Just two weeks after Arlington's 28 schools sounded their last bells for the 1984-85 school year, the School Board met yesterday morning to talk about September.

The board welcomed new Superintendent Arthur Gosling and new board member Judy Connally, re-elected Gail H. Nuckols to a one-year term as chairman and vowed to make reaching out beyond the students a priority for next year.

The appointment of Connally to the seat vacated by Simone J. Pace gives the five-member board four Democrats.

"We believe it is important to expand our outreach programs to the community, and we feel that the schools would benefit by improving the working relationship among students, staff and parents," said Nuckols.

U.S. Census figures for 1980 showed that only 19 percent of Arlington's households had children under 18. Arlington school officials have stressed in the past the importance of making education a priority for the majority of citizens who do not have young children, but whose taxes help support the schools.

The draft of a management plan designed by Gosling to address the board's priorities for 1985-86 outlines specific ways of reaching out to the community, including expansion of the Adopt-a-School program, in which local businesses agree to help certain schools with money and volunteers, and the development of plans in each school to improve communication between students, staff and parents.

"The board will make every effort to communicate openly and effectively with citizens, students and staff," Nuckols said.

Other priorities for next year include starting staff development programs that focus on classroom management and reviewing the impact, particularly for elementary students, of "pullout" programs that remove students from regular classrooms and put them in special classes or programs, Nuckols said.

In addition, she said, the board will continue to work on this year's priorities, including improving intermediate school and guidance programs, basic skills work for underachievers and recruiting teachers.