All the attention nearly obscures the fact that Rocketship runs only five schools — two of which, including Discovery Prep, just completed their first year and lack state test results. But internal tests given five times a year showed that by May the new schools were on track to perform as well as the others, Rocketship officials said.

That’s significant for a school population where the percentage of children eligible for free and reduced lunch, an indicator of poverty, ranges as high as 92 percent and the portion learning English can reach 80 percent.

“There aren’t a lot of proven solutions out there, and there’s a tendency for people to glom onto something that could have a lot of impact,” said Jim Ford, an education consultant who once worked for one of Rocketship’s earliest funders.

In addition to Milwaukee, Rocketship has won approval to open schools in Indianapolis, New Orleans and Nashville. And it has permission to open 20 additional schools around San Jose, as well as one in San Francisco.

Some of Rocketship’s special education students have progressed enough to be reclassified as regular students, said Melissa McGonegle, Rocketship’s regional vice president of Bay Area schools. In addition, more than half of its students are younger than the typical age — second grade — when disabilities are detected, she said.

Three of the five Rocketship schools are still building out, adding a grade a year until they reach fifth grade. Of the 2,400 students who attended Rocketship schools in May, roughly 1,800 are in kindergarten through second grade.

McMahon, the union president, has challenged Rocketship to take over a failing public school in San Jose to test whether it can educate all children. “Then we can answer the question — is it the instructional model or is it the students?” he said.

Rocketship is cool to the idea. Autonomy — freedom from the bureaucracy and union rules that come along with traditional schools — is key, Danner said.

The chain operates only elementary schools; Danner said he is dedicated to closing the achievement gap in the early grades.

Rocketship relies heavily on Teach for America, the nonprofit organization that gives new college graduates five weeks of training before placing them in teaching jobs. Three out of every four Rocketship teachers are either in the program or recent alumni. Danner said he is using Teach for America as his human resources department because it vets candidates well.

Critics, including several school superintendents in the San Francisco Bay Area, say Rocketship uses a low-cost “industrial” model that depends on inexperienced teachers and computers. And they question whether a national chain would interfere with local control over education.

Sobered by its early political fights in California, Rocketship now has three requirements before it considers moving into a new city: authority to create at least eight schools, $3.5 million commitment from local private donors to pay start-up costs and school leaders who have worked for Rocketship for at least two years, so that they are immersed in its culture.

In the ‘Learning Lab’

There is scant research about the impact of computer learning on students, particularly those in primary grades.

At Rocketship, it’s hard to say whether strong test scores are the result of the computers, teachers, school culture or some combination.

In each Rocketship school, children file into a “Learning Lab” every day, where they sit at computer carrels that line the perimeter of the room.

In the center of the room, tutors work in small groups with children in need of more intense help. In a traditional public school, students would be pulled out of class for that kind of extra help, losing valuable classroom time that can often push them even further behind.