In the 30 years I have been studying the growth of Advanced Placement and other college-level courses in American high schools, no development has been more surprising or controversial than what I call the “Catching Up Schools.”

That is my label for about three dozen schools across the country in low-income neighborhoods that offer an unusual number of AP classes despite the fact that very few of their students are able to pass the difficult three-hour final exams.

Each year, I rate local and national high schools based on AP test participation. My latest rankings appeared this week. In 2008, I removed schools from the main lists of what we call the “High School Challenge” if their passing rates were below 10 percent. I put them on a separate “Catching Up” list. I calculated that once a school with high participation rates reached a 10 percent passing rate, it was producing as many successful AP students as a school with average participation and passing rates.

Many readers said the educators running these schools were hurting their students by having them take tests they could not pass, and doing so only to look good on my lists.

I disagreed. I had spoken to principals and teachers in several of the schools and was convinced if the teaching was good, struggling in an AP course would be a better educational experience than sliding through the relatively easy regular course that was the only practical alternative in these mostly urban schools. The students shared that view. They knew they were unlikely to pass the AP exams, but they said they were learning much and were more likely to succeed in college having experienced the academic demands of higher education. Several who went to college said that proved to be true.

One large study in Texas indicates that mediocre students who got a 2 on an AP exam — just below the passing mark of 3 on the 5-point scale — did significantly better in that subject in college than similarly mediocre students who did not take an AP exam in high school.

Principals said they hoped their passing rates on AP exams would rise each year as their AP teachers developed better skills and as the teachers in lower grades did a better job preparing students for AP.

Is this happening? I looked at the four years of data I have on Catching Up schools’ passing rates. There is both bad news and good.

Here are the local high schools that would have appeared on my national list of challenging schools except for their passing rates. I have ranked them in the order they would have appeared on my list, with the change in passing rate from 2008 to this year:

●SEED (D.C. charter) 2.5 to 8 percent;

●Hospitality (D.C. charter) 3 to 0 percent (since 2010);

●Crossland (Prince George’s) 3 to 2 percent;

●Forestville (Prince George’s) 7 to 3 percent;

●Cesar Chavez-Capitol Hill (D.C. charter) 10 to 7.4 percent;

●Surrattsville (Prince George’s) 3 to 1 percent;

●Fairmont Heights (Prince George’s) 7 to 2 percent.

Those are not encouraging numbers, although SEED at least is making progress. I have left out schools with similarly low passing rates whose participation rates were not good enough to make the national list.

The bright spots are schools that were once on the Catching Up list but are now above 10 percent passing, including Thurgood Marshall (D.C. charter), from 0 to 26 percent; Friendship Collegiate (D.C. charter), from 1.2 to 12 percent; McKinley Tech (D.C.), from 5 to 13 percent; and Columbia Heights (D.C.), from 8 to 11 percent.

I am abandoning the Catching Up list and will add the Catching Up schools to the two regular lists, but with their low passing rates marked so readers will know what is going on. Their principals say they want to improve. Some have done so. We shall see how seriously they take their commitment to not only give students a challenge, but also see that more of them meet it.