What would a good written policy for scaling exam grades look like?

Question

I'm not in the habit of scaling exams, although I'm aware that the practice is widespread and highly recommended in some circles (such as grading on a curve). To my recollection, none of my college instructors scaled exams or wrote any policy about such on their syllabi. I'm wondering if one did commit to an official policy of scaling exams, what would a reasonable written policy look like?

The goal here would (hypothetically) be similar to Krantz in How to Teach Mathematics (Sec. 2.10): "My main goal in formulating my grading policies is to make the greatest number of students feel that they have been treated fairly (and, not incidentally, to reduce student complaints)." Secondarily (and again hypothetically), to defend against possible future administrative complaints that the instructor is not matching some recommended grade proportions (same section by Krantz).

Please assume that the individual exams are adequately fair assessments themselves (not broken, vague, or overly-hard questions, cover same topics covered in class and homeworks, sufficient time permitted, significant advance time taken assessing questions and grading rubric, etc.).

Background: I'm at an open-admissions community college where high failure rates are historically common, often half or more of many math or computing courses. Among the things I'm worried about if I started doing that are: Would there be any lower bound to what might wind up being passing work?

For example, I had a colleague at a different university (top-20 in U.S.) who got in trouble a number of years ago in that, when pressed by students on his scaling policy, said that if every single student got a zero on a exam, then the scaling process would turn all of them into 100% marks. Surprisingly, the students successfully organized a total boycott of the final exam, and my friend followed through and gave 100% marks to everyone as per his word. (This turned out to be quite embarrassing for him.)

So I'm wondering what kind of formal, mechanical policy for scaling would prevent no-lower-bound situations similar to this one?

Answer 1

Scaling or "curving" grades so that a fixed proportion of students get each grade is unethical. There is extensive evidence that student cooperation helps students learn more. If you fix the proportion of students that get each grade, then you incentivize students to stop cooperating. This will reduce how much your students learn.

@PatriciaShanahan is right that this grading approach is also incorrect because your student body does not remain the same across semesters.

Answer 2

In general scaling is a mistake as it introduces uncertainty into the student's calculations. But some adjustments are proper and you can publish statements about them.

First, you can agree that no one will "miss" the next grade by a small percentage. This is better done overall, than on a per exam/paper basis. But if it takes 90% (overall) to get an "A", then, at the end of the day give the A to someone with 89. This merely recognizes that your grading scheme isn't perfect and may disadvantage people in small ways occasionally.

Second, agree that your grading rubric is clear that you are allowed to adjust upward when you think it justified. Mine would say something like, "If you get 80% you will get at least a B". This is just a reinforcement of the first point.

Third, permit people to do work over if they have fallen short. Regrade it for "most of" the lost points. My policy was 90%. If you lost 30 points on an assignment you could get 27 points (max) back if you re did the assignment properly. My policy was generous, permitting several attempts. The repetition was good for the students and worked to assure learning.

Fourth, at the end of a course, look at how the students did overall and compare it mentally with what you think they really learned in the course. If you think the learning was actually better than the distribution shows, bump it a bit. This will push a few students up to the next partial grade, say from B to B+.

Finally, avoid marking using only a few high-risk exams, but spread the marks over a large number of tasks. All or nothing final exams eventually leads to trouble, even in less extreme cases than the one you mentioned. This leads to a practice of continuous study and learning rather than "cramming" for the big one. Cramming results in more memorization (short term learning) and less deep learning.

My students all knew everything about the above policies. I seldom got complaints about grading. I could be as demanding a professor as I felt necessary (students viewed me as very demanding). At the end of the course surprises were always happy ones and students felt good about themselves and encouraged to continue.

Finally, let me note that strict scaling, making the course distribution into something like a normal curve is, IMO, always a mistake. It turns the course into a zero-sum game for students who can only win if someone else loses. In theory it should be possible for everyone to do well, even full marks, based only on their own work. Such scaling is also unjustified as it assume that a given sample (your students) perfectly match a population (all students). Statistically that is a serious error to make unless your scale is huge.

