My Math Forum Grading on a Curve

 August 1st, 2017, 04:16 AM #2 Global Moderator   Joined: Dec 2006 Posts: 17,719 Thanks: 1359 One has to wonder whether those who didn't get even half of the available points were just guessing their answers, especially the student who got only 7 points.
 August 1st, 2017, 04:34 AM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,285 Thanks: 439 Math Focus: Yet to find out. This is just one quiz? What is its overall weighting for the unit? I don't see why you would need to boost them at all.. Especially if it is open book without time limit etc. as you have stated. Last edited by skipjack; August 1st, 2017 at 05:46 AM.
August 1st, 2017, 03:44 PM   #4
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 Originally Posted by skipjack One has to wonder whether those who didn't get even half of the available points were just guessing their answers, especially the student who got only 7 points.
Do we know if the questions are multiple choice? There were 106 out of 350 points not earned. If the questions had 4 choices and all the wrong answers came from random guessing where the points not earned should be about 3 times the amount of points earned from correct guesses. 106/3 = 35 when rounded to the nearest whole number. This would mean 209/350 = 59.7% of points that were earned without random guessing. Of course sometimes students eliminate some choices and then guess, and some wrong answers are by students who were confident they were right rather than guesses.

Hofstra Law School require course grades to be curved with a mean of about 3. The grade distributions must be close to:

A or A+: 8%
A-: 14%
B+: 26%
B: 19%
B-: 13%
C+: 7%
C: 6%
C-: 5%
D+ or D: 2%

August 1st, 2017, 06:34 PM   #6
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 Originally Posted by skipjack One has to wonder whether those who didn't get even half of the available points were just guessing their answers, especially the student who got only 7 points.
I spent an hour working 1-on-1 with that student today. The student claims she read the text and listened to the lectures but still managed to struggle. We went through each quiz question and it was clear she didn't really know the material. Nevertheless, she was one of students that got the difficult comprehensive question correct. It turns out that was a lucky guess because she had no idea how to approach the question when we went over it. Her actual score would have been a 3 out of 25...

I am sure that some other students were guessing at some point too. I try to make each potential answer seem plausible, so on some questions ruling out a couple of choices is not really possible unless you know the material. There are quite a few aspects of partnership taxation that are not obvious.

August 1st, 2017, 06:53 PM   #7
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 Originally Posted by EvanJ Do we know if the questions are multiple choice? There were 106 out of 350 points not earned. If the questions had 4 choices and all the wrong answers came from random guessing where the points not earned should be about 3 times the amount of points earned from correct guesses. 106/3 = 35 when rounded to the nearest whole number. This would mean 209/350 = 59.7% of points that were earned without random guessing. Of course sometimes students eliminate some choices and then guess, and some wrong answers are by students who were confident they were right rather than guesses. Hofstra Law School require course grades to be curved with a mean of about 3. The grade distributions must be close to: A or A+: 8% A-: 14% B+: 26% B: 19% B-: 13% C+: 7% C: 6% C-: 5% D+ or D: 2%
I don't have a similar requirement, but I nevertheless would like to see my students performing along those lines if not better because they all truly know the material. Obviously, not every student is going to earn an A. If they don't in my class, however, it will have a lot to do with effort as opposed to just ability.

The material itself isn't rocket science, but we do have a lot to cover. What is difficult for these students is if I pose questions that they have to research an answer for. They are still developing their ability to research despite the expectation that they are able to at least look up and cite the Code and Regulations. That is why I generally quiz on principles instead of having them dig for specifics at this point. Everything is addressed by the text in some form when it comes to the quizzes, whereas in their discussions and papers I require proper citations and reward them more for researching.

August 1st, 2017, 07:10 PM   #8
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I like your thoughts. The students have plenty of room on their papers and discussions to improve their grades.

You're quite right in that, when we screw up, people sometimes can really be hurt by it. Thankfully we're not surgeons in that regard, but still, it hurts with respect to peoples' pocketbooks and also in terms of stress and time lost.

I recently published a paper in TAXPRO Journal where I advocated for regulating paid tax preparers. To quote myself, when it comes to your average chain outlet, "preparers only correctly prepare [relatively simple returns free of legal ambiguity] somewhere between 19.68% and 37.19% of the time." That stat is computed with 95% confidence using the conventional formula for an interval estimate of a population proportion given the limited sample I had to work with of 102 tested returns. Still, that's really bleak. Tax pros certainly are not all created equal and their services are not a commodity.

To that end, I want to be a bit of a hard ass but I'm really not. On the quizzes, my hands are tied because their score is what it is absent a curve. On their papers and discussions there is more room for subjective grading.

You know what the scary part of this is though?... Most of my students are themselves seasoned tax professionals. When I went through the Masters program, I had already been working for about a decade. I got a 4.0 and often times 100% throughout entire courses because I didn't need to relearn it. I already knew it. That's what I'd expect from anyone holding themselves out as a tax professional.

Anyways, sorry for the bit of a rant, but one more question please. Assuming I did want to curve a quiz like this, how would you suggest I go about doing it based solely on the information in the OP?

 August 2nd, 2017, 12:26 AM #9 Global Moderator   Joined: Dec 2006 Posts: 17,719 Thanks: 1359 Grade Points $\ \ \$ A $\ \$ 22-25 $\ \ \$ B $\ \$ 18-21 $\ \ \$ C $\ \$ 14-17 $\ \ \$ D $\ \$ 10-13 $\ \ \$ E $\ \ \ \$ 6-9 Ideally, D and E grades should be treated as unsatisfactory.
August 2nd, 2017, 05:33 PM   #10
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 Originally Posted by skipjack Grade Points $\ \ \$ A $\ \$ 22-25 $\ \ \$ B $\ \$ 18-21 $\ \ \$ C $\ \$ 14-17 $\ \ \$ D $\ \$ 10-13 $\ \ \$ E $\ \ \ \$ 6-9 Ideally, D and E grades should be treated as unsatisfactory.
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.

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