Making the Grade - 3

So if percentage grading doesn't make it and the various scaling schemes have little to recommend them, what do I recommend?

Before I answer that I suggest you read ASSESSING TRUE ACADEMIC SUCCESS: THE NEXT FRONTIER OF REFORM by Dan Kennedy of the Baylor School in Chattanooga, Tennessee. This article deals with a lot more than scaling test and is well worth reading. Dr. Kennedy is the co-author of a popular calculus textbook and has been involved with the AP Calculus program for many years. His wide ranging ideas on assessment make a lot of sense (to me at least). 

As I discussed previously, scaling is often used to raise students' grades when the teacher has given a test that is too hard, when the mean score was too low. Dr. Kennedy writes, "If you want your students to think on the test, then you will have to give them a question for which they have not been fully prepared." Certainly posing questions for which the class is not fully prepared will make the test "too hard." His answer is to stretch the students by asking challenging questions on the tests and the protecting then students' grades by scaling the results. He points out that "[you] control... the grading algorithm." His conclusion is that "we ought to present students with challenging, relevant, useful, and varied assessments all of the time, and then scale the grades to conform to our expectations." (Emphasis in the original)


Here is Dr. Kennedy's suggestion on a method for scaling test grades. Take two order pairs. The first is (class mean on this test, desired class mean) and the second (the highest test score, 99). Write the equation of the line containing these two points and use it to scale the grades. (The "desired class mean" can be set in advance and adjusted slightly and can be different for different level classes. It can be the historic mean for each course.)

He finds that,

Freed from the shackles of unreasonable numbers, I can now challenge my students to do just about anything, then see how far they can go. They, in turn, have been freed from the burden of getting a certain percentage right, so they can concentrate on doing as much as they can as well as they can.

What more could you ask for? 


Again, I suggest you read  the entire article. It suggests other methods of assessment that the author has used in mathematics classes.


While no scaling method is perfect and will work for everyone, I think that this one has a lot to recommend it. First and foremost you can and will ask challenging questions. You also will be able to test that do not total 100 points. If your test is too long for the time allowed, well it's too long for everyone and, because of  the scale, no one will be hurt.