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This question is partially related to this question.

By trying to understand which one is the correct way to grade an exam I came out with this doubt. Should each exam be considered as independent or should a mark be assigned based on the other students' performance.

As an example

  • if all the students final exams are from 80% to 100% correct should be considered the fact that the exam was too easy while grading it?
  • if all the students final exams are from 30% to 60% correct should be considered the fact that maybe the exam was too hard while grading it?

To resume, while preparing/grading the exams should the results respect somehow the normal distribution or should each one be graded independently?

EDIT:

Based on my career as a student for every exam we had statistical results from all the students (min, max, avg) with the grades distribution. Most of them respected the normal distribution. So what it is not clear to me is if it depends on how the teacher create the exam, on how it is graded or just on how usually students perform.

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    Why do you think that a grade distribution should possibly normal? Not all phenomena yield a normal distribution. Actually, a lot don't.
    – Massimo Ortolano
    Commented Mar 10, 2017 at 20:19
  • Because most of the general results of the exams I did in my career respected the normal distribution, so I don't know if it's a matter of how the exam is prepared, of how it is graded or just of how usually students perform.
    – user21043
    Commented Mar 10, 2017 at 20:24
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    Both of them. you need to evaluate the students independently, However the overall statistics of the students "may" give you hints on the overall difficulty of the exam.
    – user35129
    Commented Mar 10, 2017 at 20:43
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    @newbie: What evidence do you have that the exams in your career (in what?) were normally distributed?
    – Daniel R. Collins
    Commented Mar 11, 2017 at 5:27
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    Most grade distributions I get are much closer to bimodal or multimodal than normal.
    – Kimball
    Commented Mar 11, 2017 at 16:07

6 Answers 6

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If the goal is to help students learn, then you should grade against an absolute standard (often called a rubric), and you should not grade by comparing students to each other. Experimentally, it has been found that if students believe their grades are under their own control, they will learn more. If students believe they cannot control their grades (because it depends on classmates' performance) then they will learn less. The difference in attitudes is known as a locus of control in psychology. According to the locus of control research, grading against an absolute standard will help students.

If you goal is to limit the number of students who pass, you might chose differently from what I suggest. But I don't agree with that goal.

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  • I agree with several of the answers so far but I have different reasons.
    – Anonymous Physicist
    Commented Mar 11, 2017 at 9:03
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I'm going to give this from a student perspective, so take it with a grain of salt. But I can say that I would hope I was graded independently of any of my peers on a given assignment*. Simply put, I want to be evaluated on my progress relative to the course objectives. I'm not interested in my progress relative to everyone else's.

* That being said, once the independent grade is assigned, I don't care about or mind any post-grading corrections (a.k.a. "curves"). But again, that's after my exam is independently graded - so I can at least see the raw grade first.

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It sounds like you are describing a grade curve. That would mean you adjust everyones grades to reflect their performance relative to the rest of the class. Grade curves usually only skew upwards (IE you wouldnt lower someones grade because everyone else did well, but you would raise it if everyone else did poorly.) Whether or not this is right for you depends on the course, your tests and your students. I can say for sure that this is a common thing to do and would not be at all out of place if you were to make that choice. However unless an unusually large number of students is failing your course, it probably isnt necessary if you would rather not do it.

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In the ideal situation, exams should be graded independently. There should be an established, fixed threshold or rubric for demonstrating acceptable or mastery skill in the subject, and each student's assessment should be measured fairly against that for feedback and certification. (Some instructors claim that setting this threshold is overwhelmingly difficult, but I do not find that to be the case.)

Whether the whole class or none of the class meets that threshold does not change the fact that certain students have or have not achieved the necessary skills. Research shows that we should not expect skill levels to be normally distributed (e.g., see Gould's Full House: The Spread of Excellence from Plato to Darwin). For example: A few years ago I had two sections of the same algebra course (with identical schedules, lectures, exams, and meeting on the same days) in which on the final exam one section had a 48% median score, and the other section an 80% median score.

Unfortunately, many institutions politically find themselves pressured to show certain success/certification rates, and so mangle actual scores to match a normal distribution of values (with most in the success/passing region), regardless of actual student proficiency. This may be done to "smooth out" passing rates between semesters, instructors, and/or different sections of the same course. I maintain that this is effectively fraud and should be resisted as much as possible.

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Grading should never take all students performance into account. Course curriculum design and placement procedures should always take all students performance into account. Anyone can design a course or design a placement system where all students put into a given course pass or where all students fail. If you have absolutes like that happening that cause you to want to resort to a grading curve then the course curriculum or the placement procedures are at fault, NOT the grading.

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You didn't specify the motivation for your question. If I assume that you are a TA getting the hang of your job as a grader, then it would be safest to follow instructions given by the professor you're grading for, or your department -- unless you haven't been given any, in which case the safe thing to do is to ask for guidance, in general terms (not as specifically as you did here).

You can certainly have your own opinion, though, and once you have tenure in a department you can try to influence department policy.

Sad to say, I have seen an Ivy League math department shoehorn the final course grades in undergraduate courses into a bell curve. They do it openly and unapologetically, as department modus operandi. I heard this from department administrators. Student reports suggest that other STEM departments in the same university do the same.

I suppose they think they are upholding the quality of a Bachelor's degree from their institution.

Said math department additionally provides no discernable departmental quality control over the teaching quality of lower level math courses required for STEM degrees. The department turns a blind eye to disastrously poor teaching, and then quietly offers one well-taught catch-up section during the off-semester, by a known and proven instructor.

It would appear that the existence of the large number of throw-away sections is inextricably tied to the bell curve assignment of final grades.

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