Monday, November 12, 2007

Grading Policy Explained

A while back, I got an email from a college professor who needed some mathematical assistance devising a grading policy for his German class. I tried to really understand what he ultimately wanted to accomplish, then work the math around it. Having taken several college courses that had a predetermined number of points built into them, I was vaguely familiar with the grading scheme he wanted, although I thought it was overly sophisticated, especially for an entry-level foreign language class. It would have actually been appropriate for and advanced math class, in which you automatically get an A in the class, if you can actually calculate your grade based on the confusing criteria. Below is my correspondence with the professor. Dr. "Fictitious German Name,"

I first apologize for being so busy this afternoon that I couldn't give your concern the full attention that it deserved. I had a terribly busy day, and was so at the time you came by my classroom to speak with me, and had several issues on my mind at the time.

Since then, I've had a chance to digest your dilemma. Here's what I found.

If I understood you correctly, by scaling the course to 100 points and making the sum of 6 tests equal to 66, you are making test performance 66% of your course. By giving students 34 "free" points, you are basically saying that if students "earn" all of the "free" points, it is possible that they need only retain or master 70-34 = 36% of the material and still pass with a 36+34 = 70%.

Also, assuming you distribute the 34 "free" points among the six tests to 7,7,5,5,5,5, you simply cannot add these to the Percentage score of, say 80, to get the new score, because the 80 is on the 100 point scale, and the 7 or 5 is on the 11 point scale. Adding 7 points, say, to a percentage score of 80, really adds:

7/100 = ?/11 ==> ? = 77/100= 0.77

This is less than a point on the 11 point scale.

However, adding the 7 "free" points on the 11-point scale (which is appropriate to the grading scheme) amounts to:

7/11 = ?/100 ==> ?=700/11 = 64 points to a 100 point exam!!

If tests are only worth 11 points, and you are giving 7 points free (out of the 34), you are giving a bonus (arithmetic shift) so that students who score perfectly ( 11 out of 11 plus 7) an 18 out of 11 (18/11 = 164) a 164 on the test.

If I misunderstood your scheme, forgive me for pointing these things out, but if I am correct, here is what I suggest:

Simplify the process. If you already grade the exams on a percentage scale, treat the whole course as such; otherwise, grade the exams on an an 11 point scale and reduce the number of "free" points students can earn (thereby making tests worth more). If you think 8 points is fair to add on a 100 point scale, use this to weight your tests to a 100 point course: the math here gets complicated

8/100 = x/y where x is the number of free points on y point scale (per test). Solving for x, we get: x = 8y/100

given this, the amount of free points per test, x, assuming they are evenly divided among the 6 tests is x = (100 - 6y)/6

setting the two equations for x equal to each other, we get:

8y/100=(100 - 6y)/6. solving for y gives 15.432...

So, you should make each test worth 15 or 16 points, leaving 100 - 6*15 = 100-90 = 10 points to divide freely among the 6 tests (perhaps 2,2,2,2,1,1). Here, by adding 2 points on a 15 point scale, you are really adding ?/100 = 2/15 ==> ? = 13 points on a 100 point scale. If you choose 16 point tests, this leaves 100-6*16 = 4 points to distribute to 6 tests (perhaps 1,1,1,1,0,0). Here, adding 1 point to a 16 point test is like adding ?/100 = 1/16 ==> ? = 6 to a test.

This is a very complicated scheme.

What I would suggest is to grade the entire course on a percentage, as you do the tests.

You can still make tests worth 66 points out of 100 total. Have a "test" category, such that the average grade of the tests (on a 100 point scale) is worth 66% of the grade (test average times .66). Then you can set an "other" category for the remaining 34%. You now have the flexibility to assign them a percentage grade for other. Say a student isn't participating much, so you give him a 70% in the other category, and the same student makes an 80% on his test. His current average would be 70*.34 + 80*.66 = 23.8 + 52.8 = 76.6 average.

Or if the student is earning all the free points, but still makes an 80 on the test, they are rewarded because their current average would be a 100*.34 + 80*.66 = 34 + 52.8 = 86.8.

I hope all of this makes sense and helps.

Again, I and assuming a lot here, based upon how I understood you. If I can be of further assistance, please let me know.


Herr Korpi

Well, did you follow all that? As it turned out, he was clueless about how to set up his grading scheme, which is why he contacted me to begin with. He did not want me to do the math to fit his scheme, but rather to suggest a simple scheme, like I did above. He eventually went with my suggestion and focussed his attention to Deutsch Sprachen.

In the end, I got a nice loaf of Frisches Brot (Fresh Bread) for my troubles, and his students got a grading scheme that wasn't a foreign language to them. Just doing my job.

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