifications for points counted off will take a huge amount of time. It occurs to me that you might want to jot down some of the common errors/oversights that you see while you are grading, and then formally write these up to return to all the students (as examples of what is "vague", "incomplete", etc.). In fact, I've seen this done often. $\endgroup$ – Dave L Renfro Aug 29 at 18:10
  • $\begingroup$ I agree with Dave's advice, except that I would submit those notes to the TA and let them decide whether to blast it out to the students or incorporate it into instruction in another way. $\endgroup$ – Matthew Daly Sep 1 at 5:22
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    $\begingroup$ Such an amazing experience: being taught by TA, having homework graded by someone even the TA may not know, while the prof doing ever important research. $\endgroup$ – Rusty Core Sep 1 at 20:19
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My advice: grade them according to the rubric. Leave instruction and feedback to the TA. You have already been told that is the agreed method. Don't circumvent it with long notes. Just do your job and follow the plan.

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