View Full Version : 'Curved' grades

Strinka

01-20-2005, 05:54 PM

Final time came and went and I managed to get 100 on my AP European History final and more than a hundred on my Chemistry final. I managed these feats because they were curved. To prevent possible misunderstandings I will describe what my teachers did to curve it, in case it is unusual or something. They took the number correct out of a number slightly less than the total. For example there were 80 points on the History final. I missed five and hence got a 75/80. But there was a curve so it was 75/75.

Why is it called a curve? It doesn't seem curved. When graphed it is a straight line.

High Cheese

01-20-2005, 06:00 PM

I understand the mechanics of "the grade curve;" but I've never been curved in any of my classes. What I don't understand is the theory of the grade curve. What is the theory behind the curve? Why would a teacher/professor give something for nothing? The fundamental principle of taking a class is to learn something, not to get a good grade. What gives?

groman

01-20-2005, 06:22 PM

The idea behind proper curving is that the best performers in the class get the best possible grade and the worst performers get the worst grade. That idea is rarely honored, rather everybody gets a small bump up by recentering the grade.

The original idea is that there are no objective grading standards and if you use one-size-fits-all scale then people who are at the top and learned the most they could still get less than perfect grades.

Splanky

01-20-2005, 06:53 PM

I think it's called a curve because to be fair, the test scores should follow a normal distribution (http://mathworld.wolfram.com/NormalDistribution.html) or bell curve. This way, a few people do really well, a few fail, but most do average (the mean score). If the distribution of scores is skewed, then the Prof. may want to change some things around so the scores are normal.

Of course, just giving a few free points to everyone may not make it normal, but will make it a little better.

Flipshod

01-20-2005, 07:04 PM

Yes, a curve is set to artificially fit an actual set of scores into a bell curve. When there is a curve, it means that grading amongst you and your classmates is a zero-sum game, i.e. you are not being judged on what you know as much as you are being judged on how well you fare against your fellows.

The curve is good for averaging out teacher skills and preventing grade inflation.

But it's bad when comparing class to class because if you happen to be in the smartest class ever, you could do fantastic work but still get a bad grade because you happen to be in an especially good group.

Is it right? There is no answer.

nivlac

01-20-2005, 07:05 PM

From experience, "grading on a curve" can mean a lot of things. What Strinka described is certainly one way. The idea is that you want to "normalize" the test results so that the best scores are adjusted closer to 100% and the average scores are closer to 70% or whatever is deemed an average performance. It is rare indeed to get test results that fit a bell-shaped curve without such adjustments. While I do grade on a curve, I don't restate scores. I just tell students that if you're near the top scores, that's good for a top grade; if you're near the bottom scores, that's a bad sign in terms of a passing grade. If you're near the masses in the middle, that's safe in terms of a passing grade, but not a top grade.

Chronos

01-20-2005, 07:08 PM

Splanky has it right, but there's also the idea that the teacher, going in, wants a certain mean and standard deviation for that bell curve. So if you don't actually get that mean and standard deviation, you adjust the scores in some way such that you do.

Of course, this is flawed in several ways. Most teachers who "curve" grades don't really understand the statistics behind it; they're just giving out some number of points that seems about right to them. And they seldom will decrease scores at all. But even given all that, a bell curve is often not an appropriate choice for a grade distribution. In many classes I've seen, the distribution is bimodal, with one clump of people who studied and did the homework, and did well, and another clump who slacked off, and did poorly. While you could transform that in such a way as to get a bell curve, it's probably not fair to do so, since that would put the worst of the good group (who did almost as well as the best) only slightly above the best of the bad group.

UncleRojelio

01-20-2005, 07:16 PM

Most of the professors I ever had used one method or another of applying a 'curve'. The most popular method seemed to simply creating a histogram (http://www.shodor.org/interactivate/activities/histogram/) of the grades. This histogram usually looks like a normal distibution (see earlier post). The prof then picks a spot on the curve to separate the 'A's from the 'B's, the 'B's from the 'C's, etc.

