At the D.C. public schools' Fillmore Arts Center in Georgetown, a red-brick building that looks almost like a castle, there is controlled chaos of sorts.

Desks and chairs are often upside down or sideways. Students sit on the floors, walk around barefoot and make the kind of noise that would send most principals angrily groping for their public address systems to demand quiet and order.

But amid this noise and seeming disorder, these youngsters are learning to read and compose music, to write and act in improvisational plays and to express themselves in song, dance, painting and poetry. In the process, they also learn how to exercise imagination and grow in self-confidence and responsibility.

Fillmore is the only city elementary school devoted to teaching the arts. Last week, it was one of 10 schools nationwide to receive a $10,000 award from the Rockefeller Brothers Fund for its curriculum and record of student achievement.

Fillmore, like the other schools honored, exhibited "outstanding instruction, significant student achievement and borad administrative and community understanding and support," David Rockefeller Jr. said in announcing the grants. Officials at Fillmore say they have not yet decided how to spend the money.

Fillmore's fare appears diametrically opposed to the D.C. schools' "competency-based curriculum," the back-to-basics thrust known as CBC, which stresses reading and math over other subjects on the elementary school level.

But Fillmore Principal Patricia Mitchell notes that every course has specific learning objectives, which the competency-based curriculum requires for every subject area.

"The creative ways in which Fillmore is using CBC are ways of making the curriculum come alive," said Superintendent Floretta D. McKenzie. She said the competency-based curriculum offers "framework for instruction," while it "was never intended to be a straitjacket of teaching strategies."

Located on 35th Street NW off Wisconsin Avenue in a building constructed in 1898, Fillmore serves 888 students attending Key, Hyde, Stoddert, and Mann Elementary Schools and the Hardy Middle School. These youngsters receive their academic program at their individual schools and attend Fillmore for a half-day once a week for arts instruction.

Fillmore and the other schools form the District's Six School Complex, which began in 1974 as a way of keeping these small neighborhood schools west of Rock Creek Park alive at a time when the system was seeking to close schools with low enrollments.

Under this concept, each school's enrollment is not viewed alone, but as part of a cluster. Each school in the cluster offers a different "educational option," says Associate Superintendent James T. Guines. Hyde, for example, has an intensive Spanish program, while at Key, there is a special science program.

Enrollment at these schools increased steadily between 1974 and 1980 but has declined slightly over the past two years. Fillmore's principal and parents say some parents took their children out of these schools because of 1980 budget cuts and teacher layoffs.

The students at these schools score well above national norms on standardized reading and math tests.

Parent Martha Evelyn says her children's instruction at Fillmore, in such courses as music, film-making and calligraphy, has been "a really vibrant experience that my kids look forward to every week." Fillmore, she added, "has been a landmark in the community, and I hope it stays that way."

Founded on the theory that play is the child's natural medium of learning, Fillmore is a whirlwind of creative activity.

In dance class, students leap, bend, twirl and turn to the beat of disco music as they perform dance routines they themselves created.

Across the hall in the drama class, a group of students transforms overturned desks and tables into a make-believe cave and ordinary sticks into swords as they prepare to perform a skit in which they improvise the action and dialogue as go along.

Upstairs in the music class, kindergarteners and first-graders learn about the relationship between the sound of words and the sound of music as they play instruments like the xylophone, metalophone and glockenspeil that are designed to help children recognize musical tones.

Teachers say the free-form approach works. In the school's play-acting course, for example, teacher Ermyn King requires students to learn the Seven Stages of Man sequence from Shakespeare's comedy, "As You Like It."

The students act out these stages and in the process learn the elements of drama and theater terminology, King said.

Science and geography courses can also be woven into the drama class, King said, noting that her students once took an imaginary journey on a boat and in the process learned about the parts of a ship and about navigation.

The lessons are social as well as academic. In another classroon exercise, the youngsters donned blindfolds and had to be led through a maze of desks and chairs by fellow students who served as their guides. Such an exercise teaches students personal resourcefulness and sharpens their ability to "create and respond to experience," King says.

Mitchell says Fillmore's teachers, mostly professional artists, are careful to stress to students that there is no one right way to express themselves in art. "The whole idea of this program," she said, "is to build self-discipline and self-confidence."