The Arlington Board of Education voted last night to raise the number of credits required for high school graduation from 18 to 20--one additional credit in both science and mathematics. The board also set September 1984 for expected elementary and secondary school closings.

The new graduation requirement will become effective for this fall's entering ninth grade class. Board member Michael E. Brunner proposed the change as part of an improvement in what he called the "academic rigor" of the county's high schools.

State law mandates 18 credits for graduation, including one mathematics and one laboratory science credit, but allows local boards to require 20.

As part of Brunner's proposal, the board also agreed to require students to take six academic periods a day, unless a student's principal recommends an exception. Students now have to take only five regular class periods.

The board approved the September 1984 school closing date 4 to 1, with Chairman Claude M. Hilton casting the negative vote. The first of several public hearings on the closings, necessary because of declining enrollment, is tentatively set for the early fall; a decision on consolidations is expected next April. Hilton argued that the period for making the decisions could be shortened.

In other action, the board approved a proposal by member Simone J. (Sim) Pace directing Superintendent Charles E. Nunley to prepare a report that would give preference to maintaining schools with the traditional closed-classroom formats rather than those with a more open system when closing decisions are made.

Torill B. Floyd was the only board member to vote against the Pace proposal.