Programs to boost the achievement of minority students in Arlington should be developed by individual schools rather than by a county-wide coordinator, the County School Board decided last night over the objections of some black parents.

The board adopted the $130,000 plan to improve minority achievement by a vote of 3 to 2, although several black parents argued the program should focus exclusively on black students and have a full-time administrator.

Frank Wilson, the only black member of the School Board, voted against the plan, saying it would produce fragmented efforts to solve a complicated problem.

Arlington's total student enrollment of 14,517 is 54.5 percent white, 16.2 percent black, 14.7 percent Hispanic and 14.5 percent Asian.

Scores on standardized tests for the 1984-85 school year showed the average scores of black students lagged behind those of whites by as much as 46 percentile points.

"We've hit an academic pothole," said Wilson. "The black youngsters are below the surface of the academic road."

Board member Margaret A. Bocek also voted against the plan, in which each school principal will devise programs to improve minority achievement and submit them to a committee of teachers and administrators for funding. Bocek argued the plan was not specific enough.

"We still don't have a plan, we have a concept," said Bocek.

Superintendent Arthur W. Gosling said each school's plan would follow the general guidelines proposed in February by a committee that spent three months examining minority student achievement. Those guidelines include working with parents, limiting class sizes for underachievers and promoting students' self esteem.

Margaret Wilson, chairman of the Civic Coalition for Minority Affairs, argued the program should focus on black students alone.

"This program is for everybody . . . it's business as usual," she said. "There has never been a program in the Arlington schools uniquely for black students."

Robert McGregor, chairman of the Education Committee of the Arlington NAACP, also urged the entire $130,000 be spent to boost black students' achievement, in part by hiring a full-time coordinator to oversee that effort.

Several board members said the money would be spent more effectively on programs anchored in each school than on a county-wide coordinator.

Gosling stressed that the plan is just one piece of the school system's effort to improve test scores of all underachieving students. "I would never characterize this commitment as a breakthrough," he said. "I would characterize it as a step forward, an attempt to come to grips with what is a very difficult problem."