The usual assumption in education is that grades follow some sort of normal curve. My question is about situations where the grade distribution curve is a rising one. More A's than B's, and more B's than C's, etc. In educational setting: Is there a name for this situation? Are there studies or methodologies related to it? Any references are welcome. (My question is not about the mathematical detail of a probability distribution function, it is about the occurrence of such distributions of grades in education, or about teaching styles that are related to them etc.)
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$\begingroup$ You talk about a grade distribution curve in terms of letters, which to me implies a curve established by a teacher or institution, like announcing on the first day "In this class, unless outcomes are unusual, 60% of students will get A's, 30% will get B's, and 10% will get C's", or do you mean that scores are coming off of some evaluation, and the resulting scores have that distribution? (And in that case, how are scores getting turned into letter grades---is there some pre-specified relation between numeric scores and letters?) $\endgroup$– Henry TowsnerCommented Dec 11, 2015 at 20:56
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$\begingroup$ @HenryTowsner The course starts with typical pre-set score levels. A's are above 90, B's above 80 etc. At the end of semester there are more students in the 90's bracket than in the 80's etc. So we do not artificially set quotas for each type grade as in top 40% get A's, the next 30% B's, the next 20% C's and the last 10% D's. $\endgroup$– MaesumiCommented Dec 11, 2015 at 21:02
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15$\begingroup$ "The usual assumption in education is that grades follow some sort of normal curve." If so, this constitutes one of the more persistent myths among teachers. A lot of my classes have a bathtub-shaped distribution (exactly opposite from a normal curve). One of the ways that grading to a curve is pernicious is that it wipes out the true observation of skill levels. $\endgroup$– Daniel R. CollinsCommented Dec 11, 2015 at 21:03
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3$\begingroup$ These are results from Polish high school exit exam: i.imgur.com/ZR4jdWt.png (some discussion at reddit.com/r/dataisbeautiful/comments/1bqf9r/…; sample size is roughly 330 thousand students). Normality is a myth. $\endgroup$– lioriCommented Dec 11, 2015 at 22:04
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1$\begingroup$ ... in other words, I would like to be in the business of teaching things, not in the business of ranking students. At the time I was told "But the Med schools need those grade averages!" My thought was "Then let the Med schools do the testing." At any rate, short of the ideal, I think a percentile system would be preferable to letter grades. $\endgroup$– Mike DunlaveyCommented Dec 13, 2015 at 14:48
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2 Answers
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The student grades could be following an exponential distribution or a Poisson distribution. Both of these distributions have been extensively analyzed statistically.
It is also possible that the distribution is one tail of a normal distribution, where the mean is greater than 100%.
Here are three scenarios that can result in such a grade distribution. The three scenarios can be combined:
a. The algorithm for solving problems is fault-tolerant. There are implicit or explicit checks built into each problem. If a student makes a small number of mistake(s), they will catch them in time, and not lose any points.
b. Multiple independent mistakes are required to mess up problem(s) badly enough that points are taken off.The student population has been pre-filtered, so that only students in the bottom half of a bell curve are in the class.
The grading standards emphasize "allowing students to succeed" or "minimizing an achievement gap". In other words, the "bar is set low".
Standardized tests are designed to have bell-curve grade distributions. Some ways they do this are to:
- Have lots of chances to score small amounts of points.
- Have an average score that is in the middle of the possible range.
- Create time pressure. Slower students will score worse because they run out of time, or do not have time to check their work.
- Have lots of trick questions (especially questions with double-negatives). These questions tend to test "test-taking ability" or "general intelligence (IQ)" instead of the specific subject matter.
- Have lots of questions with an "obviously correct" answer that is actually wrong.
- Have a variety of difficulty levels of questions, so there are some questions that most students answer correctly, and some that most students answer incorrectly.
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$\begingroup$ Do you mean that the problem is broken into multiple stages, and student gets a red flag at each if it is incorrect? Are there references or papers you can cite? $\endgroup$– MaesumiCommented Dec 11, 2015 at 20:54
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3$\begingroup$ @Maesumi -- A normal distribution is built from lots of independent chances to get small differences in scores. If your grading takes off points for small mistakes that the student could have caught later, you are more likely to have a normal distribution of grades. If your grading allows students to catch some mistakes without penalty, you are more likely to have an exponential distribution of grades. (You will tend to combine the students who rarely make mistakes with the students who catch mistakes in one bucket.) $\endgroup$– JasperCommented Dec 11, 2015 at 21:11
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Although I have serious issues with "outcomes based" education, its philosophy does combat the pernicious notion that grades should have a normal distribution centered on "average."
It is not unreasonable to expect that most students will meet the learning objectives of a class. If most do not, then there might be something flawed with the preparation of the audience, or with the instructor, or with the purpose of the course. In this perspective, one might expect most grades to be A or B.
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6$\begingroup$ Specifically, if the class and the test aren't designed to distinguish between good students and excellent students, then the learning objective of the class might well be to get a score around 100%. This needn't necessarily be based on a big ol' educational philosophy, but you do have to resist the temptation to put "stretch goals" into the test. So for an obvious example, a one-day occupational training course should have a pass rate higher than the fail rate or else the time available is clearly inadequate for the material. So question then is, why grade at all rather than pass/fail? $\endgroup$ Commented Dec 11, 2015 at 22:12
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5$\begingroup$ @SteveJessop I used to have an issue with curving because it seemed eminently unfair that not all students could get an "A" just because of some arbitrary decision. Then I spent 6 years teaching. Now I have a problem with curving since I don't see why someone who knows nothing should get a "C". $\endgroup$– DRFCommented Dec 12, 2015 at 8:52
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3$\begingroup$ @SteveJessop: I've been thinking about your comment for the past few days. With the amount of material over a semester (not a one-day workshop), it seems hard to expect 100% mastery of everything. So it seems like we should communicate to students a difference from "passing and allowed to take the next class, but will need to do extra work to succeed", vs. "passing with a few minor gaps to fill in", vs. "passing with total mastery to succeed at next course", etc., which winds up looking a lot like the standard A-B-C-D-F grades. For me this does argue to abandon +/- grades. $\endgroup$ Commented Dec 14, 2015 at 5:17
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1$\begingroup$ @DRF: That is such an insightful comment I may share it with others in future discussions, excelsior. $\endgroup$ Commented Dec 14, 2015 at 5:18