Ruken

01-20-2005, 07:45 PM

The "Swarthmore Chemistry Prof Curve Method" seemed to be, "I [the prof] look at all the averages at the end of the semester, then dole out grades as I see fit." People still called this "curving". They would often speak of "curving up" and "curving down" (where your actual grade was lower than it would be on a traditional 10-point/letter scale.) I do not pretend to understand all of this.

Strinka

01-20-2005, 07:46 PM

:: Reads link supplied by Splanky ::

:: Head explodes ::

Thanks for the answers.

I don't think my teachers were concerned with making normal distribution. They're high school teachers. I wouldn't be surprised if my math teacher did that, but my history teacher. Also my history teacher said she reduced the curve because it was evident from our answers that we talked to a previous class about it.

Mathochist

01-20-2005, 08:02 PM

Final time came and went and I managed to get 100 on my AP European History final and more than a hundred on my Chemistry final. I managed these feats because they were curved. To prevent possible misunderstandings I will describe what my teachers did to curve it, in case it is unusual or something. They took the number correct out of a number slightly less than the total. For example there were 80 points on the History final. I missed five and hence got a 75/80. But there was a curve so it was 75/75.

Why is it called a curve? It doesn't seem curved. When graphed it is a straight line.

This "curve" is a rather awful misnomer. Proper "curved" grading is a method for applying a letter grade to a numerical one, and doesn't alter the numerical scores at all. The idea is that a C sits across the median score evenly, and Bs, Cs, and Ds are the same width (in multiples of the standard deviation).

Mathochist

01-20-2005, 08:05 PM

It is rare indeed to get test results that fit a bell-shaped curve without such adjustments.

In my department that's regarded as a sign of bad test-writing. Out of dozens of tests I've given and helped score, only a handful had a distinctly non-Gaussian distribution, and all but one of those was basically that the test was far too easy or difficult, so the curve got shoved off one end of the scale or the other.

chaparralv8

01-20-2005, 10:26 PM

In my department that's regarded as a sign of bad test-writing. Out of dozens of tests I've given and helped score, only a handful had a distinctly non-Gaussian distribution, and all but one of those was basically that the test was far too easy or difficult, so the curve got shoved off one end of the scale or the other.

Not sure about that.

One of my professors writes tests difficult and varied enough to use the whole range of scores from 0-100, with the mean and median scores being around 45-55%. He then used the class average as a dividing line between C and B; if you either got a straight score of over 85% or were in the top 20% of the class you got an A. He also puts some questions onto the test that weed out those who clearly didn't have a clue; those are the Fs. I don't think he gives Ds on exams.

I think this is the best grading system I've seen. First, a silly screw-up* that costs you 15 points on an otherwise perfect paper shouldn't cost you an A - it doesn't here. Second, it allows the professor to give a test that really tests what you know; if there's a 30-point question that belongs in a graduate class and very few get the right answer, it allows the professor to reward those who did it without heavily penalizing those who had a good undergraduate-level understanding of the material and no more.

*The classic example of this is when Jason Fox spills root beer on Peter's calculator and Peter gets unreasonable values for the answers on a physics test.

OxyMoron

01-20-2005, 10:50 PM

Curving also happens in some law schools, although in a different way. At my school, for large lecture classes professors got a sort of grading budget. IIRC, they could award no more than 4% A, 8% A-, 20% B+, and 10% C+ or below. Everyone else got a B. In my experience, it fairly accurately representated reality at a competitive law school: most people can do the work (and are inclined to do it), very few people are superstars, and a somewhat larger group are fuckups or have Intefering Life Events.

Mathochist

01-20-2005, 10:56 PM

One of my professors writes tests difficult and varied enough to use the whole range of scores from 0-100, with the mean and median scores being around 45-55%. He then used the class average as a dividing line between C and B; if you either got a straight score of over 85% or were in the top 20% of the class you got an A. He also puts some questions onto the test that weed out those who clearly didn't have a clue; those are the Fs. I don't think he gives Ds on exams.

What does the distribution of raw scores look like? Roughly Gaussian? I'm not saying anything about where the curve lies, but that a well-written test has scores that "look Gaussian".

if there's a 30-point question that belongs in a graduate class and very few get the right answer, it allows the professor to reward those who did it without heavily penalizing those who had a good undergraduate-level understanding of the material and no more.

