Final Student Grades, TAM 2030, Spring 2011
- Andy Ruina
Grades are like sausages.
They cease to inspire respect
in proportion to
how much you know about
how they are made.*
About an earlier version of this page a student nicely wrote:
...thank you for being incredibly transparent in how you assigned and reported grades. I have never seen another professor do anything as in-depth or complete as the system you used. I wish that more faculty would employ a system like yours that informs us students of how the grades are calculated. A simple letter grade on student center isn't enough information, hopefully you can convince some of your peers to take up your system.
So, please don't complain to us about our sausage on account
of our showing you inside
the sausage factory.
At least please read this page through, and the relevant downloads linked here, before asking questions of your TA about your grade.
Here is all of our data about you, including your final letter grade. It's listed by your code name, find that on Blackboard.
Grades were calculated using these Matlab programs. One reads an excel file of raw grades, one calculates grades, one formats output, and one makes various distribution and cross plots.
As per the course exam page, your grade was determined by these 20 numbers:
1-9) Prelim grade (or two prelims and the makeup). Each raw prelim grade was averaged with a redo grade if there was one. Then each prelim grade was rescaled to a median of 18 while preserving the scores of 0 and 25. To be precise, the scores were rescaled by the formula ax + b where a different a and b was used for scores less than, or more than, the median: below the median 0 mapped to 0 and the median to 18; above the median the median mapped to 18 and 25 mapped to 25. Each of the nine problems had a different pair of a's and b's. Using this calculation there would be too much skewing for those problems with very high or very low medians, so the rescaling was somewhat supressed for those problems. Read the Matlab code to see the exact scheme.
10-14) Final exam. These problems were rescaled according the to formula above. Then the score was multiplied by 6/5, effectively making the problems out of 30 points each instead of out of 25. Why? So there is no incentive to take it easy on the final if you have done well previously.
15) Clickers. By the end of the semester there were 21 days where we succeeded in collecting clicker scores. For each student the clicker score was 0, 4 (for voting) or 5 (if a right answer was recorded) for each question. Some days there were two questions. Of the 21 scores (0,4,5,8,9, or 10) the best 17 were kept and summed. The best student got 130 on this sum. This sum was multiplied by 25/130 so that the best student got 25.
16) Labs. The four lab scores were averaged. No scaling.
17) Problem sessions. The four problem session scores were averaged. No scaling.
18) Homework. The lowest 2 were dropped. The rest were summed and rescaled to 25. The median was 23.6 and was not further rescaled.
19-20) Bonus projects. About 15 people did one of these, a few did two. Graded, completely subjectively, out of 25.
Of these 20 numbers the best 14 were selected and summed and then multiplied
by 100/152 to make it so the best student got close to 100.
Then one point was added to your Course_total if you weren't one of the 14 people who did not do the course survey.
Your letter grade was determined by your Course_total according to these cutoffs:
letter grade: A+ A A- B+ B B- C+ C C- D+ D D- F cutoff: 97 92 88 85 79 77 73 65 62 62 45 45 0 (e.g., Everyone who got 97 or more got A+ and nobody got a D+ or D-)
If you were within 0.45 points of a cutoff, your grade was pushed up.
Why .45 instead of .5? So that no two people with the same posted Course_total (Course_total was posted after rounding to the nearest tenth) would
have different letter grades. Had we used .5, then two students with Course_totals
of 96.46 and 96.54 would both see rounded Course_totals of 96.5 yet one would get an
A and the other an A+. It happenned once. And the student, lawyer-like, complained "Same number, different grade, no fair." But with a .45 push they would both get A.
"I'm so close!" Note, there are about 10 cutoffs in about a 40 point range. That means that about one quarter of the class is within one point of that crucial cutoff that they really care about. That's 33 students within one point of that grade they really need. And 16 within a half a point. And 8 within a quarter of a point. Push everyone up a grade who is within a quarter of a point? Then that makes a new lower effective cutoff, and the same story repeats. Please ponder this if you are close to a cutoff. How do most professors deal with this? In a small class they put the cut off at the high end of a gap in grades. In a big class they don't announce the cutoff. Or they kind of lie, they announce a cutoff and then push up everyone who is within two points. So the actual cutoff is hidden and no-one thinks they are close to the cutoff. Despite the deception (white lying?), the pressure on faculty to do one of these things is irresistable.
If you are curious, concerned, or annoyed by any of this grading stuff, please read on.
Various errors could have affected your grade:
Our recording errors. Your grade is determined by a bunch of numbers. With so many students that's thousands of numbers to keep track of. These numbers are passed from graders to TAs to the head TA to blackboard downloaded to Excel, edited and loaded to Matlab. Meanwhile there were Blackboard glitches with sets of data lost. Did we make errors? Yes, dozens of them.
