In this brick building on Wilson Boulevard, some see a historic gem in one of Arlington County’s oldest schools, where President Woodrow Wilson would pause and chat with children on the lawn.

School officials see an outdated structure and an opportunity to relieve crowding elsewhere in the district, which is seeing unprecedented growth in the student population. The district, which owns the building, plans to tear it down and erect a building about eight times the size to house the H-B Woodlawn program and a program for students with special needs.

But a civic association has made a final attempt to save the building, known as the Wilson School, calling for it to receive historic designation. The fight is emblematic of the growing pains in Arlington, where a population boom has put the squeeze on parks and historic structures. The district grew 5.2 percent this school year, putting enrollment at about 24,500 students.

In Rosslyn, the Wilson School is among the last remaining structures that might be considered historic. Tall office and condominium buildings dominate the skyline, towering over the school. The parcel it sits on is some of the last green space in the neighborhood.

“We have borne the brunt of much of the development in the county . . . the garden apartments and houses are gone, now replaced by large buildings, apartments, office buildings,” said Stanley Karson, the president of the Radnor/Fort Myer Heights Civic Association. He petitioned for the designation on behalf of a dozen fellow residents. “It’s wonderful having something historic in our area instead of ever-encroaching new high-rises.”

But school officials have said the building is unfit for the district’s needs and that a historic designation would be costly and onerous. The building, which has been renovated and expanded, is home to weekend classes for the Mongolian School, community events and a voting precinct.

The school board, which voted to not support the designation, has been inclined to agree with school officials.

John Chadwick, assistant superintendent of facilities and operations, said it would be a major challenge for the district if the building received historic designation, given that the school system hopes to put 775 students and 30 classrooms on the site. The current structure has about nine classrooms.

Karson sent a letter requesting the designation in mid-November, when the school board was considering multiple sites for a new middle school. The county’s Historical Affairs and Landmark Review Board voted unanimously — twice — to give the Wilson School building historic designation.

But the school board voted Feb. 17 to not support the designation. The board also rejected support of designation in 2009. The matter now goes to the Planning Commission and the County Board, which will have final say on the matter.

The building was constructed in 1910 as a two-story, four-classroom schoolhouse. It was topped with a cupola and tall columns graced the entrance.

According to Karson, Wilson often stopped by the building on his way out of town on country drives, waving to children on the front lawn. After the president’s death, school officials asked his widow for permission to name the school in his honor.

“The children who will attend this school had learned to know and to recognise you and your late lamented husband on your many drives through the territory, and now honor and revere the memory of our greatest President,” the letter to Edith Wilson read.

Eric Dobson of Preservation Arlington views the building as a history lesson.

“President Wilson was a Virginian. What better way to talk about Virginia history?” he said. “That’s a great story.”

But the building doesn’t look the way it did then. It was renovated in the 1950s and many of its distinct features were removed, including the cupola and an interior staircase. That’s why the designation could require the district to add historic elements to the structure.

Chadwick said the school district supports the general concept of historic designation, but not in this case.

“The historic features of the outside of the building have basically been gone” for several decades, Chadwick said. “It’s kind of ridiculous. The building’s been ruined.”

But Joan Lawrence, chair of the historic review board, envisions a blended architectural approach, merging a new structure with a restored version of the old one. She said she thinks it can be done affordably.

“There’s a creative solution. When you start from the premise that there’s only one way to develop a site and it doesn’t include accommodating a historic building, then you’re not going to be receptive to historic ways of accommodating the building,” she said.

Moving H-B Woodlawn to a new building in Rosslyn is one part of the plan to add middle school seats. The district also intends to renovate the Stratford building on Vacation Lane, the current home of H-B Woodlawn, to transform it into a middle school. Elsewhere in Arlington, existing middle schools will get additions. The entire project is designed to add about 1,300 middle school seats by 2019 for less than $126 million.

With limited funds, the school system has not made keeping the Wilson School building a priority, Chadwick said.

“The school board doesn’t believe its job is to be taking limited funds and using it to restore a building that’s already had all its historic features removed,” he said.