In Alice Roosevelt Longworth's living room, where presidents have come calling and political darts have been thrown, 11 Washington high school students gathered Friday to talk about Utopia.

At 11 a.m., Mrs. Longworth, 93, who is Teddy Roosevelt's daughter, came downstairs to talk to the students who have been meeting in her living room two mornings a week since November.

"Oh, this is education?" Mrs. Longworth asked.

"Yes, this is what we call education," said Kristie Twaddell, the teacher in blue jeans who is a friend of Mrs. Longworth. "I've been educating them here right before your eyes."

The teen-agers in Mrs. Longworth's living room, with its old political drawings, Chinese prints, and fraying chairs and carpets, are students at an unusual D.C. public school with the somewhat confusing name of School Without Walls.

Actually, the school does have walls and a building, the old Magruder Elementary School, a shabby red-brick remnant of the 1880s, on M Street NW, just a block from the Mayflower Hotel.

But both teachers and students say the building isn't important, because the idea behind the school, which opened in 1971, is to use the city as its classroom. Besides, with 275 students - almost double the number a year ago - the old building is seriously over crowded.

"Learning can become relevant if you combine textbook theory with real life situations," said school principal Antoinette Corprew. "It's from the combination of the two that you can achieve the best understandings."

While some students have been studying utopias in Mrs. Longworth's living room, others have taken walks with their history teacher around 14th and U Street NW. There prostitutes gazed on them curiously, and one wino asked teacher Herhert Lambright: "What are you doing on my street?"

Other students take art classes at Corcoran Gallery, work as interns (with school credit) for Del. Walter Fauntroy and members of the D.C. City Council, or do chemistry experiments at Walter Reed Army Hospital.

One youth said he got a B in English by working as a waiter and turning in a four-page paper on how to manage a bar. Many students with poor academic skills take almost all classes in the Magruder Building, except for occasional visits to museums and to D.C. elementary schools where they tutor. Some students with high grades said they spend only two or three hours on homework per week.

"You can get by without doing much," said senior Kenneth Fain, whose teachers sent him lessons by mail when he spent several weeks last fail in the Bahamas. "Sometimes you can do almost nothing. Then again, if you study hard, you can learn more at this school than any place else in the city. The apportunities are there."

When the School Without Walls started six years ago it was part of the "greening" of American education, a nationwide movement against traditional structures and curriculums that extended from nursery schools to colleges.

The school here was modeled on the Parkway Program in Philadelphia, a much-publicized "alternative school," which held many classes in that city's museums as well as in churches and businesses. The idea of a small special school with informal, innovative classes using resources, throughout the city was copied by many big urban school systems, including Chicago and New York, as well as Washington. Most programs continue.

But none has enrolled more than 1 or 1 per cent of any city's high school students. Also, despite hopes of their founders who saw them as catalysts for widespread educational change, the impact on most schools and students has been slight.

"A lot of people think that kids should be outside (of school buildings and) in the community," said Vernon Smith, director of the Center for Options in Public Education, a research group in Bloomington, Ind., which keeps track of alternative schools nationwide. "But there's obviously a limit to the number of kids that the community can absord."

"Not too many people even know we're here," said Corprew, as she walked around her office in the M Street school. "And the other schools aren't copying what we do here. That's a disppointment."

D.C. School Supt. Vincent Reed explained why the impact of the School Without Walls has been limited: "I don't think many of our kids oculd handle a program like that for lack of discipline," Reed said."You have to be self-disciplined to do it."

"Ideally, the School Without Walls should be for the gifted and talented students, the highly-motivated ones," Corprew said. "We want students who accept responsibility, who are well-in-formed and excited about learning who respect others.

"As a practical matter, the only way you can have internships with professional people is if the students show up for them regularly and don't have deficiencies in the basic skills so they can do useful work."

On the other hand, Corprew added: "We have to remember we are a public school. You can't be too elitist."

To choose new students for the School Without Walls Corprew said she interviews at applicants herself along with a teacher and three students. They don't look at grades, she said, but they do ask for an essay on why an applicant wants to come to the school. The interviews usually last about 30 minutes with parents present but silent.

