Teacher Christopher Budano prepares his students for the Advanced Placement tests at Potomac High School in Oxon Hill, Md. (Andrea Bruce/The Washington Post)

In two landmark studies, quantitative data expert Nat Malkus has confirmed the rigor of the most successful high school program of the past three decades, Advanced Placement, and revealed what might be a troubling decline in AP use in small and rural schools.

Malkus is a research fellow at the Washington-based American Enterprise Institute with much experience investigating educational finances, school choice and standardized testing. Since, he said, “AP courses have become the primary avenue for delivering advanced coursework in public high schools,” has the program expanded too quickly and been dumbed down as a result?

The cover of his first study shows the growth of AP students from 330,000 in 1990 to 2.2 million in 2013. That extraordinary surge brought a drop in the percentage of students who passed the three-hour AP exams, which can earn college credit. But the number of students passing AP exams has increased greatly, raising the level of American high school education like nothing else since Los Angeles teacher Jaime Escalante led the introduction of AP to ordinary public schools in the 1980s.

Malkus looked at the scores of AP students on the National Assessment of Educational Progress math tests in 2000, 2005 and 2009 and found no signs that the achievement of graduates with AP course credit had been watered down. He wrote, “The extent of the program’s growth alone is impressive, but AP’s apparently effective quality control during a period of extensive growth is much more so.”

Malkus then analyzed the differences in AP success between students of various ethnic and income groups and looked at the changes in the number of public schools offering AP. The cover of his second study shows the portion of U.S. public schools using AP was 71 percent in 2000, climbed to 79 percent in 2008 and dropped to 74 percent in 2012. Although the number of public schools using AP has continued to increase, from 9,665 in 2000 to 14,729 in 2014, the recent drop in the percentage of public schools using the program raises new issues.

For several years, critics have said that AP and similar programs were losing support in the best schools in the most affluent neighborhoods. This is false. What Malkus discovered was different, a drop in the percentage of public schools using AP that are in rural areas or that have fewer than 500 students. The percentage of small public schools using AP increased 11 percentage points from 2000 to 2008, then lost nearly all of that gain by 2012. The percentage of rural schools with AP gained 16 points from 2000 to 2008, then dropped five points by 2012.

Malkus says those schools may be cutting their AP programs because their students are not ready for them, though I would like to find such schools — Malkus doesn’t identify any — to ask them about that.

“In schools that do not have sufficient numbers of students prepared for AP courses, leaders would be wise to focus their limited resources on improving student proficiency in the years leading up to high school,” Malkus wrote.

I think he is wrong about that. Districts have no incentive to prepare younger students for AP if the courses are not up and running. Teachers have to gain some experience teaching AP to be ready for younger students learning how to handle long reading lists and analytical writing.

Malkus suggests online or video-conference AP courses as one solution for schools that lack capable AP teachers. He says more data will be necessary to see whether the decline in AP use among rural, small schools is a trend.

But he also acknowledges that because such schools have so few students, their drop in AP involvement has not changed the fact that the number of students in AP and similar programs like International Baccalaureate and Cambridge continues to increase significantly. That means many more students are having challenging academic experiences than when I was in school. That is a good, big trend.