### TAM 2020 Grading (Final grade calculation. Updated on Dec 14, 2010)

* Student Center (letter grade only)
* Blackboard (course records on blackboard may not be totally up to date).

## Want to know more?

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.

Please don't complain to us about this sausage on account of our being one of the few sausage makers that shows you what happens inside the sausage factory.

## How is the grade calculated?

* Here. This is a complete set of our records about you (and everyone else). On Blackboard is a customized 4-letter code. Each person has a code, sometimes two people might have the same code. Use that to find all of your final grade data (check above and below to make sure you are at the right block of data, use your known scores to identify yourself). Codes are in alphabetical order, attached to students in random order. Here is some info about the data.

What did we do with all those numbers? Roughly, we did what we said we'd do, on the bottom of the course exams www page. The grade is determined by a sum of numbers. Below is the list of all those numbers and how they were determined. Here is how the sausage is made.

Homework. There were 14 homeworks each with a nominal maximum score of 10. Some people got extra points some weeks. For each student the lowest two scores were dropped. The average of the remaining 10 makes up the homework grade. As you can read on your data set linked above, the course median for this was 9.8 (2nd row under HWtot).

Labs. Each lab was graded out of 15. The lab grade was the average of your three. The class median lab grade was 13.3.

Bonus. As announced in lecture, you could do a bonus project. Three people did these and got up to 25 points for doing things that will be of use to future TAM 2020 students. Actually the highest was 15. A few other people got bonuses for finding several errors in solutions and such like. This bonus was divided by 3 before being added to the course total.

Survey. The intention was to give one point to people who did the course survey. The registrar did not give the list in time. So everyone got a zero. In the survey column you can see your score of 0 as well as the class median and max of 0 and 0.

iclicker. We intended to give more credit to people who got right answers. In the end the iclicker software was a pain (exacerbated by some people registerring late) so we just graded on voting. We got clicker scores for people on 34 days. You got one point if you made one or more right or wrong votes on one day. We said we'd drop the lowest 20%. That turns the grading formula into:

clickerscore = minimim of (27, rawscore).

If your raw score was 32 you got a 27. If your raw score was 25 you got a 25. To make this five points on the total grade, this was multiplied by 5/27. So the clicker score used was:

clickerscore =(5/7) * minimim of (27, rawscore).

Exams. This is the most important and most tricky. There were two prelims (P1 - P6), a makeup (P7-P9) and the final exam (F10 - F14). Of these14 exam scores each person has three zeros (either you didn't take the makeup and have zeros there or you did, and have zeros for another test). For each person who did a redo, that was averaged with their original score. Then, each person gets to drop their lowest. But the questions were not equally difficult. So it would not be fair to have everyone drop, say, problem 2 on the final when someone who got 15 there (class median was 6) was doing great on that problem. So all the problems were rescaled. A bilinear rescaling was used which made 0 map to 0 and 25 map to 25. Ideally the median would map to 18 but for some extreme problems that would be too big a stretch. So the grade that mapped to 18 was the original median if the median was between 12 and 21 and was 12 or 21 if the original median was outside that range. This rescaling lowered all students' scores if the median was above 18 and raised all students' scores if the median was below 18. We didn't post the median of the scaled grades, but here they are (truncated at 12 and 21):

```      P1  P2   P3     P4  P5  P6     P7   P8  P9     F10  F11  F12  F13  F14
21  18  19.5    21  17 17.5    21 19.25 12     16   12   20.5 20   21.
D   S     D     D   U    U     D    D   U      U    U    D    D    D```

So your score, taken as the average of your raw score and your redo, scaled down (D) on problems 1, 3, 4 7 8, 12, 13, and 14 and scaled up (U) on problems 5, 6, 9, 10 and 11. It stayed the same (S) for problem 2. If on any test question you got the number listed above your rescaled score should be 18. After this scaling, your best 10 were added. This sum was divided by 2.5 to give a score with a nominal maximum of 100. The class best was 99.9 and the class median was 76.3. Before adding to the grand sum, this total was multiplied by .7 (to make up 70% of the total grade).

Grand Total is the sum of the numbers above. The class best was 99.1 and the class median was 80.2. The course grade was based on this number.

Cutoffs. We made a ranked list of all students and then had to decide what score would get what grade. To get a D you had to participate in the class. The cutoff for C- was most significant. We picked a number so that we were rather confident that all students below that number (we looked at the final exam scores of each) would be in trouble if put in later classes that depended on this class. Everyone below B- (that's C+, C, and C-) was deemed to be within reach. That is, if they are going on, we think they can make it if they study before the start of next semester (Message to C students: study up over winter break). The median student got a middle B. On the other end, the A+ cutoff was reserved for people who we thought were stellar. Not just really good, but beyond that. The other cutoffs were spread in between. Here are the minimum cutoff's to achieve a given grade:

