Here is what Elbert T. Brown, student representative to the D.C. School Board, president of the District's student advisory council, thinks of the 11 adults who run his school system, the D.C. School Board.

"They're childish," says Brown, a 12th-grader at Woodson. "I tell them they act like they were in the 5th grade. They don't talk right, they don't act right, they don't think right. They haven't done anything to improve the schools since I've been in them." An episode from the board meeting on April 28:

Frank Smith Jr. (Ward 1): "As a result of the policy [ending social promotions], many minority students are being pushed out of schools. . . . It pains me for this board to be pushed into making such policy. . . ."

Frank Shaffer-Corona (member-at-large): "I'm sorry to hear that my distinguished colleague from Ward 1 is in pain. The nurse goes home at 3 p.m." A second episode:

John Warren (Ward 6): "Mr. President, I will not let you determine my agenda. . . ."

Board President Carter Lockridge (Ward 8: "Mr. Warren, you are out of order."

Warren: "I can do it in order or out of order but I will be heard. . . . It appears, Mr. President, that you have your own agenda."

Lockridge: "You can be heard and not say a damn thing. . . . My agenda is to put forward the board rules. . . . I don't have any hidden agenda."

Eugene Kinlow (member-at-large): "I'm confused."

Warren: "Join the club."

Lockridge: "Wait a minute."

Warren: "I'm not going to sit here while you lie and twist the rules. Don't treat us like a bunch of fools. . . ."

"They're into power," Elbert Brown says. "Everybody here wants to be a baby. Marion Barry, who goes from the school board to the city council and then becomes mayor. You ask them something and they love to jump up and say, 'I run the schools,' like they are gods. That's why they're always fighting to outdo each other."

Anyone who talks to a dozen District residents at random knows that Brown's opinions on the school board are not unique. For years the board has been criticized for having its members swipe and snap at each other while doing little or nothing to improve the ailing D.C. schools. Now there is a new element: Mayor Marion Barry, the former school board president, and his aides privately suggest that the school board be done away with.

Publicly Barry is coy, attributing to "others" the notions that the mayor should appoint school board members or run the schools through a department of education. "I still believe that an elected board is preferable," he says.

Barry's public stance is a counter to charges that he wants to get rid of one of the few elected boards in the city at a time when the city is fighting for the right to take part in more elections.

In fact, he probably would not be hurt politically if he publicly criticized the board. Many a mother would like to ride the school board out to town when she looks at a son who doesn't read well enough to get a good job.Every father who has to pay to send his child to parochial or private school would agree.

Barry's antipathy toward the board is not all a matter of concern for education. At large part is personal dislike. Within weeks after he took office as mayor, the board forced a strike issue with the teachers' union. The mayor wanted to make a good show of settling the strike, but for weeks he couldn't even get the board to meet with him. Barry could not afford a strike. He needed a political victory. The mayor finally went around the board and pushed the courts to order an end to the strike. Since then, the major has looked at the school board as enemy territory to be conquered.

The territory includes the largest budget in the city government, large land holdings and empty old buildings, schools in every ward that hold a key to every neighborhood. There are also 11 public offices that could be held by the major's supporters. Four of six candidates he supported won school board seats last November.

Barry is currently fighting the board over millions of dollars the board did not spend last year but wants to add to its budget this year, over cuts in a school budget the board does not want to accept, over demands that some school buildings be closed and so on.

The mayor's tangle with the school board resonates to a dissonate chord that has been in the city's politics since the school board was first elected in 1968. The disagreement vibrates with the constant bickering on the board, the repeated firings of superintendents every year or so before Vincent Reed took the job in 1976, the strikes and -- worst of all -- the ever-present sight of city school graduates who read poorly after leaving public schools that rank among the worst on test scores in the nation.

On the college boards, D.C. students score more than 20 points below the national average and rank in the bottom 20 percent of all students in the nation taking the test. An average 9th-grader in the D.C. schools reads and does math on the 6th-grade level.

John Ray, one of the mayor's political allies, held hearings last summer on the problems of the school system. He recommended this month that a joint study commission generate a "comprehensive action plan and strategy for improving the school system." The city charter intended, of course, that the school board be that joint commission. But everyone is looking for a way to get around what one parent-activist calls "those clowns."