13 responses to “Comprehensive Exams and Curves”

  1. Chris Zeh

    I tend to agree that option 3 is the best for the development of the students and puts minimal work on the professor and TA’s (no need to have to write more questions/solutions).

    When I was an undergrad (EE) I know I took many tests where the main contributing factor for getting low grades was the lack of time. The professor threw in some tricky problem that if you started off down the wrong track at first, it was impossible to recover from before the end of the hour.

    At least with the chance to look at the problem again with more time you can prove to the instructor that you’ve learned the material, but that you might just not have mastered it like the students who Aced the test on the first pass.

  2. Wesley

    There’s two that I’ve used in previous classes taught. One isn’t applicable to you at this point, since you’re just getting started at , and have obviously taught this particular class a total of 0.5 times so far. :)

    1) From previous experience with the class, scale the difficulty of the exam relative to the rest of the course so that you don’t get a 47% exam mean. In my experience, any time I’ve done a ‘hard but fair’ exam, it’s been more emphasis on the ‘hard’, less emphasis on the ‘fair’, no matter how hard I’ve tried to make it fair. My typical rule now has become ‘make it easier than you think you need to’, and it works out around the right spot. I don’t trust myself to remember what the proper difficulty should be for the course, even though I’m the one who taught it.

    2) Scale the exam to the highest grade. This obviously only works if everyone did more poorly than expected — if you have a couple of wunderkind in your class, this will do absolutely nothing. I personally experienced several classes back in my undergraduate education where the professor gave apologetically brutal tests and exams … but scaled them to the highest mark in the class. On our midterm, the highest score was an 89: the test was therefore out of 89. On the final exam, the highest score was somewhere in the high 70s: that was what your personal score was out of. As I remember, I did quite badly on the midterm, but with the scaling, still got a ~ 60% or so.

    It works well if your grade shape is correct, but scaled poorly (in more than just mean). In the case where your shape is right, but linearly scaled downwards, you can do a so-called ‘vertical translation’ and just bump everyone up a certain number of points.

    With respect to grade distribution and engineers (I mostly have taught engineers, and was one in undergrad), I have tended *not* to aim for a Gaussian distribution of grades. Most classes that have worked out well tend toward more of a bimodal distribution, with a peak in the mid-to-high-80s, and a peak in the mid-to-low-70s (maybe high 60s). These are (respectively) the students who ‘got it’ and did all the work and earned their ~ 90%, and the students who didn’t really ‘get it’, but did all the work and did enough work to pass with a non-51% grade. Emphasizing the exact shape of the distribution of grades was way too much hassle, and almost never worked out as intended.

  3. gasstationwithoutpumps

    I’m not sure what your problem is. A well-designed test has a mean around 50% and a standard deviation around 20%—that gives you a lot of information about where each student is, without wasting a lot of time on questions that no one can answer or everyone can answer. It sounds like your test was at exactly the right level for the class.

    How you interpret the test results depends on what level of performance you were expecting.

    If you really thought that the test as so easy that everyone should get 70% or better, then maybe 2/3 of the class is failing. I’ve taken a class where 80% of the class failed the first midterm and the high grade was a C. It was a wake-up call for everyone that we were not performing at the level expected, and almost everyone stepped up their studying. (I ended the class with an A.)

    On the other hand, if you expected the test to be tough, then it may very well be that getting 30% right was a perfectly acceptable pass level. I have taken week-long take-home tests (a qualifying exam in grad school) where getting any one question right out of ten was enough to pass. Getting 2 right was an exceptional performance.

    Why do you feel that the pass level on every test must be at 70%? Especially on tests that have never been calibrated?

  4. Jed Sutherland

    I’d be inclined to go a little further than ‘gasstation’. As an underachiever from the get go, I never did all that well in engineering school if you measured my grades.

    After 4 years of a BSEE degree and 3 years of an MEng (separated by 5 years of work experience), I discovered that very little of what I supposedly learned was of any use to the people I worked for.

    They would have preferred that I understood relay control arrangements, the correct way to size and test electric motors and why it was that commutator bars built up an unwanted patina after a few months of operation.

    Maybe I was sick the day these subjects were covered in one of the many math classes I took.

    The point? Your students will not “grok” all the course material in quite the way you’d like. For some, this may be a problem in their careers. For the other 99%, not so much. I know that this doesn’t solve your grading problem, but it seems that grades are …
    “a tale,
    Told by an idiot, full of sound and fury,
    Signifying nothing.”

  5. Tobias F

    If you really feel, that the average of 0-100 points should be 75 percent, then you should just make half the questions so easy that a monkey could do them.
    Or you could just add 50 points to everyones result.

    Personally I think having a distribution like this is ideal. If you have 50 of 100 points you are in the middle, that is how tests should be.

    btw.: The System where I am at is: Curves like you had, lower then 30-40 percent fails. If you fail you can repeat the test with no impact to your other studies, at the next exam period (half a year later).

  6. AS

    Best class I ever had from a grading prospective was an advanced analog class where the tests were 300 points, the mean was always in the 120-180 range, and nobody really got below 20 or above 280 (unless you got really [un]lucky or were possessed by Bob Widlar’s ghost (depending on BAC)). The “curve” then didn’t care about making a 70% mean, but just put the B-C cutoff around the mean (50%) and shifted grades from there.