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I'll be teaching a graduate-level mathematically oriented class with probably less than 20 students. I have to grade the students (our system doesn't allow for pass-fail grading), and while I don't want to be overly fussy about the grades (this is after all advanced level material and mostly Ph.D students), I would like to provide some incentive structure so students will do the classwork and hopefully learn something in the process.

One possibility is "coarse-resolution" grading where in each homework, the possible grades are +, 0, -, where + denotes having done about 75% or more of the work, 0 is between 50 and 75%, and - is below 50%.

At the end of the semester, the number of +/0/- determines the grade, with "mostly +" getting an A, "mostly 0" getting a B, and mostly - getting a C.

Is this likely to be effective ? Is there something else I should do ? I'm open to the idea of not grading at all and giving out dummy grades, but I do think that people who put in effort should be rewarded in some way.

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I'm not sure this question can be answered in the abstract; what works depends on the local grad-student intellectual culture. In particular, what worked at Berkeley doesn't seem to work as well at Illinois. I think. –  JeffE Dec 11 '12 at 4:20
    
That may be true. I was hoping for some general principles or "statements of experience". –  Suresh Dec 11 '12 at 5:26
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I think this [web.mit.edu/fnl/volume/204/winston.html] is relevant to the discussion. –  Naresh Dec 11 '12 at 8:11
    
Nice. that's quite interesting. –  Suresh Dec 11 '12 at 9:26
    
Especially at the PhD level I expect the student to be more or less self motivated, and not needing additional incentive to do his/her job. That said, providing feedback at the end as to how good someone performed can be valueable information for the student (do I need to invest more time for example). –  Paul Hiemstra Dec 11 '12 at 9:33
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5 Answers

One approach is to have a number of clear learning objectives. For example:

At the end of this course the student will be able to differentiate functions of a single variable.

Then for each of these provide a description of what it means to obtain each of the various grades available.

F: The student does not grasp anything about differentiation.
D: The student is able to differentiate simple functions.
C: The student is able to differentiate many functions, but has difficulty with composite functions.
B: The student is able to differentiate most functions and employ the chain rule.
A: The student is able to differentiate all functions and can apply first principles.
A+: The student employs novel approaches to differentiation.

Of course, you'd need to tailor these to your course and make them more precise than mine.

The learning objectives and the descriptions of what each grade means can be given to the student. A course may have different learning objectives, each with their own description. Your assessment can be tailored to measure the learning objectives based on these criteria.

The idea, apart from making your job of assessing more objective, is to replace scores by learning objectives, so ultimately the course will not be about scoring points, but learning. You could even disassociate the grades from the learning objectives and replace them by unsatisfactory, satisfactory, good, very good, excellent, and fantabulous.

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You are describing a rubric. Some rubrics are qualitative, using words like "novice", "proficient", and "expert" to delineate student achievement. Some have numerical values attached. Both need to be provided to the students at the beginning with a description of what each level of achievement looks like.

For my upper level courses and my courses with large independent projects, I use a five-point rubric (technically six, since I can assign a Zero):

  • 5 - Exemplary
  • 4 - Above Expectations
  • 3 - Meets Expectations
  • 2 - Below Expectations
  • 1 - Deficient
  • 0 - Absent, Missing, or Irrelevant

With the above descriptors, most students earn a 3 with good students earning a 4. A 5 is difficult to earn. However, since I provide my students with examples of each level, I give out very few marks of 2 and even fewer marks of 1. I reserve zero for when the student did not do what was asked, or turned in something else entirely. For example, if you ask for Problems 1, 7, 8, and 11-15 from Chapter 6, and the student turns in several problems from Chapter 5, that warrants a zero for not following directions.

Now, you have a simple and rapid grading scheme that still has numerical information. You can average over all of a student's scores (or weight them or whatever) to then assign a final grade. For an entry level undergraduate class, maybe the following is appropriate:

  1. F
  2. D
  3. C
  4. B
  5. A

For an upper level undergraduate or a graduate level course, the expectations are higher (and the grading should reflect that, i.e. it should be hard to get a 4 or 5), the following might be appropriate:

  1. F
  2. C
  3. B
  4. A
  5. A+
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I had mixed experiences with a three point grading scheme.

On the positive side, grading is easier for you. Also you have very clear rules for who gets which grade. On the downside students tend to find the system unfair. The main concern was the following. When a student was able to solve, say 70% of the assignment correctly, he only gets the second highest grade. The complaint was that they solved 20% without getting credits for it. (I had a slightly different system, I think 1 point for 50% and 2 points for 80%). Let me add that this is not my point of view, since they also get the full score when they only solve 80%. So in the end these effects will cancel out. The next term I used a more granular system and giving up to 15 points per assignment. All students that took both classes preferred the 15 point system. For me it was not much difference (grading was done by TAs), so I stayed with the 15 point system.

