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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.

  1. Do I give this student 110 marks for the assignment?
  2. Or do I cap the max score of the student at 100 marks?
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    In my experience, the undergrads would riot if you didn’t give them the extra marks they felt they deserved. – Thomas Jan 18 '18 at 6:42
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    This, to me, means the grading scheme is not balanced well : I try to set questions that an "average" student will score 65-75, then a "good" student scores 76-85, an "excellent" student scores 86-95 and a student who is exceptional can score 100. This means that one or more questions can be "easy", some more challenging and one, maybe two, are really challenging. This, for me, avoids having to deal with trying to give 110%, especially in an academic records system that will not accept more than 100%. – Solar Mike Jan 18 '18 at 8:09
  • One possibly way around your situation is to "curve" the results - ie those who got 110 get 100, those who got 100 get 90 etc - the actual multiplier is 0.9090909... – Solar Mike Jan 18 '18 at 8:12
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    @SolarMike: strong disagree - the whole point of making that question extra credit was to curve the results in the other direction: OP feels that answering 90.9% of the questions is enough to merit a 100. – nengel Jan 18 '18 at 11:35
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    I was an "excellent" student most of the time, competing for top grade with the other very high performer. Our teacher curved the grades to the average, and once I did end up with a 23/20. But for a short time, we had an "exceptional" student added to this class, and on the same curve he obtained a 40/20. With your suggestion, us "excellent" students would have barely scraped a 50%, and everyone else would have failed. Just because that one student was so good. Or the teacher could not have added extra credit questions for him, and he would have been bored as hell. Neither option sounds good. – nengel Jan 18 '18 at 11:43
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The policy that I have used on extra credit problems is that they allow students to "earn back" points they have lost (or will lose) in that particular category. For example, suppose I had four homework assignments worth 50 points each, and the last assignment had a 10-point extra credit assignment. Suppose my students got the following grades:

 Anna      Elsa
-----     -----
30/50     50/50
40/50     50/50
40/50     45/50
60/50     60/50

Then when I calculated the students' final grades, Anna would get 170/200 = 85%, while Elsa would get 200/200 = 100%. Elsa "earned" 205 points in all her homework assignments, but I cap the category at 100%. This is basically for the reasons stated by nengel, but applied at the level of the grading categories (homework, labs, tests, etc.) rather than at the level of individual assignments.

This system works best when you have a large number of similar assignments over the course of the semester, for which the work necessary for each assignment is well-correlated with its point value. In my case, these assignments are usually problem sets with something like 10 points per problem, so that fits the bill.

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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.

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It only makes a difference on a combination of multiple assignments. If you grade on a single exam, presumably you can't give them more than an A in the class. Effectively, giving a 110% then means they can make up a lower grade on a different assignment, while capping at 100% means they have to show mastery on each assignment (presumably on a different topic each) to get the top grade. So I would choose based on how important you think it is to show consistency in this course.

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It's perfectly fine to have grades above 100%, and I do that myself. So I recommend that you do whatever is logistically easier for you. For example, it's probably an extra step for you to calculate a minimum function min(score, 100) when computing grades, so feel free to skip that. Likewise, the common learning management system will compute grades above 100% in the case of extra credit, without any obvious way to set a ceiling on the total, so it's most straightforward to just let it do the same thing.

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