Students rush by between classes at H-B Woodlawn Secondary Program in Arlington, Va. in Nov. 2014. The school ranked No. 1 in the Washington region on The Washington Post’s 2015 America’s Most Challenging High Schools list. (Melina Mara/The Washington Post)

When my wife and I lived in Scarsdale, N.Y., in the 1990s, I was surprised that our son Peter had to take an entrance exam to get into the Advanced Placement U.S. History course at the local public high school. I remembered the five years I spent writing a book about an inner-city East Los Angeles school that had great success letting anyone who wanted to work hard have a chance at tackling AP.

I discovered that that California school was an exception to a national, unwritten rule restricting access to those courses. Most high schools did not go as far as Scarsdale in requiring entrance tests, but students usually could not get into college-level AP courses unless they had a strong grade point average, a good grade in the AP subject the year before or a teacher’s recommendation.

That seemed idiotic to me. Why would anyone stand in the way of motivated kids who would be better prepared for college if allowed to struggle in the most demanding courses available? When we moved back to the Washington area in 1997, I saw the beginnings of a change. The Fairfax County schools opened their AP and International Baccalaureate courses to all students. Not long after, nearly every district in the metropolitan area had done the same.

Students entering the Signature School, a charter school in Evansville, Ind., which ranked 10th on this year’s America’s Most Challenging High Schools list. (Courtesy of the Signature School )

The Washington region has become a national model for challenging high school students. Many more students here have a chance to do AP, IB or the Cambridge University courses that can lead to the Advanced International Certificate of Education (AICE) diploma. Many more succeed in those courses than do in other parts of the country. According to the College Board, Maryland ranks first and Virginia third in the nation in the percentage of graduating seniors who have passed an AP exam.

Yet a survey I did as part of the latest Washington Post America’s Most Challenging High Schools list — the 2015 edition was released Sunday night — shows many schools still keep average students out of their best courses even though research shows they do better in college when given that opportunity.

Thirty-four percent of the 1,403 high schools that responded to the question said they had traditional rules barring enrollment in AP, IB or AICE if a student lacked the necessary GPA, teacher’s recommendation or good grade in a previous course. This suggests that many U.S. schools still have such rules, since I was surveying only the top 11 percent of schools as measured by participation in AP, IB and AICE.

One reason why 89 percent of U.S. public schools don’t make The Post’s list is that rules limiting access are still widespread. About 75 percent of Washington-area public high schools make the list every year.

The list is based on what I call the Challenge Index. Schools qualify only if they give at least as many AP, IB or AICE exams in a year as they have graduating seniors. They are then ranked by their tests-to-graduates ratio. I also include a sampling of private schools.

When I started the list in 1998, I could find only 243 public schools that qualified. The 2015 list, based on 2014 data, has more than 2,300 schools.

That’s progress, but not nearly enough. In one recent year, 300,000 students who showed readiness for AP based on their PSAT scores were denied a chance to take those courses, according to a College Board study. That waste of time and talent is rarely discussed in education conferences or political platforms.

Students gather for lunch in the foyer of the Schools Without Walls in the District. It ranked second in the Washington region on the America’s Most Challening High Schools list. (Marvin Joseph/The Washington Post)

One Texas study showed that even mediocre students who failed an AP exam had better grades in college than similar students who took no AP courses at all.

Qualifying for the Post list is not that difficult, and schools know how they can make the list and move up on it. A school need only have half of its juniors and half of its seniors take one AP course and exam in each of those years.

Educators sticking to the old access rules “believe that schools are a true meritocracy, which they are not,” said Carol Burris, New York’s 2013 High School Principal of the Year. “Studies consistently show that students from upper middle homes have an advantage in placement in ‘high track’ classes that goes beyond test scores and grades. There remains a stubborn resistance to opening opportunity.”

Daniel A. Domenech, executive director of the American Association of School Administrators, was superintendent of Fairfax County schools when they opened AP and IB classes to all. The district required that all AP or IB students take the independently written and graded exams at the end of those courses, and the district paid the test fees. Many more students passed AP and IB exams than before. Even in schools with a majority of students from low-income homes, achievement soared. “Education should be inclusive, not exclusive,” Domenech said.

Some administrators at schools that are on the Post list but still have the old rules say they try not to lock the door to AP.

“Students have the option to override a teacher’s recommendation,” said Parry Graham, principal of Nashoba Regional High School in Bolton, Mass. Letting anyone into AP “is a positive idea so long as the school is providing the academic supports necessary . . . to experience success,” he said.

Jeffrey J. Thoenes, principal of Williamston High School in Williamston, Mich., said his students must have at least a B in a previous course in the AP subject and a teacher recommendation to get into an AP course. An override form allows a parent to put a student in AP without meeting those requirements.

“The form is seldom used, but it provides clear knowledge to all parties that the students will be in the class but may not have strong prerequisites,” he said.

That seems like ancient history to Washington-area AP, IB and AICE teachers. They tell stories about students who struggled in their classes but found later that the experience eased their adjustment to college.

That message is spreading, but more slowly than it ought to in a country where high school students on average have made no significant reading or math gains in 40 years.