I started grading homeworks in fall 2019 to earn some extra money and because I had some extra time. Since then I’ve graded for Math 113 for three semesters and Math 53 for one semester (over the summer). Over this time I’ve learned some tips I’d like to share, because I would have liked to learn these things earlier myself.

1. The types of problem sets that get assigned for Math 113 actually have varied quite a bit between professors. That is, some professors are more difficult than others. It is very worthwhile to do your research on the professors before enrolling. I’m sure most of you know that, but having a side by side comparison of four (including the semester I took it myself) Math 113 professors is striking and it can be a completely different class depending on who you have. If you can, choose a professor that aligns with your learning; some assign many easy problems and some assign only a few nontrivial problems every week. Most of them leave their course webpages up after the semester ends so it’s not hard to check.
2. If you are using Latex and you’re not comfortable with it, it can show. If the professor allows it, I’d rather grade work that the students were confident writing. Oftentimes I see people writing stilted answers in Latex because it’s more formal. If you can’t include your work, and you don’t describe it thoroughly enough, then it’s not a better format.
3. Don’t be afraid to take up space. It isn’t better to have all your answers on one page. It can be difficult to find the problem I’m looking for in a wall of text, and if I’m grading a hard copy, there’s no room to leave comments. I also have found that when I limit my own space I’m less inclined to show my work, which means I’m less likely to get full credit.
4. Sometimes things in proofs seem obvious and it feels like you shouldn’t have to say them. Say them anyway. A great example of this: every semester of 113 there are questions asking to prove a set is a group under some operation. Every semester a nontrivial number of people doesn’t prove the identity is in the set. Every semester a nontrivial number of people lose points for this. They reply that the identity is implied by the other group conditions, but in fact without proving the inclusion of the identity the set could be empty. It’s not always apparent why obvious things are important but it’s worth it to include them.
5. Symbols are great, but writing your reasoning out alongside them is even better! If I’m looking at a proof that only uses symbols and there’s a mistake in it, it’s harder to give partial credit than if there’s a correct written explanation alongside it. I also find that it’s easier to study from my past homeworks that way.
6. If you’re in the type of section that has nontrivial problems, it’s likely you’ll get stuck at some point. If you can’t think of anything, still write down facts or theorems that seem relevant, and a sentence or two about the problem and what you need to show. If I can give partial credit for some portion of a correct approach, I will. It can also help to get you thinking, and it makes it easier to come back to or study from.
7. A lot of the time I’ve seen a decline in the number of submissions over the semester. That’s fair, we’re all busy! But instead of submitting nothing, even if you’ve only done one problem, submit it! You might get lucky and that’s one of the ones getting spot graded, and something is better than nothing!
8. Alternatively, ask for an extension. I never wanted to do this because I felt bad about it, but after grading I can see that plenty of people do, and professors generally give them! Especially in times like these.
9. Ask for regrades. We aren’t machines and sometimes we miss things. If you feel like you’re right, odds are you are.

I hope this was helpful! I remember upper division problem sets giving me a lot of trouble in the beginning, so my final tip is to not give up! They’re always tricky but you get the hang of it, and after a while you see how to prove things faster. Best of luck!