Fifth-grader Matthew Benitez, right, pumps his fist after being sorted Tuesday into Lealtad, the Occoquan Elementary “tribe” that typifies loyalty. Principal Hamish Brewer celebrates with hands raised. (Jonathan Hunley for The Washington Post)

The outdated stereotype of the school principal as a foreboding figure ready to punish wayward children is a particularly foreign concept at Occoquan Elementary, where Principal Hamish Brewer was greeted with high-fives from students as he walked through the cafeteria one day last week.

Also erased: the idea that new students aren’t welcomed by their peers. Fifth-grader Matthew Benitez’s introduction to Occoquan came with cheers from his fellow pupils Tuesday as he was assigned to one of four “tribes” at the school.

But if the fun atmosphere at the eastern Prince William County school doesn’t seem like education business as usual, neither are the results Brewer and his staff have seen in the five years since he took the helm. Despite overcrowding and a student population that includes a high percentage of English language learners and children from low-income homes, the school has seen gains in standardized test scores and now has a national honor to its credit.

In November, Occoquan Elementary was named a National Title I Distinguished School by the National Title I Association, an organization of the state directors of the federal Title I program, which provides funding for the education of children from low-income families.

Occoquan was chosen for excellence in serving special student populations, such as English language learners and students with disabilities, according to the Virginia Department of Education. It was one of two schools in the state to receive the award last year — the other was in Chesterfield County, near Richmond — and the first in Prince William to be recognized.

It also means the school has overcome challenges that are frequently perceived as barriers to learning. About 67 percent of Occoquan’s student population is eligible for free or reduced lunch; 53 percent of students are English language learners; and 12 percent require special-education services, according to the Prince William school system.

On top of that, the school serves about 620 students in a facility with an official capacity of about 512.

But Brewer said he and his staff think all students can succeed, regardless of circumstances. They choose not to worry about what they can’t control and concentrate instead on creating a nurturing setting where children want to learn.

“We’re doing all the things a lot of people think can’t be done,” he said.

For instance, passing rates on Virginia’s Standards of Learning reading tests for economically disadvantaged students at Occoquan increased to 87 percent from 59 percent over four years, according to the county school system. The same group’s passing rates for math tests also increased to 94 percent from 68 percent, besting the state average of 69 percent.

Pass rates for students with disabilities rose, too, to 72 percent in reading from 40 percent, outshining the state average of 46 percent. And math passing rates for the same students went to 85 percent from 62 percent in two years.

Brewer, who’s from New Zealand, has achieved this growth while creating an environment in which many teachers and students are so comfortable and engaged that they’re disappointed when school is canceled or when sickness means they can’t attend class.

Karla Cygan, whose daughters Kayland, 8, and Kylee, 5, are Occoquan students, said children at the school are so eager to learn that they communicate with their teachers even when they’re out sick.

And instead of using a minor illness as an excuse to stay home, Cygan said, Kylee once downplayed symptoms — “It’s just a little cough” — in an effort to go to school.

“That, to me, speaks so much volume,” Cygan said.

Kayland is in Heather Ballew’s third-grade class, and her teacher confirmed the students’ enthusiasm.

Ballew pointed out that when Occoquan started a Saturday program for students who needed extra help, even children who didn’t need the added assistance began asking to come to the morning sessions.

But while the students and teachers have a good time at Occoquan, Brewer said, education is still the priority. Everyone is expected to be serious about schoolwork and respect one another.

“We’re big on manners around here,” Brewer said.

Occoquan Elementary also is big on its tribes.

Harry Potter readers liken the tribes to the houses that students are sorted into at Hogwarts, the books’ main wizarding school.

But because the mascot of the 90-year-old Occoquan school is a brave, Brewer configured the school’s four tribes to reflect four of the 14 leadership traits of the Marine Corps: integrity, unselfishness, initiative and loyalty, each virtue translated into a different world language.

The tribes compete in a points race, and everyone at the school, including staff, is a member of one of the tribes. Newcomers learntheir tribal designation by spinning a wheel on the wall in the school office.