At Woodridge Elementary School in Northeast Washington, many students sit in classrooms where their parents studied before them, and it is common to find, among the 193 pupils at the school, numerous sets of cousins.

The red-brick school on the corner of tree-lined Carlton Avenue is an institution in this stable, middle-class community, where well-worn but tidy one- and two-story wooden single-family homes are often passed on from generation to generation.

The community's stability is an asset for the many government employes and blue-collar workers who live there, but it is a problem for the school that bears its name. Although a number of Woodridge graduates now send their children to the school, there are not enough young people with small children moving into the neighborhood to replenish the school's enrollment.

And that is a major reason why Woodridge is on D.C. School Supt. Floretta D. McKenzie's list of 14 underutilized city schools slated for closing in an effort to save money.

This is the second time in four years that the school system has recommended closing Woodridge, which had so many students in the late 1960s that teachers were holding classes in the auditorium.

The last time, teachers were so sure that closure was imminent that they packed up all their classroom belongings and threw a farewell party with the neighborhood people and Woodridge graduates.

But parent protest marches and a letter-writing campaign convinced the school board that Woodridge should remain open. Parents argued that the youngsters would have to cross heavy traffic on Bladensburg Road to get to the next nearest school, Fort Lincoln Elementary, a mile away on 31st Street NE.

The safety question is bound to come up again, but this time the parents and school staff also intend to wage an educational argument: whether the money saved by closing small schools outweighs the loss of the more familial learning atmosphere and individualized instruction that can be provided in such schools.

"It's a small school in a neighborhood setting. A student doesn't get lost in the crowd. We know our students' parents or we taught their parents," said sixth grade teacher Doris Brunot, who has been teaching at Woodridge for the past 15 years.

The superintendent has not made individual school-by-school estimates of the amount that would be saved by the proposed closings, but has told the school board that between $150,00 and $200,000 will be saved for each school that is shut down.

The board is scheduled to take a preliminary vote on the closing proposals April 26. For the time being, the Woodridge community is in limbo, uncertain whether this latest proposal will prove to be just another false alarm or whether their children will be going elsewhere when school opens next fall.

"This does cause anxiety for the students," said Gloria Dickerson, who teaches first and second grade. "My children are first and second graders and some of them heard about this on the news. The next day they wanted to discuss it, you know, 'Where am I going to go to school next year?' "

Parent Valerie Brevard said she is already worrying about how her daughter Sakinah, a fourth-grader, is going to get to a school that is a mile away from her home. She said Sakinah walks 2 1/2 blocks to school now and crosses only one side street that has a safety patrol.

"It bothers me a lot that she might have to cross both South Dakota Avenue and Bladensburg Road. I'll have to take her to school every day or make a car pool arrangement," said Brevard, herself a Woodridge graduate, now a machine operator for IBM.

Those Woodridge students who do not transfer to Fort Lincoln would be reassigned to Langdon Elementary, 20th and Evarts streets NE, according to the superintendent's plan. Langdon is also about a mile away from Woodridge.

News of a possible closing has hit hardest at the fifth-graders, who would have to finish their last year at another building if Woodridge closes in September.

"I'd like to stay here. This is where I started out and I wouldn't like to go to another school to finish," said Delicia McCain, 10.

Walter Ferguson, 12, says he attends Woodridge because his grandmother did not want him to go to an open-space school like Fort Lincoln because "people can just walk through the classrooms there and it might be hard to concentrate."

The 55-year-old Woodridge is a traditional-looking three-story school with enclosed classrooms and those old-fashioned dark wooden doors with the little rectangular windows.

Fort Lincoln, located in the middle of a sprawling new-town development on the city's Northeastern border, has many amenities that Woodridge does not, including a swimming pool, elevators and built-in television sets.

The third- and sixth-graders at Woodridge score below national norms on standardized reading and math, but their test scores are in the same general range as those of other D.C. elementary students. Most Woodridge students qualify for free or reduced-price lunches. Only 35 of the children receive public assistance, according to school records.

The building, decorated throughout with student artworks, shows its age in fallen splotches of wall plaster and buckling floors. But parent Brevard says the building's condition doesn't matter to her: "Sakinah has always had good communication with her teachers, and my education there was well above average."

Superintendent McKenzie says Woodridge should close because the school was built for 434 students, but, with 126 students, is only 29 percent filled.

Assistant principal Leslie Y. Davis, however, says the superintendent's figures are obsolete and that there are actually 193 students.

He said the superintendent's report does not reflect several student transfers since the beginning of the year or the arrival of 63 handicapped students who were moved to Woodridge in February for special classes. For the most part, these are students from Northeast, but not necessarily the Woodridge community, Davis said.

If the school were counted as having 193 students, it would be at 44 percent of its capacity. There is no official enrollment "floor," no percentage above which schools are automatically safe from closing, but 10 of the 14 schools recommended for closing this year are below 40 percent enrollment.

The superintendent has previously said that special education students are not considered as part of the school's regular enrollment because they could be moved to another location.

Many of the special education students now at Woodridge have attended three different schools so far this year as the school system searched for a permanent place for their programs. Their teachers say another move would cause unnecessary strain on the youngsters.