Making the Grade - 2

In a previous post I discussed percentage grading. The big problem with percentage grading is that it does not allow for differences in the difficulty from test to test, class to class or year to year.

So if you do not use straight percentages, what do you do? You "curve" or "scale" the grades.

But curving (I'll use that term from here on) can be and is being, done lots of ways. And some of these may be worse that percentages. Let's look at a few common ways and see how they work.

(Disclaimer: I've used some of these myself and with the benefit of hindsight wish I had not.)

One common approach is to list the grades in order from highest to lowest and look for natural breaks to divide them 4 or 5 groups. The high group gets As (or numbers above 90), the next group gets Bs and so on. This is often used when the grades were not as good as the teacher would like; it is never used when the percents come out okay as it may lower grades. It's just a way to recover from a hard test.

Then there is the "Square Root Curve." Here you multiply the square root of the percentage correct by 10 to calculate the grade. An 81 becomes a 90, a 49 becomes a 70, a 36 becomes a 60, etc. This has the effect of raising all the grades and raising the lower grades the most. (Max/min question: What grades is raised the most? Answer 25.) Now even if you use this all the time and give very easy tests you will not lower anyone's grade. But what is the assumption behind this? Darn if I know. You just raise everyone's grade using some pseudo scientific formula. Maybe it appears "mathematical" since the formula has the strange radical sign in it. I've even seen a state exam that I am pretty sure was curved this way.

While we are on state exam, I also saw one where I am pretty sure they used 4 data points: 0 was scaled to 0, 87 (the highest possible score) to 100, the minimum passing grade to 55 and a high score (distinguished or something) to 85. Then they used a cubic regression through these 4 points and used that to curve the other scores. Obviously, a lot of mathematical thinking behind that idea.

One could normalize the scores and then curve using the bell curve. 3 standard deviations above the mean = A, two a B, one above to one below a C, 2 below a D and 3 below an F. (Of course with a small class you may not get any As or Fs.) This makes the assumption that the grades should be normally distributed. I don't think that's true especially in an AP class. Also most of your grades will be C: that won't do.

Then there is the tried and true: throw all the paper up the stairs and those that go the highest get an A. Good as any.

The AP exams are curved. The goal is that the same amount of knowledge will get the same grade from year to year. This is done to allow for the difference in difficulty of the exam from year to year. By reusing questions from previous exams the Educational Testing Service can judge the difficulty of the current test compared to previous years and set the cut point accordingly. The scores are not normalized and there is no predetermined percentage of students who are given a 5, 4 ,3 2, or 1. This is great for the ETS, but not practical for a single teacher.

So what to do? My next post will discuss the best system I've hear of. Perfect? No, but pretty good.