Without taking away from whatever credit Runey and Attleboro High School deserve for their achievements, let's call national rankings of high schools what they are: nonsense. There is no way to say, with any degree of accuracy at all, where any given high school ranks in relation to others in terms of how good it is or how challenging it is. And the claim that Attleboro High School, which was not even fully accredited as recently as seven years ago, is now in the top ten percent of America's high schools -- among the most challenging -- seems improbable, at best.

And yet, every year since 1998, Jay Mathews, an education journalist at the Washington Post, has been putting together a ranking of what he calls "America's Most Challenging Schools," or the Challenge Index. For years, this national list was published by Newsweek, which was owned by the Washington Post Company. When the Post sold off Newsweek in 2010, it kept the Mathews index for itself. Newsweek then produced its own ranking, which has been continued by the Daily Beast. And, of course, US News & World Report, an organization famous for fueling Americans' obsessions with rankings (colleges, law schools, hospitals, etc.) started its own high-school list, too.

All of these lists have flaws that stem from the inherent absurdity of presuming to rank schools around the country according to how good or challenging they are. And they all come in for criticism. Recently, Matthew Di Carlo, a senior research fellow at the Albert Shanker Institute, took a critical look at the Newsweek/Daily Beast and US News rankings, finding some good and some bad features in each of them.

But it's the Mathews "Challenge Index" that has given rise to the sharpest criticism over time (see here, here, and here, for example) because of its methodology, which is reductionist in the extreme. It uses only one factor to calculate its rankings: It divides the number of Advanced Placement (AP), International Baccalaureate (IB), and Cambridge (AICE) exams taken at each school by the number of graduating seniors. Note that the numerator is not even the number of such exams passed, but merely the number taken. So, a given school can rise on the list by increasing the number of its students who take "advanced" classes.

Conversely, schools that are more discerning and thoughtful about which students ought to be taking AP classes end up suffering in the rankings. So, the list produces nonsensical anomalies such as high schools with very low graduation rates ranking much higher on the "Challenge Index" than excellent schools that don't game the ranking system, or that, like Scarsdale High School, have joined the growing list of schools that have eliminated AP courses so that, as Bruce Hammond puts it, "students and teachers could rediscover their passion and creativity" once freed of what is too often a rigid and stultifying AP curriculum.