.4 EVALUATION SKILLS AND GRADING SYSTEMS

Another skill is evaluation and teachers are not very good at this. I really think that teachers need to learn how to use the skill of evaluation in a very different way. I'm going to try and teach you the skill of combining grades this morning. You may be confused because it's complicated and it's an issue that most teachers don't do very well. We're going to have three students: Students A, B, and C. Each of these three students is going to take three tests during a six-week period. One rule is that we don't which grades came first or last. It's not important. All three tests should count equally. One is no more important than the other is. Every single one of these is equally important. You are equally thrilled about the way the students performed on all three tests. Let's just say for the purposes of our grading that on every test, one student gets an A, one a B, and one a C. Everyone did equally well. The point is how do you combine these grades to tell me who the top student in this class is?

Student A grades: 20, 10, 30
Student B grades: 19, 20, 28
Student C grades: 18, 15, 29

These are the three sets of grades. Now I want you to tell me what grades they should get. Who is the top student, the middle, the bottom, or are they all tied? Do you understand the mission?

Okay, how many say that student A was the top student? Nobody here. Anybody in Virginia Beach? Nobody. The middle student? How many think that student A was the middle student? 2 people here. So how many here think student A was the bottom student? Okay we have a forest of hands, let's say we have 24.

Student B. How many say B was the top? We have a forest here 22. Middle? Student B? Nobody. Bottom? Student B. Nobody.

Student C. There must be a forest in the middle. Am I correct? How many think that student C is the middle student? Okay so we have a forest. 21.

Notice that you have now agreed that B is the top, C is the middle, and A is the bottom. Is that correct? I would point out how professionally irresponsible you are. Because I would point out to you that student A was the top student in the class on two of the three of exams, and you put that student on the bottom. And student B did the top on one, middle on one, and the bottom of the third exam. This is your top student? And the student that got two out of three of the top grades in the class is the bottom student. Come on. What is going on here? You can see why I say that so many teachers goof up at all levels. Right here at ODU you are getting professors who are giving awful grades because they don't know how to combine grades.

The rules are that one student got an A, one a B, and one a C; remember that rule? It wasn't that student A failed one test; he got a C. What you really did, if you look at your scores, is you didn't pay any attention to tests one and three and you used test two as your entire grade. Because A is the bottom, B is the top, and C is the middle. You didn't pay attention to any other scores; you paid attention only to test two. You didn't intend to do that, at least you shouldn't have, because that wasn't the rule of the game, the rule of the game was you should pay attention to all three tests equally. What went wrong? What happened? Well, it's the concept, and you had it right, that when the range is only two versus the range being ten, that the range being ten absolutely overwhelms the other. So it doesn't make any difference what the students get on the tests with a low range. This is an extreme, but very real, example of what goes on in classes. We don't realize how to combine grades. To combine grades accurately, you have to have ranges of ten or two for all of the grades.

To make the ranges ten, you have to multiply 20 times 5 is a hundred and 18 times 5 is ninety, now you have a range of ten. This becomes ninety-five.
You have a range of two to make that ten, this has to be 150, 140, and 145. Now we can add them together. 110 and 150 is 260 and 255, is that right?
And 90, 105 and 145 is 250. So the right ranking for these is student A gets and A, student B gets a B, and student C gets a C.

Student A grades: 20, 10, and 30
Student B grades: 19, 20, and 28
Student C grades: 18, 15, and 29

This tends to be really confusing. What's going on here is that you have two choices. One is to understand it and the other is to avoid it. You can avoid this problem if you always put standard grades into your grade book. If you always change your grades to standard grades, a, b, c, then you can add them together. But if you leave them as points, you can't add them together.

Teachers give meaning to points however they choose to. Points don't mean anything until you give them meaning. I didn't tell you what the points should mean. I'm only saying if you were equally satisfied with the performance on all three tests that's one of the premises. If you really believe that on each test, one student got an A, one got a B, and one got a C, then how do you combine the grades? Notice that in the class we have here, we use raw points because we choose to have the points that we give you criterion-referenced rather than norm-referenced. In other words, 90-100 is always an A, 80-89 is always a B, and 70-79 is always a C. And remember, whenever we get a result that we don't like, for example if we goof up on a question, what do we do? We add a point to you or we do something so that the points that goes in the book mean what we want them to mean. And we say, by the way, that we know everybody needs some slack so we always give you an extra point. A 21-point quiz but we only count it for 20. All of that is deliberate. It has nothing to do with arithmetic; it has to do with instructional policy and how we're going to run the class. But having decided that, then we can add the points together fairly because we know what we're adding. If you wanted one of those tests to count double, you'd change those scores to 3's, 4's, or 5's and then double the 5 to 10. It then counts double because it will also double the range. In fact, what I recommend that you do (this is the easy way so you don't have to remember all this garbage), is that you always enter the scores in your grade book as standard scores. And I recommend a twelve point scale: A, A-, B+, B, B-, 12, 11, 10, ... so your top score is always 12 and your bottom score is always 0. So you know what grade you are giving and you always enter that grade. Then if you want something to count double, you double it. At the end of the semester you have a bunch of scores and the ones you want to double, you double, and the ones you want to leave the way they are, you leave. Then you add them all up and you divide by however many trials you had to come up with your average. If your average is 11.2 then that's an A-. That's a very easy, automatic correction and you don't have to remember anything about this range bit. But if you start entering raw points in the grade book, you're going to be penalizing people who you don't want to penalize. I'm not telling you whether the quiz should count double or triple or half, or the homework paper or anything else. You decide what its going to count, but after you've decided, let's have it count for what you've decided rather than something else. Standard scores. Okay. One more time.

Back to our original example of A, B and C. The problem on that example was that test two had a range of ten. In other words, student A got a 10 and student B got a 20. That just didn't feel the same to you as student A getting a 30 and student B getting a 28. In other words, 28 looked a lot closer to 30 than 10 did to 20. Mind you, the way you assign points is arbitrary. People sprinkle points like salt and pepper. Points mean whatever you, as the teacher, say they mean. But after you've given them, the way you combine them together doesn't always mean what you think they mean. And to combine them together, they have to be in some sort of a standard currency. Like, for example, if I buy a ping pong ball for a dollar and I'm going to sell it for a yuan when I go to China, one yuan doesn't necessarily equal one dollar. I need to know what the conversion rate is. The conversion rate between yuan and dollars is 8. So, I have to multiply yuan by 8 before I get something that's equal to a dollar. So if I have ping pong ball in the US for a dollar, in China the same price would be 8 yuan. So if you have one grade that has a different level of range than another grade, you have to convert it so that you're talking about the same unit of measure. The way you do that is you always enter standard scores. If you enter points you have to worry about being very sophisticated in terms of knowing how to deal with range. If you enter standard scores you don't have be sophisticated at all. So the lesson is always enter standard scores. That's the lesson. Always enter standard scores so that you automatically correct for any differences in points.

 

What is the simplest way to keep accurate, fair grade records?
No ferret question


Answer Here