Since there is no factual answer, I thought this better served in GD.
Let’s say that for ever reason you want to adjust test results that reflect a high F really should be a low C so the adjustment is 50 => 70 points. The quick solution would be to add 20 points to everyone’s test and I see teachers do this a lot but what about adding 40% of the student’s score? with this technique a 0 stays a 0 which kind of makes sense, a 50 becomes an 70 which is what I want, but an 80 becomes a 112 which most teachers would be hard to justify.
So if you were adjusting a test, would you add 20 points, add 40% or some sort of hybrid (+20% and +10 points) and why?
The standard procedure for my classes in college was to make the exams difficult enough so that the mean grade was below an 80. Then the mean grade would be curved to a B-minus. From there, each standard deviation was 1 letter grade above or below a B-minus. So if you got 1 standard deviation above the mean, you got an A-minus, and if you got one below, you got a C-minus. Factoring in homework, the mean final grade for the course was usually a B.
Example with numbers: say the mean grade was a 75 with a standard deviation of 12. It would take an 87 to get a A-minus. An 85 would be a B-plus.
If you believe that the test is just harder than you wanted, you could try setting the curved score to the square root of the original score. This preserves the 0-100 range, and turns a 50% into a 71%.
It does give a much bigger boost to low-end scores though. This isn’t terribly important when tests are the vast majority of the final score and you need a 70% to pass, but might be bad in high school if a student can pass based on copied homework and a 25% (uncurved) test average. For HS students I would be inclined to just add 20 pts; I’m not inclined to argue about exponentiation with 150 students, then again to another 30 parents who think they know the course material, math, logic, and the law.
The most direct way to get what you want is to define how many A’s B’s and C’s you want and then order the scores from least to greatest and assign grades according to your desired distribution. There is no reason the relationship has to be linear or a step shift.
The issue is that I took over my new position after the students had 7 weeks of subs to start off the new year and taught 5 weeks of material in 2 days. While I could grade the student based on knowledge of the standards e.g. 50%, a fairer way may be to grade them on their expected knowledge based on the cluster that the traching has been before I got there e.g. 70%.
I’ve never done this before, (at most I’ve dropped questions I thought had somehow provided evidence I’d failed to sufficiently teach the necessary material), but if I did, I guess (on a first pass) I’d need to use a function that, for each grade N, makes sure that the ratio (N-50)/(50) equals, for the new grade M, the ratio (M-70)/(30). (That’s for grades over 50 at least. Some trickery with signs may need to happen for grades below 50.)
So for example, an old 70 is 20 away from 50, for a ratio of 2/5. So the new grade needs to be 2/5 of the way from 70 to 100, so it becomes an 82.
I don’t know if this is how anyone does it, and I’m only sort of sure it’s a good way to do it. Sounds alright on a first pass though.
And something different would need to happen for N<50 because as it is the lowest M anyone could get would be 40. It should be zero. Perhaps the whole approach is flawed.)
Things have changed since I was in college, looks like.
Back then, every prof that I had that put a curve on a test took the highest score, subtracted it from 100, then slapped that many points on everyone. If there was a “curve-buster” student, he would use the next guy’s score.
I would never have passed Money and Banking without those points.
That would only work if the test has a large number of discrete points such that the likelihood of many test takers getting the same score is very low. If you want 5 A amd 10 Bs and 2 people get 92% and 8 get 90% and 12 get 85%, what do you do?
Don’t most graders who want to curve either use a bell curve (issues outlined above) or just reset the denominator to the highest score?
Side story: My 12th grade English teacher told a cautionary tale about curving from here college days. The professor let the class vote on whether or not to curve the grades. Overwhelming vote for curving resulted. Unfortunately for them, the mean score was almost 90%. Sucks to score 95% and get a B or 74% and fail.
What I usually do when grading my tests is equate a 50% result with a score of 70. This precludes the need to write a bunch of questions a comatose chihuahua could answer correctly so that a person who has managed to learn the bare essentials, and thus will be adjudged to “pass” the class gets a 70% on the test. In short, I write the test so that missing half the available points is still sufficient to demonstrate the knowledge that will allow you to pass the class, and then create an equation of that result to the score that will indicate course passage.
Thus, a function is created whereby the score assigned is equal to 100 - (x*30/c), where c is equal to 1/2 of the total points on the test. When x = c, the result is 70. When x = 0, the result is 100.
The downside to this method is that you can miss all the questions and still receive a grade of more than 0. But this worries me very little, because any grade of less than 70 is essentially equivalent (0 to 69 = failing). From my experience, students who score less than 60 on a test are not going to pass your course, regardless of what you do grade-wise.
I might mention, also, that in high school, bell curve grading schemes are highly discouraged. Students are supposed to be adjudged not in comparison to other students, but rather in comparison to some arbitrary standard of “excellence”, “above average”, “average” or “failing” work output. It is not unusual for an honors class, for example, to have 25 students and 25 As. MINE don’t, but it’s rare that my honors Geometry students get either a D or an F; to do so requires that they refuse to do large amounts of work, fail to turn in projects, refuse to study, etc. A bell curve would require that there be an equal number of As and Fs, and Bs and Ds. That’s not particularly helpful.
That seems wrong… suppose there are 10 students, and you decide you want the grades to be AABBBCCCDD, and the scores look like:
100
99
98
80
79
78
60
59
58
57
56
Then 99 is an A while 98 and 80 are both Bs.
Obviously a contrived example, but I think a rigid system the way you’re describing is going to very easily end up in situations where the result seems intuitively unsatisfying.
In a case where there was no teacher for six weeks, I’d probably just not give anyone a failing grade: if the cut-off for failing is 70, give no one a grade below that. Generally speaking, the ones that “should have” failed will not be successful in the future, and so will end up failing for the semester, which is what matters–who cares if it is with a 46 or a 64? The ones that “should have” passed, in that they would have, had they had a teacher to work with, will work hard and learn the rest of the year, and receive the credit.
