Grading formula, ME 2030, Spring 2014
- Andy Ruina

Why write this all out in such detail? Because, for example, a student nicely wrote about a previous version of this page in a previous course:

...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.

We will post all of our data about you, including your final letter grade. It will be listed by your code name which will be posted on Blackboard.

Grades will be calculated using Matlab programs which we will post at the end of the semester.

1-9) Prelim grades (or two prelims and the makeup). Each prelim will have 3 problems and each problem will have a score of  0-25. You will be allowed to redo any problem to get a score of up to 20. Your provisional grade for a given problem is the average of the prelim score and the redo score. Then each problem grade is rescaled to a median of 18 while preserving the scores of 0 and 25. To be precise, the scores are rescaled by the formula ax + b where a different a and b are used for scores less than the median than for those that are 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 is somewhat suppressed if any problem has a very low or a very high median.
Note: students who do unusually good work on a prelim problem may get a score of more than 25 on a given problem. They could get these points by a mixture of getting the right answer a clever way, having an unusually clear presentation, making appropriate checks (e.g., units and special cases), and making explanations about unusual or interesting behavior of the system. This "extra credit" is to make it so people can get a sense of nearly full credit if they have basically done a problem right, while we still reward students who demonstrate having even more useful skills in the course material.

10-14) Final exam. These problems are graded out of 25 and rescaled to a median of 18. Then the score is 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 exam if you have done well previously.

15) Clickers. By the end of the semester there will be clicker scores for most days. For each student the clicker score is 0 (no vote), 4 (for voting) or 5 (if a right answer was recorded) for each question. Some days there are multiple questions. Of these scores, the lowest 5 will be dropped. The resulting total will be rescaled to 25.

16) Recitations. If you are there, alert, trying hard and being helpful you get full credit. This part of the course is A for effort. No scaling.

17) Homework. The lowest 2 are dropped. The rest are summed and rescaled so the best student gets about 25.

18-19) Bonus projects. If you do one or two, they will be graded, completely subjectively, out of 25.

Of these 19 numbers the best 14 are selected and summed and rescaled so the best student gets close to 100.
Then one point is added if you do the online course survey. This is your Course_total.

``` 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 (***tentative!***)
(e.g., Everyone who gets 97 or more gets A+ and nobody gets a D+ or D-)   ```

If you are within 0.45 points of a cutoff, your grade is pushed up. Why .45 instead of .5? So that no two people with the same posted Course_total (Course_total is posted after rounding to the nearest tenth) would have different letter grades. If 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 happened once. And the student, lawyer-like, complained "Same number, different grade, no fair." But with a .45 push, instead of a .5 push, they would both get A.

Homework exam correction. If you took the homework exam and your grade, above, comes out below a C we will grade your homework exam and give you a C if you passed it (got 3 of 4 problems completely correct).

Finally, we give a few students bonus points for things like being extremely helpful or insightful in recitations. These situations are rare and not worth chasing. But we note it here for transparency.

## Errors?

Our recording errors. Your grade is determined by a bunch of numbers. With so many students that's thousands of numbers. These numbers are passed from graders to TAs to the head TA to blackboard then downloaded to Excel, edited and loaded to Matlab. Meanwhile there can be Blackboard glitches with sets of data lost. Do we make recording errors? Yes, many of them.

Your recording errors. If we make an error, post it, and ask you to check it and report back to us, and you don't, we call that your error.

Your strategic errors. If you don't bother to turn in a prelim redo, or a late homework, or you don't get around to registering an iclicker, that's your strategic error.

What to do depends on the reason and your goals.

Our recording error? If you find an error soon after we post the number 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 the head TA with the subject line "Grade error, please fix."

Your recording error? If it's an error that we made but that you should have caught before. We'll still probably fix it. But curse you for not telling us sooner.

Your strategic error? While we may be sympathetic, it is just not fair or practical to let our sympathy affect your grade.

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 student suggestions.

## Important statistics:

In the past, essentially no-one who sincerely participated in lecture, section and HW ended up getting below a C. Presumably this extends to the problem sessions. This is a statistical fact. Why does it work out like this? It's not just because of the points for clickers and so on. It's because people learn by participating. The people who end up getting below a C have almost inevitably skipped a good portion of one or another of the course activities. Yes, some people who skip this or that do fine. They are smart or they learn on their own. More power to them. But some people who skip this or that get C- or D. If you are worried, just drag yourself through all parts of the course and you have an extremely high probability of getting at least a C, no matter how il-prepared or misfit you think you are (which you probably aren't).