The Arlington School Board has formally endorsed locating the Hoffman-Boston-Woodlawn alternative school at the Stratford school building and using the Gunston school for adult education and the county's performing arts program.

At the same meeting last week, proposed cut in state aid to Arlington schools for fiscal year 1980 may be less devastating than the board originally feared.

The uses of Gunston and Stratford had been vigorously debated by residents from both areas who attended several recent board meetings. Residents near both schools had asked the board to locate the new merged Hoffman-Boston-Woodlawn program in their respective neighborhoods.

Gunston and Stratford currently are junior high schools, but the board decided last year to close the schools at the end of this school year because of declining enrollments.

The proposal for a performing arts center was brought to the board three weeks ago by William Hughes, director of the county department of community affairs. He suggested that the county move the current program from the Stewart School to a larger facility of Gunston. He told the board at its meeting Feb. 16, however, that he could not guarantee that the county board would either approve the plan or increase the funding needed to operate at Gunston.

Gunston area residents had stressed that they wanted an educational program at the school, but had said they were leery of the adult education program. John Quinn, who often served as the Gunston spokesman and was a co-chairman of a citizen's task group studying possible uses of the building, had told the board that the adult education program should be limited so that parking would not spill over from the school into adjacent neighborhoods. In its decision, the board specified that the adult education classes be scheduled carefully to avoid a parking problem.

None of the Gunston residents spoke at the meeting last week when the final decision was made.

In voting 4 to 1 to approve the Gunston and Stratford proposals, the board accepted the recommendations of Superintendent Larry Cuban. Board Chairman Thomas Penn said later he felt Gunston area residents had not been given ample opportunity to express their views to the board at the meeting.

The board did not make any decisions on how to fund the operations of the schools but agreed to make those decisions during budget considerations for next year, which the board currently is working on every Tuesday and Thursday evening.

The board followed the recommendations of Cuban for 10 buildings. In other decisions the board unanimously agreed to:

Locate a new traditional alternative school at Page School.

Continue the current uses of Langston, Wilson and Clay schools and the George Mason Center.

Declare the Marshall, Marshall Annex and Woodlawn buildings as surplus and work with the county board to find other uses for them.

direct the staff to locate an editional program at the Hoffman-Boston building. The prime possibilities recommended by Cuban are the kindergarten and Montessori pre-school program, special education classes or selected adult education daytime classes.

The day before the meeting all the board members, except Richard Barton, went to Richmond to testify before the House of Delegates Appropriations Committee and to meet with Gov. John Dalton to lobby for retention of the "no loss" provision, which allows a school system to receive at least the same amount of state aid as the previous year.

The proposed state budget for fiscal year 1980 does not include the "no-loss" provision, and the Arlington board estimated it could lose up to $5.2 million or more than 10 percent of its current budget, without the aid.

Broder said several of the delegates which met the group said they would work to ensure a compromise on the funding issue. Penn said he had been contacted earlier in the day by a member of Del. Mary Marshall's staff who said a new formula had been agreed on that would restore $3.5 million in state aid to Arlington schools.

In other action, the board appointed G. Franklin Miller, a mathematics specialist with the school system, as the principal of the new traditional alternative school.