- Don't grade by going through each paper in its entirety before moving onto the next. Instead, go through all the papers marking only the first problem on each. Then give them a shuffle, go back to the top of the stack, and go through question 2 on all of them (and so on). Only add up the points at the very end. This does two things: it helps ensure you grade each question in a consistent manner for everyone, and it prevents a student's performance on the previous questions from unconsciously biasing how generous you are on later questions. If you will be working with other graders to mark the same set of assignments, this is generally how you have to do it anyways to ensure fairness.
- Try to avoid looking at the student's name when marking the paper. You can have the most egalitarian views in the world on gender, race, and culture, but biases still have a way of creeping into how much we are willing to give different people the benefit of the doubt—even if you're not aware of it. Ideally, names on assignments should be written separately on a cover page that can be folded back on every paper before starting to grade. If this is not the policy of the class you are marking, just do the best with what you have.
- If you are required to produce your own solutions to the assignments you grade, don't be embarrassed to ask for help from the professor or other graders if you find yourself stuck. It's obviously essential that your solution set be accurate, and everyone needs help now and then even on things they know well.