It looks like a birthday cake with blue and white icing.Children crowd around it as a teacher lights three candles and a small boy blows them out.

But at National Child Research Center, a private nursery school in the Cleveland Park section of Northwest Washington, this birthday cake is not for eating.

It isn't cake at all - just a decorated tin box from an old Christmas fruitcake. After the candles are blown out and everyone sings "Happy Birthday," the "cake" is put inside a cupboard. Then the children eat graham crackers and apple juice - and they seem to enjoy themselves immensely.

"The students think it's wonderful way to celebrate their birthdays." said Emily McCormack, the director of the school, which is celebrating its own 50th birthday this year. "We do it this way because children should eat nutritious foods and we wanted to stop any competition among the parents (who used to bring birthday cakes to school)."

When it opened in 1928, National Child Research Center was headed by a psychiatrist. Children came not only to play, learn and be social, but also to be studied themselves. Even though the name has stayed the same, research activities have dwindled. But the school, the oldest nursery in Washington and one of the oldest in the United States, has helped set patterns for nursery education that have become increasingly widespread during the past decade.

According to the U.S. Cnesus Bureau, the number of children enrolled in nursery schools had increased by 39 percent nationwide since 1970. By 1976, the census said, about one-third of all 3-and 4-year-olds were in schools, compared to about 20 percent enrolled in 1970.

No figures are available on nursery school enrollment in the Washington area, but officials of nursery education groups believe a similar increase has occurred here.

During the 1930s, when President Franklin Roosevelt's grandchildren attended National Child Research, the school help train teachers for the U.S nursery program set up by the Works Progress Administration. In the mid-1960s, it served as a model for the Head Start program, started by President Lyndon Johnson, whose daughter Lynda Bird attended the school.

Over the years the list of parents also has included Sen. William Proxmire (D-Wis.), Sen. H. John Heinz III (R-Pa.), Rep. Morris Udall (D-Ariz.), and former White House press secretary Ron Nessen.

During the early 1970s National Child Research became almost a "free school" (not a reference to its tuition, which ranges as high as $2,225 for allday kindergarten). It was loose and informal with no group lessons, little discipline, few scheduled activities and wide opportunities for children to choose what to do.

"It was a very free and open place," one parent recalled. "The director really believed that children should discover things on their own with a bare minimum of interference from adults. Some children did a lot of interesting things, and some children wasted their time."

In 1976 the school abruptly changed course as the board of trustees, made up mostly of parents, ousted as director the late Janet Weaver. All 10 teachers resigned rather than work for MacCormack, her replacement.

MacCormack and the trustees then hired 10 new teachers, and the school has become a much more structured place.

Each of its five classrooms still has a science corner, centers for reading and art, a corner for playing "grown up," and an exercise area. For part of each day children choose between them freely. But now there are times reserved for group lessons, too, with teachers gathering the children around to talk about particular topics such as turtles or pine cones, colors, fire houses or holidays.

There is an American flag on the porch, one-way traffic on the tricycle path, and firm rules about what birthday parties ought to be.

MacCormack and the current teachers describe their course as moderate and "eclectric." Parents and children seem enthusiastic.

"The school is a much more balanced place than it used to be," said Suzanne Murphy, a long-time member of the board of trustees. "We went through a difficult period. Now we think things are looking up."

The teachers who quit and some of the parents who pulled their children out - enrollment fell last year from 128 to 101 - believe the school has become unpleasantly old-fashioned.

"It used to be a very exciting place," said Kay Stafford, one of the former teachers. "There was a creative time, an interesting time. Now that's gone, and they're doing things in an old-fashioned way . . . I went back once and that was enough."

"I don't think we're old-fashioned at all," MacCormack responded. "We just don't use what they did 50 years ago. That would be very limited. I think we take the best we have found from over the years . . . But we don't believe that children can discover everything on their own. Now the children get introduced to things they haven't come across. They find it exciting."

Regardless of how its program is described, the setting of the school is old-fashioned - a large red-brick house at 3209 Highland Pl. NW. There is a wide porch, and about an acre of wooded property provides plenty of space for outdoor play.

The house was built by a lawyer in 1905 and served later as an embassy for the Menshevick Russians before it was bought by the school in 1931 for $32,500. Smaller houses nearby recently have sold for more than $250,000.

When the school opened in 1928 it occupied another large house at 1828 Columbia Rd. NW. For its first three years it was financed largely by a grant from the Laura Spellman Rockefeller Foundation. When the grant ran out, the school was continued by the parents, including a flock of prominent New Dealers, as a private non-profit enterprise.

During most of the 1930s it had about 40 youngsters - aged 18 months to 5 years old. The Highland Place house was fitted with low toilets, low sinks and play kitchen equipment that young children can easily use. Some of it is still being used, although the school underwent a major remodeling in 1964.

Groups of education and psychology students from local universities still visit regularly, MacCormack said, to watch what "normally healthy young children can do." The school also has a small program for teaching cued speech to deaf youngsters.

The scientific flavor that marked the school until the late 1950s - daily visits by a pediatrician, extensive psychological testing, daily charts of foods eaten, naps taken, and bowel movements - has disappeared.

By the early 1970s even regular snack-times had disappeared in some classrooms. Instead, food was set out for children to eat, sometimes when and where they wanted to and sometimes as a reward for doing jobs around the classroom.

To the teachers who arranged snacks this way, they fit in with the school's informal, unpressured atmosphere. To many parents, though, the sight of children dropping cheese bits and peanut shell around the classroom seemed messy and contrary to their own efforts to teach table manners.

Now all the children in each class eat snacks together at low tables. Teachers encourage them to say "please" and "thank you."

The parents and trustees who changed the direction of the school two years ago said they were more disturbed by two other problems. Many thought their children were not learning skills needed to do well in first grade, such as listening, holding a pencil and telling left from right. They also thought that youngsters in the school behaved too rough.

"Almost every singled day for three months," one parent said, "there was a child who waited until the other children built something elaborate in the block area. Then he would come in and knock it down, and the teacher wouldn't say much about it. Well, enough is enough already. What about the other children who are building nice things with the blocks"

Stafford acknowledged that some children at the school were 'very strenuous, very active, very rough," but she said, "They weren't poorly behaved. They just needed a lot of support. They needed to grow a lot, and some of the parents just didn't understand our methods of dealing with children."

Stafford said she doubted that the blocks were knocked down as regularly as the complaining parents said they were. "To have it happen in few times," she added, "is probably good because children have to learn that these kind of things go on and they have to deal with it."

Tuition at the school now is $1,315 a year (including snacks) for morning nursery classes, $250 less for afternoon classes, which the school has troble filling, and $2,225 for all-day kindergarten.

Despite these high fees, the school has run a deficit since 1970 although Murphy said it should break even next year.

Besides the bitterness that accompanied the change in directors, Nancy Harter, a trustee, said the school also has been hurt by competition from newer private nurseries, many in churches, and from free nursery classes for 4-year-olds offered by Washington's public schools.

In addition, many more middle-class mothers are working or taking college courses, creating a demand for fullday care that National Child Research does not offer.

Many of the changes in the school, she said, reflect much wider changes in American schools and society.

"The pendulum tends to swing," Harter said. "You try one thing, then something else comes back. Children need an opportunity for self-selection; they also need some examples. Right now we think too much of either way is poor for them."