A charter middle school that promises a private school mentality in a public school package — read: free — could have Park Slope parents tripping over their strollers to sign up.

Though the application to found the Brooklyn Prospect Charter School has not yet been approved, more than 500 people have already signed an online petition pledging that they would consider applying, with many adding comments such as “We need this school in Brooklyn!” and “Bravo.” The school’s founders, Luyen Chou and Daniel Kikuji Rubenstein, are both fathers who live in Park Slope, where they said demand is obvious. “All of those strollers are turning into bicycles, and these kids are all marching off to middle school,” Mr. Chou said. “But there’s just not enough inventory right now.”

He and Mr. Rubenstein hatched the idea to build a new middle school, which they hope will eventually extend through high school, during shared car rides to Columbia University’s Teachers College in Upper Manhattan, where both studied independent school administration.

The two administrators said that while most of the city’s charter schools are run by people with public school experience, they have different backgrounds. Mr. Rubenstein most recently headed the math department at a K–12 boys school on the Upper West Side, the Collegiate School. Mr. Chou works for a private consulting firm but was first a teacher and then administrator at the East Side’s co-ed Dalton School, which is also K–12. Their private school experience makes their application for a charter school special, they said.

One advantage has to do with management. Like private schools, charter schools often operate outside union contracts, giving administrators more freedom over which teachers to hire and fire and how much to pay them. Private school heads are familiar with those decisions, which Mr. Rubenstein calls among the most important in education.

He said private schools also bring advantages to the classroom. Though he praised some of the city’s charter school networks for their measurable successes, Mr. Rubenstein said the schools’ styles — which he described as regimented, teacher-centered, and test score-driven — are “not the kind of models I would want to be around.”

Private schools, Mr. Chou said, are more holistic. “We want to create a school where we absolutely nail the standardized test, but where the mission of the school is really focused on those larger, loftier habits of mind and habits of heart,” he said.

The school, whose application was first reported by the Brooklyn Paper, will use an International Baccalaureate curriculum, which offers an additional diploma to graduates, and a program that pairs students with advisers on a daily basis, cultivating, Mr. Rubenstein hopes, not just academic but personal relationships.

They said they also want their school to be distinguished by its diversity. While many of the city’s charter schools focus on low-income minority populations, the Brooklyn Prospect Charter School will recruit applicants from all neighborhoods and races in District 15, which includes Park Slope, Sunset Park, Gowanus, and other areas.

Wesley Weissberg, the president of the Parent Teacher Association at P.S. 321, one of several popular Park Slope elementary schools, said parents she told were “thrilled” by the idea.

“It wasn’t like hearing about another new stroller,” she said.