The fight broke out Tuesday in the school cafeteria. There was a racial slur, a counterslur, and 15 blacks and whites were up and swinging.

Race relations and educational quality are improving in South Boston High School, headmaster Jerome C. Winegar contends. But he admits, as the fight indicated that the improvement is "a little shaky."

U.S. District Court Judge W. Arthur Garrity Jr. will be considering the extent of any change at the high school, the antibusing symbol of this city, as he begins hearings Thursday on whether to lift the federal receivership he place over the school 14 months ago. The move would return the school from court control to the control of the Boston School committee.

The NAACP and black plaintiffs in the five-year-old Boston desegregation case already have filed briefs opposing the move charging that the school isolated in a rundowns, Irish-American enclave, is still dominated by racial hate and violence.

Boston Mayor Kevin H. White and the School Committee have filed separate briefs claiming that the receivership is responsible for a continuing "stigma" of racial tension.

Claims and counterclaims have been escalating all week, as one again South Boston High School dominates the public debate. But what is being obscured is a more significant development in the other 154 public schools in Boston: a change in focus from busing to the quality of education, marked by a flurry of programs to improve the quality of a once-shoddy school system.

During the same hour that the school cafeteria in South Boston was in pandemonium, there was a contrasting scene in Mae Ella Peeples' seventh-grade English class in another section of the city. The 31-year-old black woman was teaching adverbs to her class of 28, about one-third black.

"Mrs. Peeples walked to the front of the room . . ." she said expecting students to fill in the adverbs. A dozen hands shot into the air. Given the ned, a bright-eyed, restless black boy in the front row spurted, "Slowly!"

"Aw," said a white girl sitting behind him as she playfully shoved his shoulder.

The school the Mackey Middle School, is a "magnet" school that specializes in the arts and humanities and draws black and white students voluntarily from all sections of the city. Red-and-white valentine displays decorated many of the classrooms in the old but clean building. Students were orderly.

The school system is in its third year of busing. About 20,000 of its 74,000 students are bused daily. For the second year, whites are in the minority, at 44 per cent, while 43 per cent are black and 13 per cent "other." A number of white student have left the public schools, either to attend parochial or suburban schools or not to attend school at all.

School and city officials and police say that other than occasional flareups in about five schools, racial tension and fighting generally have subsided to levels similar to that before busing. The rate of suspensions this year, for instance, is only slightly about that in 1972.

School officials admit that a beneficial side effect of the desegregation order was that it focused public attention on the quality of education in the schools.

"We were in bad need along those lines," said Associate Superintendent Charles W. Leftwich. "The order enabled us to take a critical look at the schools and gave us a chance for renewal."

Leftwich points out that every middle and high school in the past two years has established working relations with local universities and businesses for job training programs, educational skills or facilities and equipment.

School Superintendent Marion Fahey has been stressing basic reading and math instruction, and throughout the systems, teachers have been devising these and other programs to fit the needs of their students, scool officials say.

At the same time the 20 "magnet" schools providing specialized areas of concentration such as sciences or art have been created.

It is still too early to tell whether the students are learning any more, school officials say. But many share what Leftwich calls a "gut feeling" that they are. Moreover, biracial councils ordered by Garrity for each school and school district have involved parents in the educational programs of the schools for the first time.

On the other hand, school department officials franky admit that the school system is still plagued by problems such as inefficiency and patronage.

And they also acknowledge that the sore that festers the most remains "Southie" - South Boston High school.

By the end of January, South Boston students were suspended almost 550 times this school year, or more than one-fifth of the suspensions in the entire school system. Moreover, headmaster Winegar has sent students home to return with their parents for readmission more than 500 times, an alternative to suspension no other school has.

The enrollment at the school is 1,205, but average daily attendance is only about half that, including about 400 whites, 225 blacks and 25 "other," mainly Hispanic-American, Winegar said. Many of the missing students can be found hanging out on the streets in black Roxbury or white South Boston.

Winegar, who was brought in from Minneapolis last year and appointed by Garrity, said that fights are less frequent this year than last year.

But uniformed state police are still spread throughout South Boston High, and students there must be searched and passed through metal detectors as they enter in the morning.

"I often wonder what it does to a kid to go through that dehumanizing experience day after day," Winegar said.

Winegar will be central to Thursday's hearing. South Boston parents resent the fact that he was brought in from the outside, school department administrators say he has been a bad administrator, and Winegar admits he is an independent-minded maverick who will likely offend his superiours. The school committee, nonetheless, in attempting to appease the judge, voted last week to keep Winegar on if the receivership is lifted.