I go to school at a University in the US. We use a competitive grading system where teachers give grades based on how you do relative to other students. This type of grading system doesn't encourage students to work together or help each other because we are all competing against one another. I'm wondering if there is another non-competative grading system that major universities are using to eliminate this competition?
As a graduate student I had to grade exams for the courses my supervisor taught. We had a very intricate system of establishing what would be a passing grade:
- Prepare a set of questions.
- Let all the Teaching Assistants (TAs) solve the problems, keeping track of how long they took for each question.
- Distribute an arbitrary number of points over the questions relative to how much time, on average, was spent on each question by the TAs.
- Let the students take the exam.
Let me be very explicit that until this point, no grading scale has been established!
- Mark the exams. This just consisted of going through the questions and assigning points for correct solutions, partially correct solutions, etc... Every question was marked by a different TA and this TA was free to distribute points as he/she saw best. Usually we would go through a pile of 10-20 exams, see how the problems were solved, e.g. what pitfalls were encountered or how far most people got, and then establish a scheme we would use for the rest of the exams.
- Every TA hands in an exact description of how they marked their question, i.e. how points were assigned.
- With this list, go through the questions one by one and decide what constituted the minimum requirement in each question. This decision was signed-off by my supervisor.
- Using the marking schemes written by the TAs, calculate how many points the minimum requirements would have given if they had been handed in as an exam.
- The number of points for the minimum requirements constitute a passing grade. Anything below that fails, anything above that passes.
In my university, grades were on a scale from 1 (fail), over 4 (pass), to 6 (perfect) in steps of 0.25 grade points. This gives us three grades to map zero, the minimum requirement, and the maximum number of points to respectively. This can be fitted to a function $G(p) = ap^2 + bp + c$ which maps points $p$ to a grade $G(p)$.
The advantage of this approach is that it is, in principle, independent of the TAs specific style of marking, as the marking is taken into account when computing the minimum requirement points. It is also completely non-competitive in that it's independent of the students' actual performance during the exam. To make sure our decisions were sound, my supervisor and I would go through the 10 exams just below and just above the passing grade and see if they were all clear pass/fails. They usually all were. When not, it was usually just a matter of tweaking the rounding.
There is an open question regarding the amount of time given to the students, e.g. is it possible for them to solve all the questions, and thus is the mapping of maximum points to maximum grade justified? Here we played it safe by choosing only a few questions to make sure nobody would run out of time. The point is that if you do or don't know how to solve a problem, time won't be an issue. We also had two-hour exams, which gave the students ample time to show what they could, and what they couldn't do.
This system also works if you're the only person marking all the exams.
I would be very interested if anybody could suggest improvements or detect amendable flaws in this scheme, as it is what I plan to use myself, now that I'm a lecturer.
The alternative is to assign grades based on non-curved performance, with cutoffs for each letter grade. That's pretty standard in many universities. The problem is you may have to wait a few semesters to optimize what the cutoffs should be, as you'll be failing or passing too many students in the beginning.
I was a TA last semester for a professor, and we had a pretty good system for giving out grade.
- Make the exam rubric.
- Grade the exams. The people who did great, the rubric was not applied to. They were just given full marks.
- For people who did not do so well, we used the rubric to award as many points as we could.
With this system, there is no direct competition, e.g., someone doing better does not make you worse off. In fact, with this system, it is possible for a class of good students to all make A's. Of course, that doesn't happen in practice though, since class performance is almost always a bell curve.
What you're calling a competitive grading system is known pedagogically as norm-referenced assessment. There are a number of ways to do this, but is based in the principle that a sudent's performance is judged in reference to other students.
The opposite is known as criterion-referenced assessment. Its name is quite appropriate — you set up criteria. If the student meets the criteria, they get the grade.
Rubrics are one way to do this that gives off a strong air of fairness (although sometimes might not jive with what holistically makes sense…see clustro's answer for one way around that).
But most people I know think when designing the methods of assessment think about three things (maybe not consciously, though):
- What performance would indicate that a student is competent in the material I have taught, such that they can adequately take follow-up courses and succeed there? (grade: C)
- What performance would indicate that a student has mastered the expectations for the course? (grade: B)
- What performance would indicate that a student has gone beyond mastery of the basic expectations for the course? (grade: A)
For example, let's say we have an exam on the preterite in Spanish (where there are both regular and irregular verbs). A C-level student ought to get most, but not quite all regular verbs, and have mixed performance on irregulars. A B-level student ought to have all the regular verbs, while having mixed performance on the irregulars. An A-level student would excel in all, consistently.
On the other hand, a D-level student might demonstrate cursory knowledge of verb formation, but not be able to apply it any remotely consistent manner. And an F-level student would be clueless.
What criteria you use will depend greatly on the topic, and there are many ways to design exams. For the aforementioned verb test, you might give 60-70% regular verbs and 30-40% irregular. Based on the criteria given, you could expect grades to fall in the appopriate letter category (based on a 10pt scale).
For a longer mathematics problem, you might distribute points in a rubric over things like, does the student how to set up the problem? do they know how to solve it? were the calculations accurate? Obviously a student who can understand how to set it up and solve it, but makes a few calculation errors has met the criteria for passing — but they haven't demonstrated the perfection needed to get the highest level of achievement.
A good instructor will constantly reevaluate the criteria (to see that they meet the needs of the course) and the assessment (to see that student performance numerically lines up with observed performance) and make adjustments as necessary.
In Mexico, the grading system is a scale that goes from 1-10 with a passing mark on 6-7 (depends on the professor)
Also, some professors would do global test averaging at least once in the semester, that is, make everyone take the test, and the average of the whole class is the mark for each student for that test.
One particular professor wouldn't say which test was this going to be (the first, second or third) so you had people making sure everyone knew the bare minimum to get a good mark for every test.