Students' work works for teachers, too
Giving assessments and feedback is always a challenging part of interacting with students, and we're tasked in our feedback with giving an amount of help that's appropriate but that also still lets the student struggle productively. It's also important to consider the context of our feedback! The feedback I give a student on a test is different than the feedback I'd give them on a quiz or on a group activity.
Here's a scan of some feedback I gave a student on a take-home quiz. On quizzes, I like to point students in the right direction, and give them a little more thorough feedback than I would on a test, but I also feel like it's important to give students the room to figure out their mistakes for themselves.
I think, as with feedback and just generally assessing and analyzing student work, too, it's important to take into consideration that students are constantly learning and that mistakes in their work are normal. We wouldn't want students to complete work perfectly on their first try, nor should we expect them to. For that reason, like I did on the quiz, I try to grade and give feedback holistically. It's important to look for student understanding in their work instead of just their correctness, especially on something like a quiz. In problem 2, for example, the student whose quiz I graded didn't get the answer right, but I was able to recognize from their work that they knew what "lateral area" was. That, in itself, indicates a familiarity with the surface area/volume "ecosystem" and indicates to me that, even though they didn't get the question totally wrong, they still deserve some credit for their work.
In all, we have to think about growth and we have to be flexible with our grading. Math is often seen as the "right or wrong" subject, but that's not the full picture! Let's be flexible, human-driven, and focused on growth in our feedback and in our analysis of student learning.