```       97  92  89  84  78  75  72  68  60  59  30  30  0
A+  A   A-  B+  B   B-  C+  C   C-  D+  D   D-  F.```

"I'm so close!" Note, there are about 10 cutoffs in about a 40 point range. That means that one quarter of the class is within one point of that crucial cutoff that they really care about. That's 60 students within one point of that important cutoff. And 30 within a half a point. And 15 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 (dishonesty?), the pressure to do one of these things is irresistable.

Homework exam. If you got 3 problems out of 4 right (right answer, right work) on the homework exam than you got a guaranteed C in the class. One person who would have got a D was pushed up to C- by this means by getting 3 problems right but without quite good enough work. The other people who got 3 or 4 problems right got at least a C without the exam. With the exception of one student, the claim "if you can do the homework you will get at least a C" is true even without the homework exam.

Matlab calculation. All of the above formulas were computed in matlab, but for the homework-exam exception. If you want to know the details its like going to the back room at the sausage factory, and it's not pretty. But here you go. The data was in this spreadsheet, read into matlab with this script, and turned into a grade with this script. Finally, the readable printout, what you downloaded at the top of this www page, was generated with this script. If you want to see interesting cross plots, like that it pays to go to lecture and do homework, look at the output of this script, or even do your own data exploration.

## Errors

There are various possible grading errors.

Our recording errors. Your grade is determined by about 40 numbers. With about 252 students that's about 10,000 numbers to keep track of. These numbers are passed from graders to TAs to the head TA. Meanwhile there were Blackboard glitches with sets of data lost. So there could be errors on our side.

Your recording errors. If we made an error, posted it, and asked you to check it, 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.

Our recording error? 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 Scott Grutzik with the subject line "Grade error, please fix." We will have one batch correction in about the first week of classes. If the fix is significant to your future, ask your TA to write an email to the relevant parties explaining the grade error and what grade you will have in the end.

Your recording error? Same as above, but with the final email having the subject "My error, can you fix it?". No apologies or promises here. We will consider all such cases at the start of next semester.

Your strategic error? Its just not fair or practical to yield to these at this point.

You think the grading scheme is unfair? Its 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. In terms of testing net knowledge of the material a more fair scheme would be to base the grade on the final exam, and that's all. In terms of maximizing motivation we could grade the homework and attendence, and that's all. If we wanted to reward steady even performance we wouldn't have any "drop the lowest". The price for compromizing on the strengths and weaknesses of the features of those systems is that ours is complicated.

Grades serve various purposes, primarily:

Motivation. Even though your motivation might primarily be education, having it be a get-a-good-grade game makes it easier for you to try hard. Conversely, a teacher wanting you to learn can use grades to motivate you to try hard.

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 others interpret that to mean that you know enough to not drag down the next class (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 like that there exists some sign 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. Recent studies show that the act of taking a test on some topic increases long term retention.

On the other hand, grades are a source of anxiety, 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 so large that I haven't even looked into the possible consequences. Instead, I just try to grade in the way that I think best serves the three things above, as seen by students and by others.

## Don't know why we bring up sausage?

Some people like to eat sausage. But they don't think about what sausage is. If you 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 you can figure out about grades without being shown explicitly.

In short: Grades are like sausages, they cease to inspire respect in proportion to how much we know about how they are made.

The origial quote is “Laws, like sausages, cease to inspire respect in proportion as we know how they are made."
- John Godfrey Saxe (1869)

email to Andy Ruina <ruina@cornell.edu>