AP Calculus Reading

I just returned from the 2007 AP Calculus reading in Louisville, Kentucky. It was a nice experience overall, and I might participate again.

What am I talking about? AP, of course, is a program where high school students take classes that provide them with content and problems at the college level. Educational Testing Services (ETS) administers tests near the end of the school year to assess the student's learning. If the student does sufficiently well, most colleges will grant credit in the corresponding course.

Unlike most standardized tests, AP exams have a free-response section that amounts to writing an essay (in some courses) or solving problems that require some serious thought. In AP Calculus, that includes tying together different ideas into each problem. These free-response sections cannot (yet) be graded by a machine, and require a human to look at each reponse and evaluate its content.

ETS goes to great lengths to ensure that papers are graded in a standard way. This year, they hired approximately 800 graders for more than 270,000 exams. The 6 problems on the exam kept most of us busy. Each grader examines hundreds of papers every day. Every grader is a different human being, and this runs the risk that certain readers (such as the current author) will grade a response more severely than other readers. This would not be fair to the students.

To avoid this, ETS commissions a team to prepare for each problem a simple, focused rubric to determine the grade. The principles of drawing up a rubric center around certain basic ideas:

• Did the student use the proper tool?
• Did the student arrive at the proper solution?
• Did the student provide sufficient justification for the response?

and so forth.

A designated question leader discusses all these considerations thoroughly with the readers in a briefing before they start that problem. The briefing typically lasts at least an hour. It includes a review of the rubric, a standard solution that the team prefers, details on anticipated alternative solutions (or attempted solutions) that some students provide, and a review of some sample papers that the team has already read, and how the readers should grade them. These sample papers make a big contribution to understanding the rubric.

I was also impressed by the professionalism of the readers selected for the reading. By and large, they executed their duties with thorough precision. Naturally, situations arise where a student provides an interesting response that does not fit neatly into the rubric; in such cases, the reader first discusses the response with a fellow reader. If they can't resolve it, they turn to their table leaders, and that settles virtually all questions. Rarely, a question will have to be referred to a question leader. Everyone I worked with took seriously our dual responsibilities to be fair to the student and responsible to the standard.

Of course, some responses contain no mathematical content. I was treated to several such responses this year, including:

• a comic strip that featured Superman saving someone, then getting eaten by a giant monster;
• a bizarre paragraph that started with some statement about invisible walls around us; and
• an appeal to "Create good karma" by writing the correct answer in the space provided and giving the student a correspondingly good score. (Sorry, chum; I don't believe in karma.)

Such responses often include student gripes blaming the teacher's incompetence for their poor performance. Once student even bragged,

I don't care. I already got into the college I wanted anyway.

Ahhh, children! our nation's future.

One of the calculus readers was a priest, so there was a daily Mass available, and I attended.—Uhm, when the alarm went off. In the evenings I tried to do research (I finished a program I've been working on for quite a while) and took some walks around Lousiville, which is a nice enough area near the Convention Center. The visitor's center had a neat display on Kentucky bourbon whiskey. I can't comment further on bourbon, since I don't ordinarily drink, and I've never had bourbon, and I wasn't about to start for the AP reading. A lot of readers visited Churchill Downs (some lost money on the horses, one won $0.83 or something like that) and others visited the Louisville Slugger factory/museum. Most commented favorably on the Fourth Street Live! district. The upper floors of the Galt House have a great view of the city and the Ohio River, if you don't mind having to walk up halfway in order to catch an elevator. (When 1000+ readers return from a busy day, the wait for the elevator is long, unless you're willing to catch it twelve stories up, after it's emptied out some of the riders.) I have to confess that I liked the area, and one day I'd like to take my family to visit.

Maybe. First I want to take them to Flagstaff, or to Yellowstone, or to Gaeta (Italy), or to...