The Arlington School Board voted last night to begin a detailed study of racial balance in the county's 28 schools, which has shifted dramatically with an influx of Hispanic and Asian children.

The move was prompted by a request two months ago from parents of 15 black third graders at Barcroft Elementary School that their children be allowed to continue through the sixth grade there instead of being bused to other schools for the fourth, fifth and sixth grades.

The board agreed with Superintendent Arthur W. Gosling's recommendation to let the children, all from the predominantly black Nauck area of South Arlington, remain at Barcroft. The board also voted to have the school staff prepare a paper, due in the early fall, on school assignments for Nauck children and racial balance in the school system, which has changed substantially in 15 years since the county's last all-black elementary school was desegregated.

While blacks once composed the only sizeable minority in county schools, Arlington's student population of 14,500 is now 16.2 percent black, 14.7 percent Hispanic and 14.5 percent Asian.

The current busing patterns date to 1971, when Drew Elementary School in the Nauck community was desegregated. It became a "model" school that stresses individualized learning and draws about 11 percent of its enrollment from the Nauck area.

A 1971 court-approved desegregation plan called for black children who would formerly have attended Drew or other neighborhood schools to be bused to predominantly white grade schools throughout the county. Three years ago, however, the School Board agreed with some Nauck parents that children being bused to the four northernmost elementary schools be allowed to attend the first through third grades at schools closer to their South Arlington homes. Those children continued to be bused to the northern schools for the fourth through sixth grades.

Portia Clark, a Barcroft parent and member of the school's advisory committee, said she interviewed several third graders who said they would rather stay than be bused to a northern school. "The statement from those kids clearly is that they do not want to leave Barcroft," she said.

Martha Manning, another member of the advisory committee, cautioned that a similar request from parents of Barcroft third graders may surface every year unless the School Board reviews, and possibly alters, the 1971 desegregation plan.

"The problem is with our adherence to the original plan," she said. "Arlington in 1986 is quite different from the Arlington of 1971 when the original plan was instituted. We are not succeeding at integration and we are asking a few families and their children to share that burden."