Answer 3

A system I have used successfully in the past: pick an upper segment or quantile of the class (e.g., top 5% or top 5 students). Compute the average combined mark of these students, and scale everyone else's grade by this value (i.e., if course marks are out of 100 and the average of the top 5 students is 95, multiply everyone's mark by 100/95). Some of the advantages of this system:

• it's mechanical, clear and transparent; even though you can't say in advance what the final scaling factor will be, you can tell students as they go along what the current scaling factor is, and they can do their own "if the scaling factor stays the same I need to get xxx on the final to get a grade of yyy" calculations to their hearts' content
• in my experience/as far as I can tell the upper-quantile students are generally getting their scores honestly (and are less likely to collude in a grade-gaming effort); in particular, the scores of cheaters are unlikely to have a big impact on the scaling factor (unless there are lots of them and they're extremely good at cheating)
• this system automatically handles assessments that were unintentionally made too difficult: if the best students lost a lot of points, then everyone gets a bonus
• the top few students automatically get 'perfect' (after rescaling) scores, but averaging by the top quantile (rather than, say, the maximum) is reasonably robust
• it doesn't pit the mass of the class against each other; the distribution of the lower 95% of the class has no effect on the scaling

This would obviously break in the "whole class cooperates to break the system" scenario, but that seems extreme to me. With regard to the "all of the students boycott the exam to get 100% marks" scenario: (1) I do this for large (>150) classes, where the odds of successfully organizing a boycott seem remote (I don't know how many students were involved in the scenario described by the OP); (2) this marking scheme applies to the overall mark for the whole term, not just the final — so students would have to boycott/collude on all of the assignments in order to break the system.

Answer 4

Each grading policy serves a different purpose, and I think that's the key question you want to answer.

The most common policy I have seen, which happens to also be the most opaque, is actually not about exams but about the grading cutoffs for final grades:

Exams will count for x% of the final grade, homework y%, et cetera. Final grades will be given with cutoffs no less generous than

A: >93% , A- : >90%

B +: >86% et cetera

The benefit of this policy is that you don't have to scale or curve exam grades at all but can still change cutoffs to give a fair distribution of grades, while still giving minimum requirements for making sure you pass or get an A. This policy is meant to fix grade distributions overall in the fairest way possible, but doesn't mess with the weighting or scoring of individual assignments or exams.

For individual exams I have also seen the policy

It will be possible to replace your lowest exam score with the grade of your final exam if it would increase your overall score.

This policy is good to make the exam a less variable and lower pressure affair, since it takes out negative noise in the midterm exams. However, it implicitly makes the final exam higher pressure/stakes. In general this is a good policy if you're trying to make midterms lower stakes but don't want to entirely drop an exam and weight the final higher.

Rarely have I seen a class where there is a written policy about scaling, except to say in the syllabus that the instructor reserves the right to change grading when necessary. In general if you are trying to curve/scale an individual exam it is in response to a poorly written or poorly timed exam. For example, this can happen when the exam turns out to be much more difficult than the instructor intended it to be, or if it turns out to be much longer than expected. When those situations occur the most common things I have seen (in order of frequency):

1. More generous grade cutoffs at the end of the course.
2. Making particularly difficult questions a bonus, so as to improve the general average while still rewarding the ones who got the question right
3. Grading exams out of fewer questions. Typically done more in written exams with partial credit, but for example where an 8 question exam is graded out of your top 6 questions. This again is meant to blunt some of the bottom end of the distribution while still evaluating students
4. Adding x points to everyone's grade. This is usually at the cost of more generous cutoffs at the end, but many instructors like it because more generous cutoffs usually mean that either homework or exams could be at a lower standard, and this is usually in response to a particularly difficult exam.

In general I think the policies are rarely written down except to assure students that you won't make their grades worse (which I have heard happening in very competitive classes, but have never experienced) or to let them know about dropped grades, and not all scaling/curving answers the same question, so which one you choose depends a lot on what you're trying to accomplish and the culture of the department and school.

In general I would say one of the best policies I have seen was using the first approach with grade cutoffs and then saying "Here is what I look for when I give each grade, roughly":

A: You can apply the material in novel situations and in non-straightforward ways

B: You can apply the material in contexts taught and in complicated multi-step ways

C: You can apply most or all the material in straightforward ways in the contexts taught