Your recording errors. If we made an error, posted it, and asked you to check it and report back to us, and you didn't, we call that your error.
Your strategic errors. If you didn't bother to turn in a prelim redo, or a late homework, or you didn't get around to registerring an iclicker, that's your strategic error.
What to do depends on the reason and your goals.
Our recording error? If it happened after you had a chance to check on blackboard, we'll fix it, and our apologies. Please get yourself all organized with regard to the issues and any documentation you have. Go over it with the relevant TAs. Then send one coherent email to Pranav with the subject line "Grade error, please fix."
Your recording error? If it's a bad error that we made but that you should have caught before, we'll still fix it. But curse you for not telling us sooner.
Your strategic error? Its just not fair or practical to yield to these at this point.
You think the grading scheme is unfair? It's the best we could come up with. If you have ideas about how to make it better, tell us. We got to this scheme by putting in sequences of improvements based on suggestions. If we wanted to grade based on net knowledge of the material a more fair scheme would be to base the grade on only the final exam. To maximize motivation we might grade based on homework and attendence, and that's all. If we wanted to reward steady even performance we wouldn't have any "drop the lowest". Our complicated scheme comes from compromizing on the strengths and weaknesses of the features of various simpler systems.
None of the above? Do you think you know more than your grade indicates? You had a bad day at the final exam? You were sick for one prelim? All of these are possible. But there is nothing we can do about it that is fair, except for this. If you think you know more than your grade indicates, show me (Andy). I'll give you a little oral exam. On the basis of that I can't change your grade. But I can write a letter to one or another person or admissions committee telling them that you know more than your grade indicates. I have done this many times. One guy got a D from me, and I wrote him a letter saying he knows more. And now he is a professor. If you are intimidated by me, I hope you aren't, but if you are, perhaps your TA would make the same offer.
Grades serve various purposes, mostly:
Motivation. Even though you might mostly study to learn, playing the get-a-good-grade game might make it easier for you to try hard. Similarly, teachers always hope that their grading schemes will get you to do things that help you to learn more.
Evaluation. You want to know how much you have learned compared to what you might have learned. You also want a label by which others can judge you. So you came to a school that assigns grades. For example, if I give some flavor of C instead of D or F, other professors interpret that to mean that you know enough to not drag down the classes you take from them, classes that depend on the material for which you just got that C grade (please study hard over break and don't let me down on this one).
Fairness. Something there is that loves a grade (Robert Frost wrote: Something there is that loves a wall) . We human beings liketo have signs showing who has done more or less well. Its a reward and a punishment, not necessarily for motivation or evaluation, but to serve our sense of just rewards.
Tests make people learn. I've read, and believe, that just the act of taking a test on a topic increases long term retention of that topic. Something about the anxiety of trying to nail things down helps cement the ideas, I think.
On the other hand, grades make people anxious, cause unpleasant competition, and can distract students from the higher goal of learning. That's what I (Andy) mostly think. I'd rather give all As and tell everyone "You don't have to stay" and then just teach to people who are in it to learn. I'd still give tests, for the 4th reason above, but no grades. But the peer pressure against that is too big. So big that I haven't even looked into the possible consequences. And I reluctantly accept that I basically have to give grades. And I do my best to serve the four things above, as seen by students and by others.
It means that a bunch of numbers were assigned to you by arbitrary rules and then cooked into an arbitrary formula to make a number which was rounded and converted to a symbol sequence inolving the letters A to F possibly followed by a + or -. Its like the joke, which is also true: "What's the definition of IQ?" Answer "It's what IQ tests measure." Your grade is just your grade. We try to make it correlate with what others would call your knowledge. But the correlation is not perfect. Some people who know little mechanics will have a high grade because they happenned to memorize the right sample problems. And some people who have deep mechanical intuitions will have a low grade because they were thinking about something else on the final exam day. And a million other things that make the correlation between grade and deep knowledge (however you want to define it), imperfect. What does your grade really mean? Your grade really means ... really ... deeply ... your grade really really means ... what the first sentence of this paragraph says.
Some people like to eat sausage but don't like to think about what sausage is. If you do think about how that sausage got into your hand you can figure it out. You don't really have to go into a sausage factory to know that animals are slaughtered there, that all manner of body parts are ground up and mixed together from, perhaps, all manner of animals.
Same with grades and grading. Even if you have not seen the video of the professor and TAs talking, you know that all kinds of numbers have to be manipulated this way and that by meer mortals. You know that someone has to decide grade cutoffs by some more-or-less arbitrary rules. You know that every semester at Cornell about 10,000 students are within one point of the cutoff for a grade. These are unpleasant things about grades which you could figure out without being shown explicitly. But, above, we have made all the crudeness explicit.
*The origial quote is “Laws, like sausages, cease to inspire respect in proportion as we know how they are made."
- John Godfrey Saxe (1869)