# Percentages Don’t Make the Grade

Well, the AP exams have been written and the dust has settled. Folks are posting their answers on the Community Bulletin Boards. (I never post mine – too many mistakes.) The other thing that always gets discussed at this time of year is whether this year’s exam is more difficult or less difficult than last year’s.

I am sure this year’s was more difficult or less difficult than last year’s because it is impossible to make two exams of the same difficulty.

But it doesn’t matter.

The grades will reflect, as best as possible, that a student knows as much calculus as students with the same score did last year. That’s the important thing.

Because it is impossible for anyone or any group to make two exams of the same difficulty, percentages tell you nothing. The percentage of the number of points that a student earns out of the number possible tells you just that and nothing more. If the tests are not of the exact same difficulty, then percentages are meaningless.

What to do?

The Educational Testing Service (ETS) who writes and administers the AP exams for the College Board carefully pretests each question. Also, there are a number of questions from last year’s exam on this year’s exam. These questions, called equators, allow ETS to judge the difficulty of the other questions on this year’s exam compared to last year’s. It allows them to judge the ability of this year’s student cohort compared to last year’s. Each question is considered individually. Questions that score poorly or questions that identifiable groups of students do far worse compared to the entire group taking the test are not counted in the final score. (For example, in 2008 question AB 19 was not counted; too many missed it.) They compare the results of questions within each exam. With this information they “scale” the exams and decide on the cut points, the high and low raw scores that earn a 5, 4, 3, 2, or 1.

A teacher on a day-to-day basis cannot do so detailed an analysis. Yet we still need to give students grades. We need to scale the exams.  I was quite happy this year using a scheme Dan Kennedy suggested some years ago (see resources tab above). This worked quite well for me in BC Calculus and in 8th grade Algebra 1. Perhaps you have another system.

Percentages just don’t make the grade.

Update September 22, 2014: Matthew Braddock, Mathematics Instructor & Webmaster, at the Dr. Henry A. Wise, Jr., High School in Prince George’s County, Maryland sent me a GeoGebra applet that will calculate the grades using Dan Kennedy’s scheme described in the link above. It runs at a website so you do not need GeoGebra on your computer or iPad to use it. Simply enter the information and it will do the rest. Thank you Matthew.

Update December 3, 2018. The link above is no longer active. This link is to a similar app by Dan Anderson on Desmos. Thank you Dan. For more on this scaling test see the post: On Scaling.

Updated: September 22,2014, Kennedy link fixed February 9, 2018

## 2 thoughts on “Percentages Don’t Make the Grade”

1. Pingback: Let ‘um Try! | Teaching Calculus

2. Good point about the tests varying in difficulty. Students have a hard time understanding that the tests are not exactly the same from year to year.

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