Every time Newsweek runs another list of "America's Best High Schools," using a formula I invented while living in Scarsdale, N.Y., I wait to see what new terrible things my former neighbors in that Westchester County village will say about me.

The latest list appeared May 9. Sure enough the Scarsdale Inquirer -- a fine weekly I still have mailed to me in Bethesda, Md. -- had a front-page item saying Mathews, the "former Fox Meadow man" (a reference to the Scarsdale neighborhood I lived in from 1992 to 1997), had ranked Scarsdale High only number 208.

An Inquirer editorial called the list "simplistic and misleading." Scarsdale High Principal John Klemme in an Inquirer op-ed said I was "off target." Edgemont resident Steven R. Cohen, in a letter to the paper, called the Newsweek list "malicious nonsense." Scarsdale High freshman Betsy Feldman, in an intriguing op-ed, said that "the notion of ranking is silly."

Knowing these were fine people who would, despite our differences, greet me pleasantly if I ever went back to visit, and having learned much from other critics of what I call the Challenge Index, I read all these assaults on my brainchild carefully and found some pleasant surprises.

The Challenge Index ranks high schools by student participation in college-level tests, particularly Advanced Placement and International Baccalaureate. It is a very simple measurement. I divide the number of AP or IB tests taken in May by the number of seniors graduating in June, and put on the Newsweek list every public school in the country that achieved what I consider a modest average of at least one test for every graduate. [For a more detailed explanation, go to http://www.msnbc.msn.com/id/7760504/site/newsweek/]

The Inquirer and Klemme got the formula wrong in their critiques. I count all AP or IB tests taken by all students, not just seniors as they said. But errors of fact and interpretation are to be expected because this way of assessing schools is very difficult for people to get used to. Unlike SAT averages, probably the most popular way of rating high schools, the Challenge Index ignores the scores students get on the AP or IB tests, and just counts how many tests they take. And unlike those SAT figures and other quantitative rating systems, schools with very low average family incomes can rank very high on the Newsweek list, and schools with very high family incomes, like Scarsdale, can fall short of what they consider their proper place in the universe.

Scarsdale High has virtually no low-income students and an SAT average in the mid-1200s. I am asked often: how can you say that school is not as good as Lincoln Park in Chicago (no. 31 on the Newsweek list, student body 51 percent low income) or Design and Architecture in Miami (no. 33 on the list, 42 percent low income) or Muir in San Diego (no. 101 on the list, 76 percent low income), all of which have much lower average SAT scores?

I love that question because it sparks a discussion of the need to challenge average or below-average students, particularly those from low-income families, which the list was designed to highlight.

The idea for the index came from two high schools. The first was Garfield High in East Los Angeles, where I spent much of the 1980s writing a book about calculus teacher Jaime Escalante, the hero of the film "Stand and Deliver." About 85 percent of Garfield students were from low-income Hispanic families, and yet the school welcomed everyone into AP who wanted to take those challenging courses. Some of them struggled, but new research indicates that even those who failed an AP test developed academic muscles that made it more likely they would graduate from college. And there was much success -- one year Garfield had more AP students than all but four high schools, public or private, in the country, and two thirds of them passed the AP test.

The second school was Scarsdale. I knew it was a terrific place to learn. My wife and I went deeply into debt and worked long hours to pay for a house there because its public education system was so good. But the high school did one thing that made no sense to me after those years at Garfield. Scarsdale administrators told motivated students that they could not take AP courses because they weren't good enough for them, even though much less qualified students at Garfield were encouraged to take the same courses and the identical final exams.

The AP classroom doors at Garfield were wide open. The only entrance requirement was an appetite for hard work. At Scarsdale, on the other hand, students could not take AP American history until they passed an entrance test. I thought this was sorting, not teaching. It did relatively little harm at Scarsdale because the school's non-AP courses were so good, but it set a bad example for the 90 percent of U.S. public schools that also barred B and C students from AP, but could not match the quality of Scarsdale's non-AP faculty and the sky-high academic standards and sophistication of Scarsdale families.

Because of its unusual strengths, Scarsdale does very well at my game even though it insists on playing with one hand tied behind its back. If it opened its AP courses to all students who wanted to take them, like similar public schools in McLean, Va., Bellevue, Wash., or Lincolnshire, Ill., it would place higher than no. 208, and find, like those schools, that the courses would work fine with no complaints from the brightest students. And if you think about it, even no. 208 is exceptional, putting Scarsdale in the top one percent of all U.S. public schools measured this way.

There is more good news, revealed by Klemme in his op-ed and an interview with me. There has been enough concern expressed about access to AP that Scarsdale deans now routinely ask students why they have not requested AP classes, and encourage those who seem qualified to enroll. At the same time the Scarsdale Middle School is giving more students a chance to complete first year algebra so they can take AP calculus before they finish high school. Klemme told me the school has checked with the 30 percent of students who still decline to try AP and has "determined that most of them have no interest in pursuing that curriculum."

And, despite his distaste for the list, Cohen in his letter to the Inquirer asked exactly what I have been asking since I bought that house on Church Lane: "Why do so many well-educated, successful people in Scarsdale accept an educational regime that denies their children opportunities to challenge themselves?"

Good question. Despite all the improvements Klemme and his teachers have made, students still have to take an entrance test to get into AP American history. I don't mind being beat up in the Inquirer every year for the rest of my life if someone will remove such barriers to learning, and make what is already a spectacular high school even better.