16

Per definition, grading by a curve usually means that the students are assigned grades based on the statistical distribution of the test/exam results. No matter what, say 20% of students will always fail, and only say 10% will get a perfect mark.

I see a number of serious problems with this, and I fail to see anything in favor. In my view, for a fair system, the following are necessary; and neither are fulfilled by grading by curve:

  1. A test/exam should have clear and absolute rules and requirements. Here, the students do not know what are the exact requirements to get the result they desire, as the point limits are, obviously, only known after the test/exam.
  2. The grade of the test should directly correspond to how much of the course material did the student learn and understand. The fact that the same ratio of comprehended material can give an A in one year, then a C in the next year, tells that the requirements of the course itself are also very unclear.
  3. Similarly, the grade should directly and absolutely reflect the knowledge of the student. An A+ should worth the same every time in the same test. But here, the grade only reflects the student's knowledge relative to class members. It can't be correlated to the amount of learned knowledge.
  4. The grade should only be influenced by factors under the direct influence of the student. Here, the mark depends on factors like how "bright" are the other students, how much effort they put into preparation, and even on whether they cheated. Hence, the student's mark is influenced by circumstances completely outside of his control, and unrelated to his knowledge.
  5. No matter the collective results, a given number of students will always inevitably fail. If almost everyone is a genius, there will be the same number of failures as if everyone did poorly. Good students may fail, and bad students may pass. In a similar way as the point before, a student shouldn't be faced with the negative, possibly serious, consequences of failing, just because by chance there were a lot of very bright students in the class.
  6. Also, it creates and encourages an unhealthy and harmful class dynamic. Ideally, the students help each other in preparation. If an otherwise smart student doesn't understand some part and is roadblocked, others would explain. If a student missed a class due to valid reasons, classmates help to give and explain the missed material. But learning by curve creates an artificial race situation, where the students are actively harming themselves by helping others. Decimating the collective amount of obtained knowledge, this goes against the very spirit of education.

All these problems, and I'm struggling to come up with any argument in favor of grading by curve. In fact, I see only two cases where it may be used, and both of them are a fault of administration:

  1. The department expects an exact number of students to pass the course. This is against the spirit of education IMO. If a student is good enough, he should pass. If not, he shouldn't. Regardless of others.
  2. The responsible teacher failed to set exact, absolute, and clear requirements, and/or is lazy or unable to do so. Because of his fault, the students are exposed to an unfair grading system.

Am I missing something here? Are there any objective arguments in favour of grading by curve, and what are these? If not, or they are weak, what are the reasons it's still used, apparently widely?

16
  • 4
    "The department expects an exact number of students to pass the course": alas, this is exactly what many departments expect, because virtually everywhere nowadays having more students who complete their studies in a reasonable short time means more funding for the university (whether from student fees, government funding, improvement in the international rankings etc.) – Massimo Ortolano May 1 at 13:52
  • 1
    @MassimoOrtolano I'm aware of this, but there has to be some arguments in favor of it to tell the angry students, university scoring institutes, and media possibly. If not, it would be more reasonable to decrease the number of passing students by raising their exceptations. Othervise, something fundamental is broken in the system. – Neinstein May 1 at 14:02
  • 6
    "No matter what, say 20% of students will always fail, and only say 10% will get a perfect mark" - this is not a form of "curved grading" I have ever seen; usually the curve is only to increase and never to decrease the grades. It sets the top grades to the top scores in the class presuming that scores lower than perfect are more due to the difficulty of testing or inadequacy of instruction. – Bryan Krause May 1 at 14:11
  • 3
    Does this answer your question? Why do educators use curve to adjust the performance? – Bryan Krause May 1 at 14:12
  • 5
    Many people writing about education--notably Alfie Kohn--have made the observation that a lot of educational practices are intended to sort students by "ability" rather than to educate them. Curving is one of those unfortunate practices. – Elizabeth Henning May 1 at 22:12
7

I agree with you for two types of courses:

  • Very small classes with fewer than, say, ten students. It is very possible that these students all deserve As or Fs and we should not try to impose a bell curve where there is none.
  • Very large classes like calculus I and physics I, particularly when there are multiple sections of each class. These classes are taught so often that it is very possible to design a sensible, static "absolute" grading scheme. Such a scheme will also give highest grades to the students who know the most, without regard to their instructors' competence or peers' ability (among the other advantages you list).

