Robert E. Shoenberg, a member of the Montgomery County Board of Education for two years, was elected yesterday to a one-year term as president by a unanimous vote of the seven-member board.

James E. Cronin, who also was elected in 1982, was elected in a separate vote to succeed Shoenberg as vice president.

Shoenberg, who succeeds board member Marilyn Praisner, said after the vote that he does not plan to set any new goals or agenda for the board, but will "in my own way and my own style" lead the board toward already defined goals.

Pointing toward expected budgetary constraints and concerns over school closings, specifically reconsideration of plans to close Northwood High School, Shoenberg said he hopes to "work together in harmony" with county officials and community members who would be affected by board actions.

"Whatever the decision," Shoenberg said of Superintendent Wilmer S. Cody's proposal to reconsider Northwood's future, "I hope it is the last time we'll have to consider it."

Shoenberg also said that drawing up an operating budget for next year, a draft that will be made public Jan. 3, will be "a serious problem for us. As we do more and more, people expect more and more . . . . We are going to have to deal with that the best we can."

Cronin repeated Shoenberg's concerns and said he hopes that "at the end of this year, we'll be further along our goal, which is excellence in education."

Shoenberg, 49, is dean of undergraduate studies at the University of Maryland in College Park and has been active in PTA work. Cronin, 42, is an associate professor of history at Montgomery College in Rockville and was active in county human relations activities before he was elected in 1982.