This goes back to the "too easy" error. A common problem with test writing is having what we call bad separation. Remember that a true Gaussian curve is characterized by the mean and the standard deviation. Low standard deviations clump all the grades together so it's tough to tell the difference between two students' scores. A related problem is where the curve looks Gaussian on the left, but falls off a cliff or runs into the top of the scale on the right. It's easy to tell the Cs, Ds, and Fs, but it's tough to tell the As from the Bs. The solution is to add hard questions that you only expect the students who really understand the material to get. This shoves everyone down the scale except those who get it right and restores the Gaussian shape.

Sure, it's a Bell Curve...it's also a fudge factor to make the teacher look better!

- Jinx

WhyNot

01-21-2005, 08:20 AM

I've never had a single teacher curve "down" - giving everyone a lower letter grade for a higher percentage grade - only curve "up." I've also never had a teacher look at the total distribution, only the fact that no one (or sometimes only one person) got everything right. The rationale I hear is that either the test or the teaching was flawed (otherwise more people would have gotten perfect scores) and that it's "unfair" to punish the students for a flawed test or teacher.

:dubious:

I always found the whole thing intellectualy dubious. If we assume the "bell curve" is an ideal representation, then in a class of 30, no more than 2 students should get a A, right? No less than 2 students should get an F. Most of the students should be getting C's. If your test doesn't reflect this naturally then either: 1. your test is poorly designed (too easy or too hard) or 2. your teaching is poor (topics aren't challenging enough or explanations aren't thorough enough) or 3. The bell curve isn't, after all, ideal* or 4. your students are codfish. None of these problems is "fixed" by artificially inflating grades.

Then again, most of my schooling occured in the "everyone should get an A if they try really hard" and "B is average" phase of education. Malarcky. When did "self-esteem" become more important than actually learning stuff?

*Which may indeed be the case, and more so the higher the education, as the sample becomes more and more biased in favor of the truly talented. At that point, it seems that following a bell curve means that the really bright are artificially failed even if they grasp the material, while the really, really bright fight it out for the 2 A's.

Mathochist

01-21-2005, 10:16 AM

I always found the whole thing intellectualy dubious. If we assume the "bell curve" is an ideal representation, then in a class of 30, no more than 2 students should get a A, right? No less than 2 students should get an F. Most of the students should be getting C's. If your test doesn't reflect this naturally then either: 1. your test is poorly designed (too easy or too hard) or 2. your teaching is poor (topics aren't challenging enough or explanations aren't thorough enough) or 3. The bell curve isn't, after all, ideal* or 4. your students are codfish. None of these problems is "fixed" by artificially inflating grades.

Which is why the proper curving method is to take the raw scores, find the best Gaussian fit (a well-written test should have a fairly decent one), and use that mean and standard deviation to assign letter grades. The idea that "90% is an A" is just ludicrous.

Then again, most of my schooling occured in the "everyone should get an A if they try really hard" and "B is average" phase of education. Malarcky. When did "self-esteem" become more important than actually learning stuff?

Oh, about the late '70s to the early '80s as I mark it.

Greenback

01-21-2005, 11:05 AM

I have had little experience with "curving" and none of it was good. I can recall several classes in college as well as one in high school where the instructor decided that the overall class score was too low and disregarded certain stumbing questions from the tests. The problem was that I would get those questions right and no longer received credit for them. The way I understand it, this isn't really grading on a curve but that's what the school called it :mad:

Mathochist

01-21-2005, 11:13 AM

I have had little experience with "curving" and none of it was good. I can recall several classes in college as well as one in high school where the instructor decided that the overall class score was too low and disregarded certain stumbing questions from the tests. The problem was that I would get those questions right and no longer received credit for them. The way I understand it, this isn't really grading on a curve but that's what the school called it :mad:

You are exactly correct: that is not curved grading at all, but a badly-written test and (if this was widespread enough for the school to call it something) abysmal pedagogical standards. What school was this (the college)?

Greenback

01-21-2005, 11:27 AM

I would rather not say. Obviously the college placed more value on churning out graduates than actually producing productive employees. Several of my employers (past and present) have told me that I was the only graduate from the college that they have been satisfied with and they would no longer be hiring from there.

