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Grading on a curve

Teaching

By jvano
from the creative algorithms department
Posted Thu Dec 05, 2002 at 08:48:51 PM PDT

As the semester draws to a close, I've had students ask me if I will grade on a curve. While I have never graded on a curve, just for fun I tried to determine how things would look if I did (a short account of my tinkering follows in the extended copy). The main thing I came to realize is one can justify many algorithms as "grading on a curve" with significantly different results. Most students seem to feel that curving the exams is somehow beneficial, but that doesn't seem to necessarily be the case.

Have you ever graded on a curve? If so, what was the algorithm you employed? When talking about "curving" an exam what method do people feel is the "best"?

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So first off, I grade on a straight 90%/80%/70%/60% scale with the caveat that I may change the cutoffs but only in the students favor (i.e. lower cutoffs). Since I usually write fairly challenging exams, I usually also have an opportunity for students to submit test corrections and allow them to earn back up to half of the points they missed.

When I calculated the "curve" for my last exam, I used a standard normal distribution taking the 90% percentile (mean + 1.29 std dev) as A, the 80% percentile (mean + 0.85 std dev) as B, the 70% percentile (mean + 0.53 std dev) as C and so forth. Clearly this isn't an ideal methods since by default 50% of the class would fail!

I also centered the curve around a C but this still gives no indication of where the cutoff for A, B or even C should fall. Should one use the 75% percentile for A so that roughly 25% of the class gets an A?

Another question is, should the distribution be centered around a C? My school gives out A/B and B/C grades but no C/D or D/F which would seem to suggest that the center of the grade distribution should be a B. Maybe take 75% for A, 50% for B, 25% for C and the rest D or F? That just doesn't seem right.

A final question for the statistics people out here, a normal distribution is clearly not a good model for the actual point distribution in any given class. Would it be better to try and fit some type of multi-modal distribution? And if so how!?

So we have the topic... Discuss...

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Grading on a curve | 4 comments (4 topical, 0 hidden)

[new] Grading on a curve (5.00 / 1) (#1)
by keludwick on Fri Dec 06, 2002 at 09:49:50 AM PDT

Three comments:

1. The next time a student asks you to grade on a curve, ask him/her why it's called a "curve." In my experience, the ones who ask for a curve don't know what it is they're really asking for. (In their minds, they're asking: "will you give me extra points that I really didn't earn, but would be happy to have anyhow?")

2. As you pointed out, centering the distribution around "C" would fail half of the class. If we take "C" to mean "passing," then the days of "C" meaning "average" are gone. (That is, unless we simply declare 3/4 of all students to be "above average!" :-)

3. I have a less scientific method for assigning letter grades. No "curving" here. Instead, I list the point totals in order, and look for "clusters" and "gaps" -- the idea being, if several students have very similar point totals, their overall letter grades ought to be the same. If there's a large gap between two such "clusters" of students, then that indicates a good place to put a letter grade cutoff (if it's reasonably close to one of the traditional 90%/80%/70%/60% benchmarks).

Granted, this method is somewhat subjective. However, until someone shows me a truly objective grading system that really works, then I'm comfortable with using my judgment, at least to this extent...

Comments?

Kurt Ludwick
------------
Assistant Professor
Dept. of Math & CS
Salisbury University
Salisbury, MD 21801

Who said |A| = |B| = |C| ... by SeminoleNo1, 12/17/2002 03:29:40 PDT (none / 0)

[new] Even a straight percentage can be flexible (5.00 / 1) (#4)
by Anonymous Hero on Thu Feb 12, 2004 at 12:14:17 PM PDT

In graduate school the TAs graded on a curve, using clusters (cutoffs were put at the bottom of a cluster so no one was one point away from the next grade up), and I found it to be a little distasteful. It felt arbitrary, and no one felt comfortable explaining to the students exactly how grades were determined. The math department where I eventually was hired used a 90-80-70 cutoff for A,B,C (+/- were a little more arbitrary) and so, in keeping with the culture of the school, I decided to stick with that. I found that I really preferred it. I give partial credit, so the first few times I teach a class I do grades initially in pencil and then see where they lie. If I feel like my grading is too harsh or too easy I can usually adjust partial credit so that the grades match my gut feeling. This is essentially like grading on a curve, but the students feel like it is "fair". And while it takes longer initially, after I've taught a course I have a good sense of how much partial credit to award for typical mistakes. Another advantage is that my classes tend to be small (under 30 students, and sometimes under 15 in upper-level classes), so it simply wouldn't make sense to assume that there is a bell-shaped distribution in every class. Last semester I gave a test where no one got an A, but I felt comfortable with it (I'd taught the class several times, and it was clear that this particular group of students was weaker overall). I've also given tests where the lowest grade was a C, and while I do keep an eye on my own trends to avoid grade inflation, sometimes it's just that I have a particularly good group of students, or even that I taught a topic particularly well.

[new] I always graded on a curve (none / 0) (#2)
by SeminoleNo1 on Mon Dec 09, 2002 at 02:09:37 PM PDT

Well, not always, but when I taught at the University of Virginia and at UCSD, I always did my class roughly on the normal bell curve. That allowed me to worry less about how I had to grade my tests to fit some predescribed 90/80/70 scale. And at UVa, that was pretty much expected by the adminstration in my time (early 90s).

The adminstration (above the dept) expected that the average grade would be a B- (UVa had +/- system). So the way the math dept interpretted that was when the final grades were set, we would figure across an entire course (say all the business calculus were we had common exams) where the 50 percentile was, and B- was assigned to an appropriate range around that. Next, we would consider what final score we were somewhat comfortable with saying "the students above this line we would feel ok saying they are ready for the 'next' course". That would be the C- cutoff point (C- being the minimum grade needed to take the "next" course"). Similarly we did for the cutoff between D and F. Usually, one standard deviation above the mean was the cutoff between A/B.

At UCSD, where I had more autonomy, I did something similar, with C+ being the target median grade. I made my target cutoff for pass/fail based on would I want a student with that score in the next class if I were teaching it, and so on.

To me, 90/80/70 is just too arbitrary. As an undergrad at Florida State, there was one girl I knew who got the top score in her class, but because that was an 89.5 or something like that when adjusted to a 100 point scale and the professor believed in sticking to a 90/80/... scale, she got a B. Since it was a class of 25 or 30 students, well, to me that doesn't sound right that no one deserved an A. Sounds to me like the teacher was too prideful to admit he made the tests too hard. That's a big reason I just avoided the arbitrary assignments of numbers to grades even before a course started -- it's just not realistic.

Additionally, it avoids students asking for a curve -- you give students feed back on "if the class ended today" after each exam, then remind them only the final scores are on the "curve".

Grading on a curve | 4 comments (4 topical, 0 hidden)

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