I think it depends very much on your students. The first time I had the 3 point grading at MIT and it worked great. In Germany I had these more negative experiences.

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One version of the three-point grading scheme I've seen is 2 = perfect, 1 = mostly right, 0 = other. When students complain about getting only 1 point even though they're 90% correct, or only had an off-by-one error, or only had one tpyo, the proper response is "Yes, that's right. It wasn't perfect." –  JeffE Dec 11 '12 at 23:17
    
These effects won't cancel out if their population mean for all their courses is around 70% and they have low marks variance. This would be a gigantic penalty to that proper subset of students. The effects can only cancel out for someone with a population mean of 75% or whatever the cutoff is (and even then they only cancel out in expectation; what actually happens is another matter). –  Jase Dec 14 '12 at 10:49
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Why are you grading at all? Do you expect students to learn anything from your grading efforts, or only from attempting the problem on their own?

If you intend to give your students feedback on how they did in their homework, then you will have all the information you need to produce a more accurate numeric grade. Giving detailed feedback can make the students feel that the quality of the work is important.

If you are not going to pay much attention to the homework, and the three-level grading scheme reflects that you won't know enough to do more, how can you expect your students to care much more about the homework? If you care about the quality and accuracy of the homework, your students will. If you don't, well, you might induce some to, but you'll be fighting a losing battle.

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I see. so your point is that a refined grading is a proxy for careful grading attention, and so if the refined grading goes away, some other mechanism needs to replace it. –  Suresh Dec 13 '12 at 19:27
    
@Suresh - Indeed. Comments are even more important than detailed numeric scores in that regard: they are directly helpful to understanding, and they demonstrate your attention to and interest in what the student did. This is neither necessary nor sufficient to produce motivated students, but it can help considerably! –  Rex Kerr Dec 13 '12 at 19:32
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The one seminar in which I put in most effort and most continuous work (and, not surprisingly, learned most) had as incentive not a grading scheme, but the following set of rules.

  • all calculations were done during the seminar (tutor realized that we wouldn't/couldn't put in much effort at home - I found that true throughout my studies, but few seminars would take this into account).

  • The work was handed out at the beginning and had to be handed to the tutor at the end of each seminar. He corrected it till the next seminar.

  • The most important rule was: if all groups over the whole semester have at least X% (IIRC 80 %) correct, no written exam was necessary. This was the incentive that kept us continuously working hard.
    I think the required level needs some experience - our tutor probably had some decades of experience with this seminar when I took the course.

  • We formed groups of 3 people at the beginning of the semester which did not change for the whole semester. The 80%-overall-rule makes these groups quite similar in expected performance: there are very good reasons why someone good should be in each group. And why the bad students not cluster together, so that the 80% cannot be reached...

  • For each task, one of the group had to declare himself responsible. There was some rule, that everyone had to be responsible for roughly the same number of questions. And anyways, there were too many tasks for even the best students to solve within the available time frame.

  • Usually it took the form that everyone started at "his" task, got the layout of the question and the rough scheme for solving. Then this was discussed in the group. Next step was actually doing the calculations, then explaining to the others. Then showing the result to the tutor, who'd accept the solution or point out mistakes. Then either get the next task, or help some group mate who was stuck (not to waste those precious 20% of "allowed" mistakes...). In between he went around and had a look that we were progressing with the calculations (I since realized that not needing a written exam is also a strong incentive for a tutor ;-) )

This was just a pass/fail seminar, but I think the tutor could have given marks for everyone at the end at least as easily as any school teacher can. I think you'll get a very good idea of the level of understanding if you just listen to a few explanations. And it is far easier to make everyone explain things to just a group of a few fellow students than make them come to the blackboard.

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So there was no lecturing ? Otherwise how could you work during the seminar ? –  Suresh Dec 13 '12 at 21:57
    
@Suresh: the seminar went along with the "proper" lecture (IIRC 2 x 90 min lecture + 90 min seminar / wk). At times there were explanations at the beginning (if the handed-in answers showed confusion). But the main part of the time was everyone working on the calculations. –  cbeleites Dec 13 '12 at 21:59
    
I see. so it was half lecture/half seminar. It's an interesting idea, but I fear that I'd end up covering very little of the material if I had to use a significant fraction of the time on class work of this nature. –  Suresh Dec 13 '12 at 22:00
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