The Montgomery County Board of Education approved its first charter school Monday night, sending a cheer through the crowded board room and signaling a breakthrough for a movement that is pushing to expand beyond struggling inner-city districts.

In a 6 to 2 vote, the board authorized a new Montessori-based elementary school and officially handed over the keys to Crossway Community, a nonprofit organization, to run it.

School board member Patricia O’Neill (Bethesda-Chevy Chase) said she was proud to help shepherd in a “historic moment in Montgomery County” by voting for the school.

“I believe strongly that Montessori education has a proven track record, Crossway has a proven track record, and that they have dotted all their I’s and crossed all their T’s and met all the challenges that we threw to them,” O’Neill said in an interview before the vote.

The school will open in 2012 in Kensington, and it will serve as many as 188 students in preschool through third grade. Crossway already runs a Montessori-based preschool program at the same site.

“We are just excited and thrilled and really looking forward to . . . this partnership,” said Kathleen Guinan, the organization’s executive director. More than 50 parents and neighbors came to speak or show support at the meeting.

Pressure to open charter schools has increased dramatically in recent years as national and state leaders have embraced the publicly funded, privately run alternatives as a stimulus for school reform.

Montgomery County and many other affluent or successful school systems have seen charter schools as a distraction from work already underway in traditional public schools.

The board rejected Crossway Community’s first application a year ago. But school officials worked with the organization in the spring to address concerns.

The revised application was backed by a review panel of educators and community leaders, as well as by Superintendent Joshua Starr and former superintendent Jerry D. Weast.

A nagging issue raised by board members was how a public charter would jibe with Crossway’s mission. The organization serves predominantly low-income families and wants to continue serving children in need. But charter-school regulations require that admissions be open to everyone in the school district.

Crossway had sought a state waiver to the law in its first application but rescinded the request in its second try. The school board delayed its final vote to explore the possibility of setting a geographical boundary for the school but could not find a legally sound solution.

So the charter school will admit students through a lottery system, though its operators will be allowed to market more aggressively to students from low-income families.

Several board members who voted for the new school said it met the letter of the law and the county’s high standards, but they were wary of signaling greater support for charter schools.

Judy Docca (Gaithersburg) and Michael Durso (District 5) opposed the school.

“We should invest in the many programs and services we already provide in this county,” Docca said in an interview.

The Montgomery County branch of the NAACP also weighed in during the final hours to oppose the application, saying in a written statement that the organization does “not support the current emphasis on charter schools as the vanguard approach’’ to education.

Maryland will have 43 charter schools this fall. Most are in Baltimore, but Frederick, Anne Arundel and Prince George’s counties also have them.