In my next life, I am just going to go to university and shoot the lights out there. From what I've read here, at least I would get credit for it.

Voyager

01-21-2005, 02:49 PM

Which is why the proper curving method is to take the raw scores, find the best Gaussian fit (a well-written test should have a fairly decent one), and use that mean and standard deviation to assign letter grades. The idea that "90% is an A" is just ludicrous.

I agree with your last, but that is the way people do it these days, at least in my daughter's high school. When I was an instructor in grad school I gave hard tests. The class was used to being graded on absolute scores, and when there was a class average of about 60 they all had fits. I was used to curves, so never thought about designing my tests so people would get good scores.

I disagree a bit on fitting the grades to a curve. First, the class has to be big enough so that you can expect a clean distribution. Second, you have to assume an even distribution of abilities. In an entry level class, maybe, but if there is filtering before people come into a class, you might want to preassign a distribution of grades, and fit the results to that (within reason.)

I TAed for a large assembly language class, that my professor made hard to help filter out students. Since the school had a liberal drop policy, we had to curve with the understanding that the low end got chopped off as time went on. Curving so the bottom 10% always got Fs even when 20% dropped wouldn't be fair.

sunstone

01-21-2005, 06:53 PM

Speaking from the experience of a 30 year career in teaching....

The usual class does not contain enough students to really apply a "bell shaped curve" to it.

Classes can vary from section to section - with one section having many top students while another section might have a disproportionate number of weak students. This variance is also evident from year to year.

I think that the best solution is to grade on a set percentage for each grade. For example, 90% would be an A-, and 94% would be an A.

A fair teacher will let the students know what it is that they are expected to learn, and then write a test that measures just that. The teacher is responsible for writing a resonable test! And in fact, after the first test of the year, it is helpful to go over the test and discuss where the answer could have been found and studied (notes, text, etc)...thereby demonstrating to students that they all have the opportunity to get whatever grade they work for. (Yes, I do realise that some students will have to work much harder than others for the same grade.)

I have no problems with having classes where there are many A's and B's, with no D's or F's. I also have no problems with a class that has no A's in it. Students should have grades that reflect what they know, rather than some artificial comparison to other students.

And I secretly believe that some teachers "curve" tests to avoid having to write good tests, and to be a "good teacher"....

Cervaise

01-21-2005, 07:09 PM

In many classes I've seen, the distribution is bimodal, with one clump of people who studied and did the homework, and did well, and another clump who slacked off, and did poorly.Would that be a Bactrian curve? ;)

Quasimodal

01-21-2005, 08:49 PM

For me curving proves one thing...the prof doesn't know how to effectively teach/evaluate.

Although often colleges require a certain grade level for a class. For example in my college students are expected to achieve a 75 average int their classes. If they don't...curving results for good or bad.

An evaluation should test specifically what the prof wants you to know. If he has taught effectively, the student should have no excuse for not knowing it (barring exceptional circumstances like a death in the family causing stress)

chaoticbear

01-21-2005, 09:15 PM

My chemistry teacher in HS did something that I enjoyed. He had a sliding scale for the curves, with fewer points added at the top and more at the bottom. That 50% I just made on that test? It's a 62% now!

Mathochist

01-22-2005, 12:43 AM

Although often colleges require a certain grade level for a class. For example in my college students are expected to achieve a 75 average int their classes. If they don't...curving results for good or bad.

This is not an accurate model for many kinds of tests. For instance, any of my qualifying exams gave a mark of "Honors" (basically, an A) for something like three questions perfect out of ten.

You don't have to dodge 75% of the bullets to prove you can survive someone pulling a machine gun on you, and sometimes survival is all that matters.

Mathochist

01-22-2005, 12:50 AM

I TAed for a large assembly language class, that my professor made hard to help filter out students. Since the school had a liberal drop policy, we had to curve with the understanding that the low end got chopped off as time went on. Curving so the bottom 10% always got Fs even when 20% dropped wouldn't be fair.

Well, this is why you use some multiple of the standard deviation (as I've said how many times now?) rather than a straight percentage of the class as a measure of how wide the grades should be. Even so, you're right that the lines shouldn't be drawn blindly.

