West Potomac High School in Fairfax County and Oakland Mills High School in Howard County are as close as schools come to being twins. Both are in affluent counties and serve ethnically and economically diverse populations. Forty-seven percent of West Potomac students and 52 percent of Oakland Mills students are black or Hispanic. Thirty-eight percent at West Potomac and 31 percent at Oakland Mills are from low-income families.

But when I indulge in my obsessive comparison of schools by their college-level course programs, significant differences emerge. Oakland Mills often bars students from taking Advanced Placement classes if they don’t have B’s in previous courses. West Potomac lets in everyone who signs up and pays the test fees. The AP test participation rate at West Potomac is three times what it is at Oakland Mills, but the passing rate on tests at the Fairfax school is lower: 61 percent, compared with 78 percent at Oakland Mills.

That wide gap in approaches to challenging courses is why I started rating high schools 13 years ago by how successful they were at giving students a taste of college trauma. In a national context, as college-level programs such as Advanced Placement and International Baccalaureate have become the prime means of preparing students for higher education, giving more students those opportunities has become crucial and controversial. Only half of students who go to college get to take college-level courses in high school, which many educators think is fine and others think is wrong. That controversy is one reason my rankings have drawn such attention.

The national list is being published now for the first time by The Washington Post. We call it The High School Challenge.

The idea for the list came to me as I was completing a book about America’s best public high schools. I kept running into the same mindless policy: Schools refused to let average students take the college-level courses and tests, reserving them for the better students. Research and common sense suggested that C students would learn much and be readier for college if they also took AP, but few schools appreciated that.

To illuminate the issue, I began ranking schools in 1998 on participation in AP and IB tests. Later, I added the Cambridge Advanced International Certificate of E ducation exam to what I named the Challenge Index. The national list started that year in Newsweek, the local list in The Post. This year’s national ranking moved to The Post after The Washington Post Co. sold Newsweek last summer.

The Challenge Index calculation is simple. I wanted everyone to be able to understand it and use it. Add up all the AP, IB or AICE tests taken in a given year. Divide by the number of graduating seniors. The target I set is also simple: Every school should reach a ratio of at least 1.000 — that is, as many college-level tests taken as diplomas issued. Any school that does will make my national list, unless its passing rate on those tests is unusually low or the school is unusually selective.

School leaders in Larchmont, N.Y., Winnetka, Ill., Beverly Hills, Calif., and elsewhere were puzzled and annoyed when I began this exercise. Because schools in those places allowed only their best students to take AP, they ranked lower on my list than some daring schools in less-wealthy communities that opened AP to all who wanted to work hard.

By coincidence, Washington area educators began a massive reform of their rules for placing students in college-level courses and tests. Influenced by the same pioneering teachers who had shown me the power of challenging more students, high schools in Northern Virginia, Maryland and the District created in this metropolitan region what continues to be the heaviest concentration of college-level courses in the country.

My list finds that only 1,910 U.S. public high schools, about 7 percent of the nationwide total, meet the target ratio. In the Washington area, 75 percent of public high schools do.

Some other regions do well, but not that well. Numerous school systems, wary of challenging students they believe are unready, hold the view that AP, IB and AICE are appropriate only for those with A or B averages. Some urban schools are discouraged by low test scores and therefore don’t encourage students to take AP.

But in some low-income communities, schools encourage as many students as possible to take AP, even if they rarely pass the exams, so they will get a sense of what college demands.

My method differs from how high schools are usually rated. Some lists use average SAT or ACT scores, state test scores or the percentage of graduates who go to four-year colleges. Those results are often so influenced by family income that you could get similar rankings by averaging the square footage of the students’ homes. Many principals and teachers have told me they prefer a measure such as mine that puts weight on efforts of school staffs to prepare students for college. They say that shows the quality of the school rather than the economic status of the parents and gives schools full of impoverished students a rare opportunity to shine.

The list draws attention in part because readers love rankings of any sort. It also is regularly denounced by educators who say it is wrong to rank schools based on just one number.

One of the most revealing arguments about this was between me and Patrick Welsh, an acclaimed English teacher at Alexandria’s T.C. Williams High School who frequently contributes to The Post. When we debated the issue in Outlook in 2005, Welsh said: “You’ve unwittingly created an out-of-control monster, a smoke and mirrors numbers game, the equivalent of ranking the teams in the NCAA basketball tournament on the basis of the number of players who got in the game, instead of the final score.”

I thought the metaphor worked better for me, since a school does not exist to beat other schools but to raise the achievement of students. Getting a lot of them into games is likely to sharpen their skills.

Welsh said adding students who read way below grade level into AP meant high achievers weren’t being challenged and low achievers were overwhelmed. I said he ought to visit Wakefield High in Arlington County, a five-minute drive from T.C. Williams. The two schools were demographically similar, serving large numbers of black or Hispanic students, many from poor families. Yet Wakefield teachers urged everyone to try AP and got award-winning results. The month after our debate, Wakefield had a Challenge Index rating of 2.030, compared with T.C. Williams’s 1.494. The percentage of AP tests passed by Wakefield students was higher: 51 percent to 39 percent. Thirty-five percent of the graduating Wakefield senior class had passed at least one AP exam, compared with 20 percent at T.C. Williams.

Mike Grill, the AP coordinator at Wakefield, told me then: “I don’t have patience for teachers who make excuses to explain why students can’t learn in their courses. The issue is not ‘why they can’t learn,’ but rather ‘why can’t you teach them?’ ”

Average students barred from AP usually don’t complain. They are used to being overlooked. But a few protest. Kerry Constabile at Mamaroneck High School in the New York City suburbs was upset when her request to take AP American History was denied because she had less than a B in social studies her sophomore year. She assigned the AP course to herself, getting the homework assignments from friends. She got a 3 on the 5-point AP exam. She was convinced that she would have done better had the school let her in the course.

Students in Howard have the same problem. If they don’t have at least a B in 10th-grade social science or a teacher’s recommendation, they can’t take AP U.S. history. Clarissa Evans, the county’s executive director for secondary curricular programs, said, “we have more work to do” in that area. Howard got a College Board award for improving AP access but still trails many other districts.

Frank Eastham, principal of Oakland Mills, said his teachers have been talking about ways to give more students exposure to AP, “but some think we are setting kids up for failure if we let them take a course for which they haven’t gotten the prerequisite class.”

At West Potomac High, AP Coordinator Drew Hamlin said: “We stress that success in AP courses is achievable for all students who are driven to succeed.”

The situation is worse in inner-city schools, where most students fail the AP exams. But those students often lack strong preliminary courses to get ready.

The inspiration for the list came a decade before I started compiling the AP participation data for schools nationwide. In 1987, I had the AP results from just one school — Garfield High in East Los Angeles. Eighty-five percent of the students were from low-income families, and AP courses had been rare. A few teachers changed that by upgrading lower-level courses so students would be ready for AP.

In 1987, 85 of the 129 Garfield students who took an AP calculus exam got a passing score of 3 or better. Amazingly, 26 percent of all Mexican American students in the country who passed an AP Calculus exam that year were from Garfield.

The famous math teacher Jaime Escalante had about half of them, but the other half were taught by Ben Jimenez. He was not a celebrity, just a competent, hard-working educator.

That statistic has haunted me since. I was glad to see the Garfield teachers recognized, but there was a darker side to the data. Why hadn’t the thousands of other schools in the country with underestimated Mexican Americans (or other kinds of students) done what the Garfield teachers had done? What was stopping them?

Take a look at the new national list and you will see which schools are asking themselves that question and trying to do something about it. I wish there were many more schools on the list than there are.