The Montgomery County school board yesterday took several steps to improve relations with the black community and upgrade the scholastic performance of minority students.

Acting in an all-day session, the seven-member board approved funds to train teachers in identifying minority students for advanced courses. The board also voted to provide resources for special academic programs to improve integration in areas of high minority enrollment.

The board also voted to rename its central office after George Washington Carver, a distinguished black scientist, and to nominate four blacks among the semifinalists in the replacement of Odessa Shannon, the board's only black member. Shannon, the only black official elected countywide, announced two weeks ago that she was resigning her post to join the inner circle of advisers to County Executive Charles W. Gilchrist.

Roscoe Nix, president of the local chapter of the NAACP and a frequent board critic in the past, praised the board's actions yesterday. "We have finally moved past the days of confrontation," he said. "Mistakes will still be made . . . . But the fact that there is discussion and some action and some evaluation and some accountability makes everyone a winner."

The actions the board took yesterday prompted several in the audience to comment on the distance the board has come the last two years as it has attempted to mend fences with the black community.

From 1978 to 1982, the board was dominated by a majority of members criticized by some blacks as being insensitive to black needs. That majority was swept out of office two years ago and replaced by a four-member slate that campaigned on a promise to improve the status of minorities.

School officials met last year to come up with a plan to improve minority achievement and those plans are being implemented in the schools this year.

School officials announced last week that black students were the only group who registered a considerable gain on a Maryland state writing proficiency examination last spring. As another sign of success this fall, officials reported a significant increase in the number of minority students enrolled in a new honors program at Cannon Road Elementary in Silver Spring which actively recruited minority students. Also, Rosemary Hills Elementary in Silver Spring, a school considered central to the county's voluntary integration program, reported enrollment this fall much higher than predicted.

In yesterday's action, the board voted to allocate almost $300,000 -- part of a $1.7 million special state appropriation -- to programs targeted at improving test scores and basic skills and enhancing the math, science and computer programs at schools with large minority populations.

In a preliminary vote, board members approved a policy giving preference to minorities and women when naming school buildings after individuals. "I hope this indicates that the black community and the white community have learned to work together," said board member Blair G. Ewing.

The four black semifinalists for Shannon's job were among 10 chosen yesterday out of 39 applicants. Those 10 are: Alan Cheung, a Veterans Administration deputy director from Rockville; Nancy Dacek, homemaker from Potomac; Roberta S. D'Oyen, legal consultant from Rockville; Jeremiah Floyd, an associate executive director of the National School Board Association from Bethesda; Martin H. Gerry, a lawyer from Bethesda; Vincent M. Hollis, a professor at Howard University; Janie M. Johnson, a junior high school teacher from Gaithersburg; James C. Moone, an assistant director at National Institutes of Health from Rockville; Timothy J. O'Shea, a corporate director of trade support from Gaithersburg; and Michael L. Subin, a market analyst from Gaithersburg.