Despite protests that using pocket calculators might render students more dependent on their batteries than their brains, the Arlington School Board mustered enough votes last night to approve the use of the devices in county schools.

"I don't want to keep Arlington students out of the next century," said Board Vice Chairman Claude M. Hilton, who led the move to allow students in elementary, intermediate and senior high schools to use calculators in a variety of class and homework assignments. The board also agreed to provide calculators to students in classes where their use is required.

But board members stressed that calculators "shall not be used as a substitute for teaching, learning and maintaining arithmetic skills . . . "

Hand-held calculators are already used widely throughout other Washington area school systems, and math educators and professionals nationwide have touted them as a way to help students verify results, save time on complex calculations, reinforce practical skills and illustrate some mathematical concepts.

An Arlington schools mathematics advisory committee, noting that many students already use calculators purchased by PTA groups, proposed introducing calculators and instruction on their use into the classroom this spring. School Superintendent Charles E. Nunley generally endorsed the proposed policy last night.

Board Chairman S.J. Pace, however, remained unconvinced. "I just cannot imagine that you improve students' skills by using calculators," he said before the vote. "There's about as much skill in using calculators as there is in dialing a telephone."

Board member Margaret Bocek voted with Pace against the measure, which was approved 3-2.