As promised, here is a recipe I have followed in previous years for figuring grades on math tests.
I begin by correcting the tests against my answer key (also known as a mark scheme). Each problem has a defined number of points (or marks) and each point is earned for either an accurate value or a a correct method. Many problems have multiple steps, some necessitate multiple methods, thus a single problem can have multiple method points and multiple accuracy points. I use the idea of follow through. This means, if a student errs in part (a), but then properly uses the incorrect answer of (a) to solve part (b), then they are not penalized in part (b) even though their solution may be incorrect.
After I correct all of the tests, I order them with the greatest number of points on top. I then go through the tests and try to determine the quality of the work produced. I begin by setting the grade boundaries. So, let's say a test has 35 possible points and the top score was a 33. I might start looking at tests with 29 points and see if I think they meet the "A" criteria. (My school has a one-sentence description of "A" work. I have expanded greatly on this to explain what I expect students to show in my math class.) Having years of experience, I have my criteria pretty well set in my head, so it isn't too hard for me to think to myself, "This 29 feels like an A-." If there are multiple 29s, then I read over one or two others to see if they also feel like an A-. Then, I look at the 28s. Do they feel like an A-, too, or are they more a B+. Then, I do that with the 27s. At some point, the quality of the work clearly no longer meets the "A" criteria. So, I might decide that 28 is the bottom of the A's. Then, I do the same thing to determine the B/C boundary.
Once I have found the A/B boundary and the B/C boundary, I calculate a best fit line to convert the number of points on the test into the 100-90-80-70-60 scale. Why? Because I have to give grades in that system. That's why. So, I then look at what that does. I look to see that it accurately represents the quality of the students' work. If necessary, I look to see what that does to the C/D boundary. Does that boundary seem reasonable? If anything seems out of whack, I tweak my boundaries. By "out of whack", I mean, are grades being assigned fairly? For example, a 15 might work out as a C-, so I ensure that the quality of work for a 15 is truly a C-. If I think, no, it's a D+, or, no, it's a C, then I adjust my best fit line.
This may seem like a laborious process, and it certainly is in comparison to the standard math teacher system (add up points earned and divide by points possible to get a percentage that converts to a letter), but I used it for several years and became quite adept at it.
I like this system better because grade boundaries are not pre-determined. With the other system, I found that sometimes a test was easy, and mediocre work was awarded a B while in other cases excellent work was awarded a C+. With my system, grades are awarded based on the quality of the work actually produced. With the other system, I have to be a fortune teller and predict what excellent work will look like.
If this system sounds at all familiar to you, then you probably have taught at an IB school. The International Baccalaureate (IB) uses a system much like this to assign grades to their exams. I know, because I used to work at an IB school and the math department graded all of its tests in this manner (minus the converting of the score into the 100-90-80-70-60 scale).
It's not a perfect method. Not all 27s on a test are the same, for example. And, it is quite different from other math teachers at the school where I teach. So, many students are confused by it and some don't bother trying to understand it. But, I truly believe it is in the interest of the student to do it this way.
This year, I am teaching a 9th grade course and, obeying a request from higher ups, I have simplified my process. I often found that when I did the above conversion, a zero score on my tests would convert to a 50. This makes sense to me because in the 100-90-80-70-60 scale, an F technically has a range of 60 points. Why? Who knows. To me, a range of 10 for each grade makes sense. So, making a zero convert to a 50 makes sense.
So, this year, all of my students begin with a 50 and then the points they get on a test are used to figure what fraction they get of the remaining 50. For example, let's say a test has 35 points and a student gets a 25. 25 out of 35 is 71.4%. So that is the percent of 50 they get in addition to the 50 they started with. 71.4% of 50 is about 36. So, a 25 would convert to an 86 (36+50=86).
Okay, I know you're likely confused, so comment away and I will try to explain it better...
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