Then the applicant is sent outside, and the committee caucuses and votes, with each student's vote counting as much as a teacher's. Sometimes, Corprew said, the students are less willing to take a chance with an applicant than she is.

However, last May Reed ordered the School Without Walls to expand because its spending per pupils was almost double that in regular high schools.

Because the decision was made so late, Corprew said the school had to take almost all applicants. In addition, she said, Reed ordered the school to accpet about 35 students, most white, who live on Bolling Air Force Base in Anacostia but don't want to attend the school closest to home, Ballou High.

For its new class next fall, Corprew said the school is being selective again, accpeting only about one of three applicants.

With so many new students this year, many of the old students think the school has deteriorated.

"We have so many students this year that we don't have enough resources outside of school for them to take," said Carl Cephus, 17-year-old junior. "The more students we get, the more we become like a regular school, and that's what we dont' want to become. Some of the new students don't know what the school is about. The aren't responsible and don't show up for classes around the city."

But he added: "Compared to other D.C. schools we are still in utopian model. There's no trouble here, and there's a lot of learning."

When the School Without Walls opened, it tried to get an equal proportion of students from all parts of the city. But Corprew said most now come from middle-class areas, such as Takoma Park, Hillcrest in Southeast, Brookland and west of Rock Creek Park.

This year 71 per cent of the students are black, and 29 per cent white (compared to just 3 per cent white overall in D.C. public high schools). About a quarter have transfereed from private or parochial schools.

Organizers of the school thoughts it would attract students primarily because of its freedom and innovation, and many students say that's why they are enrolled. But many add they wanted to get away from the violence and disorder in regular schools.

"I couldn't cope with large classes to well and the disrupters at Kramer Junior High school (in Annacostia)," said Renee Blakemore. "The kids just kept on fighting constantly, and I don't like this type of atmosphere. . . . At the School Without Walls we never have any problems with fighting violence or students beating up their teachers."

If students do cause serious trouble, they can be sent back to their neighborhood schools, but Corprew said this has rarely been done.

Besides being calmer than most D.C. high schools, the School Without Walls also give higher grades. About 20 per cent of its students are on the honor roll this year, compared to just 5 per cent citywide. Corprew says the marking isn't easy (although some students say it is) but that many of the students are bright. Over the past two years 80 per cent of its graduates have gone to college, including a few to prestige schools such as Johns Hopkins and Sarali Lawrence.

Last year about half of the school's 11th graders scored over the national average on standardized reading and math tests, compared to about 25 per cent who di that well in the D.C. school system. The range of achievement was wide, though, from college level to fourth grade.

Although the School Without Walls is more ordinary than it used to be, there is still much unusual.

Classes usually meet 2 1/2 hours two days a week, instead of 50-minutes periods five days a week. Most courses are offered in nine-week segments, called minicourses.

The school relies heavily on volunteers, who have included an economist from the White House Domestic Council and the director of a modeling agency.

Many nonprofit organizations have been happy to have students as file clerks, research assistants and volunteers - all for high school credit. The groups have included Common Cause, National Organization for Women, National Wildlife Federation and both the Carter and Ford campaigns.

Some groups have sen people into the school to teach, including Planned Parenthood, which trained 10 students to serve as sex counselors.

But the school without walls has no cafeteria, no library and no gym. There are no physical education classes, required in other high schools. Students get books from the public library. Most go out for lunch or eat sandwiches in the student lounge.

Ben McDaniel, 16-year-old sophomore, said last year at a conventional senior high in Richmond, "School was so boring, it was pitiful." He said he resented the discipline, cut most of his classes and got poor grades even though he read a lot on his own.

At the School Without Walls he is attending regularly and doing well.

"When I first came I skipped a lot," McDaniel said. "I just couldn't get used to it, but the principal checked on me and I straightened out.

"This building is terrible, its paint is peeling of. But the students get along well here.There's no busy work from the teachers. No one expects you to be a robot. I guess it's like a college-type thing. It's nice, very nice."