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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?

  • What is your purpose in scaling? – Patricia Shanahan Sep 8 '19 at 3:35
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    A better policy would be one for writing said exams... and an apropriate marking scheme... – Solar Mike Sep 8 '19 at 4:03
  • The example you give is stunningly stupid on two levels: one have a calculation to test the spread of marks and deal with it and two: actually opening the mouth and telling the students... – Solar Mike Sep 8 '19 at 4:53
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    the students successfully organized a total boycott of the final exam --- Going out on a (very short) limb, I'll guess that this person's research expertise was NOT in cooperative game theory! – Dave L Renfro Sep 8 '19 at 11:33
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    It is hard to answer because pre-planned scaling, not as a correction for e.g. an over-hard final, is inherently unfair, especially in an open-admissions environment. One year, you may have a lot of students who are just going through the motions because their parents let them live rent-free while registered as students. Another year, your class may be all serious, capable students. I don't think it is fair to give two individuals with identical performance different grades just because of the luck of the mix of students in their year. – Patricia Shanahan Sep 8 '19 at 14:22
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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.

  • I agree and that's been my policy for roughly 2 decades now. But the practice seems to be so widespread, I'm a bit surprised that no one seems willing to defend it or try to make it coherent. – Daniel R. Collins Sep 9 '19 at 15:10
  • I'm picking this as the accepted answer, because it seems like the clearest expression of an apparently unanimous view here. If someone were to add a coherent defense for grading on a curve (with objective rules for it), then I would be prone to switching to that other answer. – Daniel R. Collins Sep 13 '19 at 21:27
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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.

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    The "normal curve" type of grading was used for pre-university exams in the UK for many years but at a national level (and therefore with large cohorts of students). Since exam grades were requirement for university entrance, this was a convenient administrative system to match the number of qualified students to the number of places available. (I'm not defending that system, just pointing out that it can have a "practical" use). – alephzero Sep 8 '19 at 12:22
  • @alephzero, and, of course, lets not confuse "making administrators jobs easier" with "actual learning". Practical can equal pernicious, in some cases, of course. – Buffy Sep 8 '19 at 13:21
  • Personally, I agree with the current last paragraph. But I think that most of this answer is missing the point of the question at hand; it doesn't suggest a "best practice" mechanic of scaling/curving grades, and the fourth point falls into subjective undocumented adjustments that I'm trying to avoid. I suppose I could imagine selecting this as the best answer if it was cut down to the last paragraph (essentially, "it can't be done fairly") and there was consensus for that. – Daniel R. Collins Sep 8 '19 at 13:21
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    I think my key point is in the first sentence, actually. I.e. "Best Practice" = "Don't". Find a better mechanism. – Buffy Sep 8 '19 at 13:26
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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

  • Some instructors just routinely drop the lowest score. This usually implies there are more than a few of them, of course. While that may ease the student mind, it doesn't guarantee learning. Redoing the work focuses more on the learning, not the grading. – Buffy Sep 8 '19 at 13:08
  • Thanks for writing this. But, a lot like Buffy's answer, this seems like kind of a verbose way of saying "it can't/shouldn't be done". – Daniel R. Collins Sep 8 '19 at 13:24
  • @DanielRCollins I think there is a difference between saying you shouldn't curve and that you shouldn't document the exact mathematical transformation that you're using. In general I'm not against curves, I think they're really useful at making courses more about learning and not grades, but I think forcing yourself to a particular curve for every situation doesn't seem right either. Instead treating each test as a case-by-case but never making grades worse seems to be an okay approach. – Juan Sebastian Lozano Sep 8 '19 at 17:44

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