A Different Kind of Curve
Next month, I'll start my 18th year as a teacher. One thing I've learned over the years is there's always more to learn. Most of the time when you turn a good idea into reality, it works for a little while before some kids figure out a way to circumvent it. But one idea a friend of mine and I came up with many years ago still works well for me today. It's a curve for grading tests that actually works!
What does that mean, that it works?
Everyone's heard of the bell curve of old, but that's been widely denounced as unfair. A certain percentage of students make A's and a certain percentage make F's, even if only a few points separate the highest and lowest grades. If the highest grade was 100 and the lowest a 90, you would still have students making F's. My friend and I agreed that was ludicrous.
Another common method of curving grades is to simply add a certain amount of points to every student's grade, the same amount to all students. Typically, if the highest grade is a 95, you'd add 5 points to everyone's grade. That certainly seems more fair, but what does it achieve, other than just boosting everyone's grade a little? It helps everyone, and it helps everyone by the same amount of points, but it still leaves something to be desired.
We were looking for a curve that would address the problems present in any grading system. I remember when the state of North Carolina passed a law that all public schools would use the 90-80-70-60, A-B-C-D-F grading scale. When I heard it, I scoffed because I knew I could write a test that anything over a 50 is an A and make sure it was so hard that nobody could make an A. I could write a test and make it take a 95 to make an A and everybody could make an A. It all depends on how hard you make the test.
Another issue we ran into was students who scored so low on an exam that it tanked their grade for the rest of the course. If you have a test where the highest grade is a 95 and the lowest grade is a 5, (Yes, I've had students earn 5 or fewer points on a 100 point test) adding 5 points to every score brings that low guy up from a 5 to a 10. If you give three tests per grading period, it's still practically impossible for your lowest to recover and pass.
The question we posed to each other was, "How can we create a curve that controls for the difficulty of the test, and prevents students' grades from falling so low there is no hope for them to recover and pass?
We came up with a system that maps the highest score to a 100 and the mean score to a 75, forcing the recorded grades to average a 75. We then use those two points to write the equation of a line that takes as input a raw score and converts it to a curved score.
Usually, this curve raises high grades a little and low grades more. But most failing grades typically remain in the failing range. However, they're lifted high enough to keep the student in that zone of possible recovery instead of dropping into a hopeless abyss.
A couple of caveats. In rare circumstances, if the raw scores fall just right, some students, typically on the lower end of earned scores, have their grade reduced by this curve. In these cases I typically revert to the old add-the-same-number-of-points to everyone's grade. This usually happens when there's a relatively small gap between the average score and the highest score.
It should be obvious this curve only works if the raw score mean is less than 75. Otherwise you're definitely forcing grades down. So I don't typically curve when the average test score is 75 or higher.
This idea came to life when I was working to increase the number of students taking rigorous math courses. Though some were successful, a significant number of students were scoring so low that it put them in a hole they could not climb out of. Too many were failing so fewer were willing to accept the challenge to take upper level math courses. This curve gave me a way to keep writing rigorous tests, eliminate or reduce the idea that upper level math courses are impossible to pass, and to keep most students in a zone where they could recover from a completely bombed test grade and still pass the course.
Feel free to share what works for you in the comments below!
Comments
Post a Comment