Should "extra credit" questions allow students to get more than 100% of the marks? This semester I am teaching a course.
Due to the fact that the students differ in their abilities,
I decided to create a few "extra credit" questions
for some of the assignments
to stretch the thinking of the more capable students.
However, at the same time,
I don't want to stress the less capable students
and make them feel that they need to solve problems that are difficult,
but not so essential to getting an adequate mastery of the material.

Unfortunately, I am not sure how to compute the scores
for assignments with extra credit.
Suppose the assignment has 100 marks, with 10 marks extra credit.
Suppose a student completes all of the regular questions
as well as the extra credit questions correctly.


Do I give this student 110 marks for the assignment?
Or do I cap the max score of the student at 100 marks?
My experience with American grading systems has been that the extra credit typically means an effective higher percentage is possible, i.e., 100% + 10% extra credit = 110% max on the assignment.  And if a student gets 110%, then that's what they get on the assignment, and great for them!

Most students will balance extra credit with mistakes elsewhere, meaning that extra credit effectively ends up acting as "forgiveness" for mistakes.  Usually, however, the students getting a lot of extra credit don't need as much forgiveness as the ones who don't, so I actually don't think that extra credit shouldn't be thought about as really being about grades.

Instead, I think it is important to view extra credit questions as places where the instructor encourages engaged students to additional exploration of the course material. The extra marks are then just a means of acknowledging that exploration within the formal incentive system of the course.

Given this, and the fact that some unusually excellent students could end up with more than a 100% overall, I would only recommend that all the rest of the students still be graded as though 100% were the maximum in the class. That way, a student going above and beyond gets acknowledgement, but other students are not affected negatively by that fact.