The D.C. Board of Education, in an act of unity yesterday, unanimously elected R. David Hall (Ward 2) as board president, succeeding David Eaton (At-Large).

The 11 members of the board, at the annual organizational meeting, also unanimously elected Linda Cropp (Ward 4) to serve as vice president, succeeding Nate Bush (Ward 7).

Bush and Barbara Lett-Simmons made the motions to elect Hall and Cropp by acclamation at the meeting, which was held at Roosevelt High School.

Hall and Cropp are expected to continue the cooperation that has characterized the board's work in recent years, several members said.

Eaton, who was elected to the board in 1981, and Bush, a five-year board member, served an unprecedented three years together as president and vice president.

Under Eaton and Bush, the board hired Superintendent Floretta D. McKenzie and students have shown considerable improvement in test scores and achievement, although there was some decline in the scores of some grade levels last year.

Hall, 35, who serves as chairman of the board's finance committee, is a real estate broker. He is a D.C. native who attended public schools, graduating from Cardozo High School. He received a bachelor of arts degree in political science from Howard University in 1971 and a law degree from Georgetown University in 1977.

Hall was elected to the board in 1981. A devoutly religious man, Hall has been characterized by some school administrators and board members as conscientious, hard-working and highly ambitious.

"He's very knowledgeable and has a lot of technical knowledge about the school budget," said City Council member Hilda Mason (Statehood-At-Large), who heads the council's education committee.

"He works well with people and loves young people."

In his acceptance speech, Hall said, "Before us lies the challenge to lift the D.C. public school system to a new height . . . . Let us build."

Hall said in an interview that his immediate goals include improving the management services of the school administration. "We need to make sure services are delivered," he said. He cited such continuing problems as providing adequate transportation to handicapped students and getting textbooks and supplies into the schools.

Among his proudest accomplishments as a board member, he said, are "getting our full budget approved in 1982, my first year as finance chairman, [and] having a balanced budget every year I've been on the board."

Hall, who founded the D.C. Street Academy, an alternative high school for dropouts, is married and the father of two children.

Outgoing president Eaton said at a news conference that he would not seek a fourth term because of "personal reasons," including church activities at All Souls' Unitarian Church, 16th and Harvard streets NW, where he is senior minister.

"I've enjoyed my three years as president," he said, adding that the board has maintained a "good" image in recent years because members keep their disagreements behind closed doors.

Eaton said more needs to be done to further motivate students and provide more cultural enrichment for D.C. students, many of whom are from economically deprived families.

Cropp, 37, has been a member of the board for four years and heads the board's education committee. She earned a bachelor of arts degree in history and political science at Howard University and a master of education degree at Howard in 1971.

She began her career in the school system as a student-teacher, she said.

She urged her fellow board members to maintain a high level of cooperation that has distinguished it from earlier years when the board was criticized for being too divisive.

"Pettiness and ego-gratification fade as we reach for quality education," she said. "We must maintain tolerance, objectivity and reason."

Cropp is married and the mother of two children.