But for classes that do not fall in either of these categories, I submit that "curving" and setting "absolute" standards are just two ways of framing the same practice (and "curving" is more honest). No teacher wants to give all As or all Fs; we all want to have a nice bell curve that separates the top, average, and weak students. "Absolute grades" in this case are somewhat disingenuous -- if everyone is failing or getting an A at midterm, for example, the instructor is likely to make some changes (e.g., making the final exam easier or harder than anticipated) in order to force the desired bellcurve. In this regard, explicitly curving is much more transparent; we are simply admitting that we will make changes as needed to ensure the desired bellcurve. Further, even "curving" does leave some discretion to the instructor: if I feel that I have a great group of students that has learned a lot and is working hard, I might curve such that the average is a B+ rather than a B. Similarly, I would always consider the tails of the distribution manually.

Given that they are equivalent, I agree that "absolute" grading gives a healthier class dynamic. As a student, I recognized that both grading schemes were effectively the same thing, and always find purportedly "absolute" grades to be somewhat disingenuous (unless the professor had actually taught the course often enough to be able to say that the exams were already written and nothing would change under any circumstances). But as a teacher, I learned quickly that most students do not realize this, and that they tend to respond better to the purportedly absolute system. In the same way, a very hard test with a massive curve is mathematically equivalent to an easy test with an unforgiving curve, but students respond much better to the latter. Irrational, but there you are.

Personally, I used both. When I was teaching a course for the first time, it was difficult to predict what grade distributions would look like so I would curve. But, I would also make adjustments to the curve based on my observations. When I was on surer footing, I would say things like "900 points is a guaranteed A, but I might give As for fewer points, we'll see how it goes"; I found that this was both honest and led to a healthy class dynamic.

5
  • 4
    Actually, I'd be incredibly happy to give all A's. Sadly, I never found it possible except with doctoral students. – Buffy May 1 at 21:40
  • 1
    Well, I am assuming the class is more-or-less typical; of course I’d be delighted to have a genius class that universally masters the material and all deserve As...I would also like a friendly pet dragon :-) – cag51 May 2 at 0:41
  • If everyone is getting an A or an F by the midterm, the instructor seriously needs to look at whether the course objectives are clear and whether the assessments are aligned to the objectives. Yes, it can happen that a whole class is awesome or horrible, but it's much more likely the instruction is off track and should have been fixed before the midpoint of the term. – Kathy May 3 at 14:29
  • I don't think we disagree...as I wrote, if everyone is failing at midterms, the exams are probably too hard, and the professor needs to change future exams. It may be that the scores are lower than expected due to issues with the teaching or course design, but this question just asked about marking schemes. – cag51 May 3 at 14:56
  • 1
    +1 for healthier class dynamic. I once gave an exam with a range of scores from 10-100 and median of 55. I chose not to curve because I thought it was a weak group (though I made future exams easier). Punchline is that students turned on me; I still shudder at the venom. I honestly believe I got students to work much harder and learn a lot more, but it was ugly out there. Looking back, I needed to soften the blow to avoid demoralizing some students. The ongoing relationship between class/instructor is a reality that can make curves "legitimate". What is "fair" is another conversation. – Gauss May 4 at 1:29
9

My firm belief and policy is that a student's grade should depend on their own efforts and nothing else. In that case, curving the class is actually just wrong.

But my grading policy is pretty different from most. First, I use (used, actually, as I'm retired) cumulative grading. Every student task was assigned a point value and those added to, say, 1000. If you did a 100 point task, you might get 90 points based on assessments of quality. The breaks between grades were defined, say 900 to earn an A.

Second, I permitted rework if a student earned less than they expected to earn, but rework only got you back part of the lost marks. Therefore, I didn't get complaints about strict grading. "If you want more points on this, do a better job of it". This also allowed me to encourage students to do better work and rethink poor assumptions.

