In a 2009 photograph, students attend Algebra class at BASIS charter school in Scottsdale, Ariz. Two other BASIS schools took the top two spots on the national America’s Most Challenging High Schools list; the Scottsdale campus is one of the nation’s most elite public schools. (Laura Segall/The Washington Post)

What intrigues me about the 2015 edition of The Washington Post’s annual America’s Most Challenging High Schools list is the jump in the number of qualifying schools, about 20 percent more than at this time last year. But there are several other takeaways, particularly about the schools at the very top of the list.

The rise of BASIS ...

The list dramatizes the rise of one of the nation’s most demanding and unusual education organizations, the Arizona-based BASIS Schools Inc.

Three of its non-profit public charter schools are in the list’s national top 10 — No. 1 BASIS Oro Valley, No. 2 BASIS Chandler and No. 6 BASIS Tucson North. A fourth school, BASIS Scottsdale, would have ranked above all three but was put on the Post’s Public Elites list because its very high SAT and ACT scores show it to be too selective for the main list.

The first BASIS charter school began in 1998, in a one-story concrete-block former day care center in a commercial area of Tucson. The founders were a married couple, Olga and Michael Block, she a former Czech college educator and he a University of Arizona economic professor. Olga was stunned that U.S. schools taught so little compared to what she experienced in Europe. When I met them in 2001, they were rectifying that by creating a high school where college-level Advanced Placement courses started in the ninth grade. I thought they were way too ambitious, but they did it, and much more.

They have 15 non-profit charter schools in Arizona and Texas and one in the District. Their education management company, BASIS.ed, has gone in a new direction by adding two for-profit private schools, one in Brooklyn and another in San Jose. The Brooklyn school already has 200 students and a $40 million building under construction. The San Jose school has 570 students. The Blocks seem confident that parents will be willing to pay $23,500, way below the $40,000 tuition charged by traditional non-profit private schools, for an approach that has brought their non-profit schools so much attention.

... and Texas and Florida, too

This year’s list has five magnet schools from Texas and Florida in its national top 10, the result of a long commitment to AP and IB in those states. The No. 10 school, Signature in Evansville, Ind., is the one of the very high performing charters that have been created in unexpected places by educators who thought their mostly average students could do more than had previously been expected of them. Signature — in far southwestern Indiana, near the Kentucky border — is the only school outside of Texas, Florida and Arizona to crack the top 10 this year.

Corbett charter falls ...

One of those out-of-the-way charters, Corbett in rural Oregon, dropped from No. 3 last year to No. 40 this year. Corbett’s leader, Bob Dunton, reduced the number of AP courses its student take, for reasons I will discuss in an upcoming column. Don’t confuse the Corbett charter with the Corbett school, No. 20 on the list, two exceptional public schools that have not gotten along.

... so does American Indian charter

The American Indian public charter in Oakland, Calif., which was threatened with closure because of alleged financial mismanagement, persuaded authorities to leave it open. After two years in a row as No. 1 on the national list, the charter dropped to No. 29 this time, the result of more graduates and fewer AP tests.

Very few adopt heavy load of college-level courses

Very few campuses have adopted the heavy load of college-level courses in ninth and 10th grades that characterize the top 30 schools. But Washington area magnets H-B Woodlawn in Arlington, Va., and School Without Walls in the District — as well as D.C. private schools such as the Washington International School and St. Anselm’s Abbey — have adopted programs nearly as challenging because more American families are looking for that.

Wanting more than to study “a whale for awhile”

Some parents have complained of BASIS schools failing to provide enough support for students with learning disabilities. But that has not reduced the flood of applicants. Olga Block said she and Michael finally gave up on regular public schools when they asked what area of science her daughter Petra would be learning during sixth grade in affluent Scottsdale. She said they were told “they were going to study a whale for awhile and then a volcano.” The Blocks wanted more than that. Many parents these days feel the same way.