My Math Forum Grading on a Curve

 August 2nd, 2017, 08:08 PM #11 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 There's too little data for complicated mathematics to be worthwhile. The nature of the quiz (untimed, open book, etc.) suggests that a student should have to do really well to get an A. From what you stated, I would guess that the number of points attained reflected not so much the ability of each student, but mainly the amount of careful thought that was applied in reading and answering the questions. I chose grade bands of equal "width", making that width quite generous. Showing the results (for this particular quiz) on a histogram suggests that the width shouldn't be larger. Being any more generous would allow students to "pass" even if they've answered most of the questions incorrectly. The grade width could be smaller, but that would split up the students who score 18-21 points, which could attract criticism unless you feel strongly that it's right to do so. As it is, more than 75% of your students "passed". If you made the grades tougher, the significant effect would probably be that 14-17 points would no longer be considered satisfactory. Letter grades are not intended to be converted back to points. Thanks from AplanisTophet
 August 3rd, 2017, 04:02 AM #12 Senior Member   Joined: Jun 2014 From: USA Posts: 617 Thanks: 50 Thank you everyone
August 3rd, 2017, 05:13 AM   #13
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 Originally Posted by AplanisTophet Here are my thoughts: I can't really use the 'old-fashioned method' because the student having aced the quiz is a curve breaker. No curve would result. I could say that I want the average score to be 85% and then use the following formula to change the maximum number of points from 25 to something else (denoted $x$): $$\frac{\text{current class avg.}}{x} = \frac{\text{85}}{100}$$ The problem with the above is that my ace student would end up with 'extra credit' in contradiction to the terms of the syllabus, as would any other student with an actual score exceeding $x$. Let's say I wanted a cutoff for those getting an A and I've decided that the top 8% of grades should earn an A. I believe then that I'm left with an integral I cannot solve (that of the probability density of the normal distribution), but could otherwise approximate: $$\Pr( \,x \geq a) \, = \int_{a}^{\infty} \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{( \,x-\mu) \,^2}{2\sigma^2}} \, dx = 0.08$$ I'm not willing to go through some complex approximation process though. Further, after getting my approximation, I would have to convert the grades back to points because the overall grade is based on a point system. That brings me back to your suggestion. How would I convert those grades you conjured above back into points as opposed to letter grades? I have no idea how you came up with that. Ok, maybe I'm thinking about this too much, but also trying to nail down an approach I could possibly use going forward and technically even include in a syllabus (no, I won't be using Latex to create my syllabus ). I was curious if anyone here had a good method.
You are thinking too much.

Decide where you want failure to be and fail those below that bright line. Decide where you want an A to be, and give an A to all those above that bright line. Decide the number of gradations you want for the remainder, for example B, C, and D would be 3, calculate the reciprocal (1/3rd in my example) and assign the top 1/3rd a B, the middle 1/3rd a C, and the bottom 1/3rd a D.

Grading on a curve is an exemption, not a science.

 August 3rd, 2017, 09:03 AM #14 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 Regarding my previous post, the histograms below show that using slightly broader grades affects the appearance a lot. Hist4.PNG Hist5.PNG Thanks from EvanJ and AplanisTophet

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