At a conference last year, social studies teacher Jonathan Keiler showed a series of slides contrasting the high Advanced Placement passing rates of Mr. Smarthead’s government class with the woeful results from Mr. Dumbhead’s world history class.

“Who is Mr. Dumbhead?” Keiler’s next slide asked.

“ME,” he revealed.

Keiler wasn’t ashamed, just annoyed. He thought his students did well when the difficulty of the course and their previous records were taken into account. Yet his principal had demanded better results anyway. At Prince George’s County’s Bowie High School, he was told, 50 percent passing was the goal for AP. His 40 percent looked bad next to Mr. Smarthead’s 60 percent.

“I don’t like the policy because it is arbitrary and not well thought out,” said Keiler, a former lawyer who is one of the rare teachers with National Board Certification.

His complaint exposes an overlooked facet of the national debate over using student test scores to rate teachers. There is no written rule that AP teachers have to reach a certain passing rate. The College Board, which runs AP, would not stand for that. But since principals usually have the power to say who teaches the courses and who does not, AP teachers sometimes worry they might lose the coveted assignments if their numbers slip.

AP exams usually provide the most difficult academic challenge in our schools. Classroom teachers cannot cover up inadequate preparation with easy exams because the AP exams are written and graded by outside experts. If an AP teacher has a strong class of students in an affluent school, and few pass the final exam, the principal knows that she has a problem. She needs to help the teacher improve. If that doesn’t work, she must find someone else to teach that course.

As Keiler says, it depends on the situation. He says Mr. Smarthead is an excellent teacher and a friend. His quarrel is with the principal — no longer at the school — who did not recognize that his class was unlikely to do as well because, unlike Mr. Smarthead’s students, the students in his class were not selected for their academic strength, had less time to learn (Mr. Smarthead’s class met every day; Keiler’s every other day) and took an AP exam with a lower national passing rate.

Prince George’s County schools spokesman Briant Coleman defended the principal’s target. “Without a goal, what incentive does a school, department or teacher have to significantly change structures for better performance?” he said.

Keiler says his students still made good progress even if they didn’t get passing scores on the AP exam. Many got 2s on the 5-point exam, just below the passing mark of 3. At least one study indicates that students with 2s do better in college than similar students who don’t take AP. His 3-and-above passing rate on that exam was also better than that of any other Prince George's school except the magnet high school Eleanor Roosevelt.

In nearly every school, different teachers find themselves with different mixes of students. The new teacher evaluation systems attempt to allow for that by measuring not how high their passing rates are on the state test, but how much their students improve.

That value-added approach makes sense, except for one unfortunate habit of us parents, taxpayers and voters. We, like Keiler’s principal, still care about the overall passing rate.

If you teach in an affluent school where the passing rate is routinely 90 percent because of the favored backgrounds of the students, we consider you a good teacher. If you are in a low-income school where the passing rate is 20 percent, we often assume you are not as good as the teacher with the 90 percent passing rate no matter how much your students improve.

I don’t think we should stop using tests as one of the ways we assess performance, but we should recognize that a high passing rate doesn’t tell us much. Unfortunately that goes against our instincts. We still see some teachers as Mr. Dumbhead no matter how good they are.