Third, I assumed that I wasn't perfect and that I occasionally was overly strict, so a student never missed a final grade by what I considered an infinitesimal amount. 899 points didn't mean a B.

When I came time to assign final grades, I'd look at the earned distribution and make a decision whether that represented what I thought they had actually learned and I might adjust all grades upwards (only upwards) a few points if I thought that, at that point I'd been too strict along the way.

I had the reputation of being very demanding, and I was, both in the quantity and difficult of work. But I was just a bit less strict than my reputation. Students after the last class were never disappointed when they saw their final grade. They were able to compute it along the way, and they might learn that they did a bit better than their expectations.


No student should suffer in a class simply because, just by chance, there are a number of genius level other students.

Curving, is, I think, an admission of failure of the admissions system itself, which tries to predict that admitted students will be successful. If the system is set up so that some are guaranteed to fail then something is extremely wrong.

Expecting that the distribution from one year to another should be the same in an individual course is also foolish. The students aren't randomly selected from a known distribution in large enough numbers (for a single class) that statistical assumptions have any validity. Some years the students just work harder than in others. Some years they have to deal with things (pandemics, say) that make their work much more difficult.

Grade individuals, based on their performance. Make it possible that the performance can be good or can improve. Don't assume that the students in your class don't really need to be there. Be a teacher, not a grader.


Also see this question and my answer there.


Note: To make rework possible and not overly burdensome on the grader, students turned in work on paper. For rework they also turned in (in a folder) all of the previous versions that had been commented by the grader. They also highlighted, in the new work, changes to the most recent version. It was easy and quick to see if additional points should be awarded and easy to mark up the latest document with suggestions, etc.

This may not scale beyond 30 students per grader, I realize. I know that at 40, scale starts to be an issue.

2

I don't agree with grading on the curve in most cases and I agree with most of the criticisms highlighted in the original post, but that doesn't mean that there aren't any arguments in its favor. Generally these arguments can be summarized as "No human is perfect and students/employers* shouldn't suffer because its impossible for a professor to be perfect". (* delete as your biases see fit)

No exam can test every single thing on a syllabus, so no two exams are likely to test exactly the same selection of material. Further, no two questions on the same material are of exactly the same difficult. Its not just that the setter failed to generate two questions of identical difficult, but that having two questions of the same difficulty is impossible.

So we must conclude that no testing systems fit all the criteria you set out above once you get above trivial knowledge-recall or mechanical-process application based tasks, which shouldn't be what university level education is about. For example, two of the Learning Outcomes on the genomic module I teach are:

"Be able to construct a convincing argument using evidence from high-throughput/genome-wide/genomic experiments"

"Create reasonable, testable hypotheses from genomic science research questions and design realistic experiments to test them"

There is no fully objective test of these with a precisely defined difficulty. For the first one there will always be a judgement on whether an argument is "convincing", but also some judgement of the extent of which an argument uses high-dimensional data. While for the second one can imagine an answer that does or does not make the criteria (although actaully designing one is much harder than you'd imagine), its impossible to come up with two questions of precisely matched difficulty.

So all systems of assessment are compromises between different priorities. What compromise you will settle on will depend on where your priorities lie. The design of valid and fair assessment is an entire academic discipline of its own.

To decide on the proper priorities for assesment design, this we must consider what the purpose of assessment is. I can think of three possibilities:

  1. Guide the student as to where their strengths and weaknesses are, help them focus their efforts
  2. Ensure to a "consumer" (e.g. an employer) of the student that they meet a certain minimum standard on some task
  3. Measure the "ability" of students, either for this particular subject or just in general.

So at one end of the spectrum you have things like a driving test, where a person must demonstrate they are capable of performing a predetermined list of skills - its not about whether you are a better driver than your friend, just whether you meet the basic safety standards. And on the other end, NASA wants to recruit the best candidates for the space program. It will spend years training them, so what they actually do now is not as relevant as just selecting the "best" people.

I, and I like to think most educationalists, don't particularly care for reason 3. But many employers do, and because the employer does, students do.

