The D.C. Board of Education, already bitterly torn by the announced resignation of School Superintendent Vincent E. Reed, faces another potentially divisive situation in January when it moves to elect its next president from among its 11 members. And even though Reed may be gone, his shadow is certain to lie across the election.

As various members begin jockeying for supporters, the dominant issue facing the board is Reed's resignation and who will succeed him. The election at this early point appears to be shaping up into a three-way race among incumbent president R. Calvin Lockridge (Ward 8), Frank Smith (Ward 1) and John E. Warren (Ward 6).The essential question dividing these contenders is whether the next president -- who would lead the search for Reed's successor -- will want someone in Reed's image or not.

"I'm just not quite sure how [the Reed resignation] will affect the presidency. I would say it's up for grabs at this point," said board member Alaire B. Rieffel (Ward 2).

Board members who have been at odds with Reed quite frequently in the past -- Warren, Lockridge, Bettie Benjamin (Ward 5), current vice president Barbara Lett Simmons (At-Large) and Eugene Kinlow (At-Large) -- hold a slim majority on the board.

The most consistently anti-Reed candidate is Warren. In announcing his resignation, Reed cited Warren's "nastiness" as one of the factors that led to his decision. Reed, who held his post since 1975, complained that the board, and Warren in particular, were trying to take away his administrative powers s superintendent and said he was simply fed up with the infighting and atmosphere of acrimony which surrounds the board.

The board members who support Reed and are still trying to get Reed to reconsider staying on say that the chances of that were blown away Friday night when Warren blasted the superintendent in a television interview. That interview is said to have made Reed more adamant than ever in his decision to quit.

Warren, a graduate of the D.C. public schools, who won his second term on the board last year by a slim vote, has overseen the budget cuts in the school system this year as chairman of the board's important budget committee. Combative by nature, Warren was criticized earlier this year by board staff members who said he "harassed" them so much that they could not get their work done.

Warren was vacationing in Florida yesterday and cold not be reached for comment on his candidacy.

Smith is the board member most supportive of Reed, having arranged a luncheon between Reed and some board members last Friday to ask Reed to reconsider his resignation. As president, he said he would make certain that programs started by Reed would continue in the schools.

Smith, who is usually quiet at the often raucous board meetings, said in a telephone interview yesterday that he sees himself as an alternative to the quick-to-anger Lockridge and combative Warren.

"What it comes to down to is a person who can work with other people," said Smith, who won his seat on the board last year with Mayor Marion Barry's support.

Smith said he would like to clean up the board's image as a group of individuals more interested in bickering than in legitimate debate, in personal vendettas than in policy-making.

But one of Smith's opponents on the board, who asked not to be named, joked of a Smith candidacy, "He hasn't done anything this past year but raise money for the Cardozo High School band to go to the Rose Bowl."

Smith, however, was the first board member to move that Reed's plan for an "academic high school" for collegebound students be reconsidered after the board rejected the plan last spring.

In-the middle is Lockridge, one of the most controversial presidents in recent board history, who insists he is a reluctant candidate and will not actively seek reelection. "I'd prefer not to have it, but if the votes are there, i'd take it."

Lockridge says, however, three board members urged him to run because "nobody knows this system as well as I do." Lockridge, who was elected on the 13th ballot in a hard-fought battle last year against Kinlow (who is apparently not running this year), evoked the ire of some of his colleagues in his first month as president when he changed the board's committee structure, eliminating some of the old committees and creating some new ones. As a result, his vice president, Simmons, promptly refused to serve on any of the committees and feuded with Lockridge for the rest of the year. Lockridge also tried to curb the often long-winded debate of board members by deeming that all of the evening meetings should end at 10:30. But as often as not, his colleagues overruled him and voted to continue the meetings until well after midnight.

Lockridge, who is generally considered a hard working member knowledgeable in almost any area of the school system, is also known for his short temper. At more than one public meeting, he threatened to "punch out" at-large board member Frank Shaffer-Corona, who kept interrupting the proceedings.

Lockridge frequently criticized Reed in the past for being too slow to implement directives from the board and for withholding information from the board.

Other board members who might enter their names for president are Benjamin, Simmons, and Carol Schwartz (Ward 3). None of these members could be reached for comment yesterday.

Besides picking a new superintendent, the board will also face in 1981 the major task of negotiating a new contract with the teachers, which could prove to be a sticky issue in light of the massive teacher cuts this year.