Also, assigning grades on a curve is really only necessary in a large class. In a small enough class that no Gaussian outline can be seen at all, the instructor should have some contact with each student to tell whether or not each one "gets it".

Mathochist

01-22-2005, 01:02 AM

The usual class does not contain enough students to really apply a "bell shaped curve" to it.

To rigorously apply a curve-fitting, no. To see the rough outline, I've yet to see a class with more than 30 students fail to show the pattern.

And I secretly believe that some teachers "curve" tests to avoid having to write good tests, and to be a "good teacher"....

As long as you intend the scare quotes around "curve" to mean the addition of points which many teachers call curving these days, I'm in agreement. On the other hand, if you mean what I've been talking about (finding a rough Gaussian outline to the distribution of raw scores and using that to assign letter grades), I again point out that well-written tests give good separation and tend to show off the curve.

As for fixed percentages, you seem to forget that the curve method not only smooths out class-by-class and year-by-year variations in the students, but it smooths out year-by-year variations in the exams themselves. For instance, I haven't taught any calculus class quite the same way twice -- the topics and emphases are slightly different each time -- and this affects the material on the test. Further, it's almost impossible to write two independent tests which are exactly as difficult at each other. Should the students in a year which gets a slightly more difficult exam be punished for that? The ones who would have gotten a 94% the previous year now get a 93% and drop from an A to an A-.

Still Gassy

01-22-2005, 01:24 PM

I've been teaching at the college level since 1991 and don't believe in curves. They artificially inflate grades and while everyone supports a curve when it raises the grades, the same students would argue against a curve if it pushed grades down (too many A's and B's). Curves are too self-serving.

I'd rather students actually earn what they earn, be it all A's or all E's. In terms where I've taught more than one section of the same class, I've seen sometimes wildly different performances from each class. As the only meaningful variable between them is the students themselves, I see no reason to adjust the content of the course. Students who are doing poorly need to rise to the occasion, as their peers in the other section did.

In the end, the curve allows the instructor to A) look on paper as though he or she is teaching to some beancounter's statistical fantasy and B) to avoid having too many students pounding on the chair's door to complain about the professor being "too hard." Neither seems to have anything legitimate to do with education.

The 27th Evil

01-22-2005, 02:00 PM

I think one of the reasons proper curves are looked down upon is that many departments require a C or better to recieve credit for the class. In a proper norm-referenced grading scale, the lowest-scoring 10% of students fail and the 25% above that get a D. In a class where the scores are all grouped in an A percentile range (say, an exceptionally bright group), is it really fair that the 35%lowest of that group do not receive credits despite what would be an A in a criterion-referenced system?

VarlosZ

01-22-2005, 02:10 PM

I've had all kinds of "curves," from true blee curve redistribution of grades to a simpler "everyone gets a ten point bump."

My favorite curve was in my high school physics class. The teacher gave very hard quizzes and tests. At the end of each quarter, he'd take your overall percentage, then take the square root of that number and multiply it by ten -- so a 49 became a 70, and hence was a passing grade. I got a lot of seventy-somethings in that class. . .

VarlosZ

01-22-2005, 02:11 PM

". . . from true blee curves. . ."

That's a pretty terrible typo. Obviously I meant "bell curves."

Mathochist

01-22-2005, 05:54 PM

I see no reason to adjust the content of the course.

I'm glad your students have such an amazing teacher that has discovered the absolutely optimal pedagogical technique for even one course which will work for any group of students and under any pressures from the administration of the department and from without the department. Please, if one of your courses is a calculus-series course, let every other calculus instructor in the country know the secret to your amazing breakthrough.

In college, in my major, nearly every class was bell curved...it sucked. Mean was centered on a B-/C+. If you were more than 1 Standard Deviation above the mean, you got an A (starting at A-, then up depending on how high)...if you got below a standard devation, you got a D+ to an F. So, 2/3 of the class was between C- and B+...it was very tough to get good grades. Because the competition was so tight, mediocre GPAs were actually pretty good. Dean's List was a 3.2, and the mean GPA for my major was around a 2.9.

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