Curve grading prioritizes measuring "how good" a student is, over whether they can perform a predetermined set of tasks. It means, for example, if the teacher is ill one day and performs the lecture poorly, the students from that class will not loose out to students from a different class when they come to apply for a job. Or students that take hard classes will not see their grades suffer for that choice.

It relies on the assumptions that your sample size is large enough that a change in mean test score is a more likely explanation than a change in average student ability. Thus, it was originally implement in massive, standardized tests, like the GRE in the US, or the nationwide GCSE (General Certificate of Secondary Education - a set of exams taken by all 16 year olds in the UK). These exams are taken by 100s of thousands of students at a time, are generally marked by more than one person, and are used to decide which subset of students gets access to some limited resource. They may well be appropriate in these circumstances.

To come back to the actaul question - how is it fair?

It is fair under two possible conditions:

  • If the aim of the exam is to sort/filter students. In particular if the student wishes to be compared to students from other classes/universities when applying for a job.
  • You believe that variation in test difficulty is greater than the variation in average student ability year-to-year.
  • You believe that the variation in teaching effectiveness varies from year to year more than the ability of students.

Note that the final two reasons are the fault of the instructor. But this immaterial. Given that instructors will be imperfect, what is the best way of negating the effects of this for students.

All that said, I am not particularly convinced of the arguments for curve grading in university class type situations.

0

Check out the four publicly available Physics GRE practice exams.

ETS have provided the % of students who get individual questions right. If you examine that statistic, it should be clear that two of the four tests are relatively hard because there were more questions which few students got right, and one of the four is noticeably harder still.

ETS got around the different difficulties by grading on a curve. To score 990 (the maximum score) in these exams, you need to get 84/100, 76/100, 67/100, and 85/100 respectively.

If you don't grade on a curve, how do you propose to accommodate the varying test difficulty? You could tell the students beforehand "to get 990 in these exams you need to score 85/100", and then 0% of the students in three of the four years will score 990. That makes the exam useless as a standardized test.

Some responses to your arguments as well:

  • The exact requirements are clear: answer as many questions correctly as you can. This is the case regardless of how the exam is graded.
  • The grade can be correlated to the amount of learned damage. If you know more you get a higher grade (for that class). Comparing students between different classes doesn't work, but then it doesn't work without curved grading either, as you can see from the Physics GRE practice exams. You can't easily compare students who took different exams.
  • Curved grading usually sets the top grade; it doesn't say "10% of students get A's and 10% of students get F's". Hence curved grading does not a priori cause students to fail if there are lots of bright students in the class. For the same reason it doesn't a priori cause student vs. student competition.
  • Curved grading eliminates grade inflation. It handles both "exam too easy, everyone getting A" and "exam too difficult, everyone failing" situations. This maintains value for the grade, since you can reasonably e.g. say someone who fails did not understand the material as opposed to simply had a very difficult exam.
12
  • 10
    The GRE is not at all the same thing. The numbers of people taking the exam are large enough that statistical assumptions are valid. That is hardly the case for course exams. – Buffy May 1 at 16:03
  • 4
    Curving can't undo "exam too easy, everyone getting A" in a remotely fair way. At the most extreme, if everyone gets 100%, there is no way to assign different grades. But even if everyone gets between 90-100%, are you really going to give the 90%-scorers anything below an A-? – Alex Reinking May 1 at 17:00
  • 2
    @Buffy Whatever the value of the GRE, it is also much more consistent than any course exam because questions are tested large-scale to ensure that the GRE is consistent. – Elizabeth Henning May 1 at 22:22
  • 3
    It's not really true that the GRE is "graded on a curve." It's designed so that the scaled scores year to year are supposedly comparable, at least within a few years. Using the publicly available tests to draw conclusions about the scoring is misleading, because they're old and they span 15 years. – Elizabeth Henning May 1 at 22:26
  • 6
    @Neinstein you are asking people to do the impossible. I have been teaching for many years and still am occasionally unable to predict how well students will do on an exam question I design. Friends of mine who are senior professors have complained of the same difficulty. Sorry, your expectations of what professors are able to do when they are experienced are grossly unrealistic. – Dan Romik May 3 at 7:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.