As students leave Jefferson Junior High School each afternoon, principal Vera White stands by the door, wishing them well and watching carefully what they carry.

"You can't get out of the building if don't have your books," said Bianca Lane, an eighth-grader at the school in Southwest Washington. "If you don't have the books, she'll send you back to your locker. Everybody has to do their homework here.

"Oh, sometimes I don't like it so much," Lane added. "But if you don't do homework, things don't stick in your brain."

At Jefferson, every student must have homework in every academic subject every night, including weekends and holidays, White said. There are even assignments during the summer. But the school, which has pulled up its test scores dramatically and won a presidential award for excellence, is more the exception than the rule when it comes to homework.

Much more common in the Washington area and around the country are schools where homework is light, particularly for senior high students who are not in college prep classes. During the past decade and a half, many teachers say, the amount of homework has diminished, though there are signs of an upturn during the past few years.

"I believe in homework. Students need that kind of reinforcement to really move ahead in class, but I assign less than I used to," said Muriel Stubbs, an English teacher at J.E.B. Stuart High School in Fairfax County. "A lot of teachers assign less than they did 15 years ago.

"Many students just don't do it any more," she continued, "and you don't want to spend all your time policing them and punishing them for what they didn't do. You want to teach what you can . . . . I do an awful lot of reading assignments in class simply because that's a way to get kids to read."

Many teachers have changed, bringing home less work themselves and assigning less to their students, teachers say.

"The idea used to be that teachers walk home with an armload of papers and spend hours grading them," said Jay Fellows, a teacher at the School Without Walls, a public high school at 21st and G streets NW in Washington. "That's pretty much disappeared. They don't pay enough to expect us to do that and spend nights and nights away from our families grading papers."

Through the decades the amount of homework in American schools has gone up and down with the changes of general education.

Herbert J. Walberg, research professor of education at the University of Illinois, said homework declined with the ascent of progressives in the 1900s and 1930s. They argued that too much homework harms children's mental health and, because it is unsupervised, perpetuates mistakes.

In the late 1950s, homework increased, Walberg said, as part of the post-Sputnik concern over academic rigor. It went down again in the late 1960s and 1970s as schools moved to "relevance" and flexibility.

"Now, homework is being again revived," Walberg wrote in a paper prepared for Educational Leadership magazine, "perhaps because of . . . national reports that point out unfavorable achievement comparisons of our students with those in other countries." But he added in an interview that it is difficult to know how far the revival has gone as school assignments compete with television and teen-agers' jobs, and fewer mothers supervise homework in the afternoon because more women hold jobs outside the home.

According to a recent U.S. Census Bureau survey, based on interviews with parents, students average about 5 1/2 hours of homework a week. Girls study more than boys, the Census Bureau said.

In high schools, where the census said most homework is done, the median time per week was 6.5 hours for public schools and 14.2 hours for private schools.

However, the figures are far higher than those from other surveys in which students were interviewed. The most comprehensive study, a survey of about 58,000 high school students in 1980, reported that the average amount of homework per week was about 3 1/2 hours for public schools, 5 1/2 hours for Catholic schools, and about six hours for other private schools.

"I think a lot of parents aren't sure how much homework their children do," said Lawrence LaMoure, a researcher at the National Center for Education Statistics. "They send them up to their rooms, but they don't really know what's going on there."

Ben West, a fifth-grader at Burgundy Farm Country Day School, a private school in Alexandria, said, "I spend two or three hours on homework a night. But half of the time I'm doodling . . . . One day we get nothing and another day we might get 15 tons of homework."

According to the national center, only about 24 percent of 1980 high school seniors did more than five hours of homework a week, compared to 35 percent who reported doing that much in a similar survey in 1972. LaMoure said preliminary results from a follow-up study in 1982 show an increase in homework, though it still lags behind the amount for a decade earlier.

The main reason for the long-term decline was the shift in enrollments from college preparatory courses, with relatively heavy homework requirements, to courses in the general track, where homework is less, LaMoure said. The Census Bureau report said the difference in public and private school homework also can be explained by this difference in courses. Most private schools stress college prep courses while public schools have large numbers of students in general and vocational tracks.

But the national center study reported that even academic students were doing less homework in 1980 than their counterparts did in 1972, and that academic students in public school spent less time on homework than those in private schools.

Walberg said the amount of homework done correlates strongly with academic achievement.

"The time spent on learning is the key," said Walberg, who has used computers to analyze more than 3,000 studies of academic performance. "The more time you spend on something, whether at school or home, the better you'll be. If you look at chess players or ballet dancers or swimmers, you'll find the same thing. Excellence requires diligence, and homework simply extends the learning time."

The pattern shows up in international comparisons, said Barbara Lerner, the head of a consulting firm in Princeton, N.J., whose analysis was prominently cited last year by the National Commission on Excellence in Education.

"Homework matters," Lerner said. "Where the children work harder, they achieve more." In Japan, for example, about the same proportion of children graduate from high school as in the United States, but the average amount of time Japanese students spend on academic work -- both in school and at home -- is about double. Average achievement, as measured on a set of common exams, is much higher, Lerner said.

Many private schools in the Washington area report large amounts of homework. At St. Albans School in Northwest Washington, even in the fourth grade, students often spend three or four hours a night on assignments, several parents said, though the school says the maximum ought to be an hour and a half.

This has brought some complaints that the school "crowds out" the rest of children's lives, including playtime and music lessons.

"Sometimes we do overshoot and over-demand," said A. Wayne Gordon Jr., the assistant headmaster in charge of St. Albans Lower School, "and we have to make adjustments. But usually the boys get into the rhythm of it. We're holding kids to high expectations, and homework is part of that."

"Often the pressure comes from the parents, not just the school," said a Washington psychoanalyst who has treated many children from private schools. "A lot of these people are successful professionals. They want the same thing for their children. There's a lot of anxiety about getting good grades and getting into college. The children get nervous too."

One outgrowth of the pressure, whether it comes from the parents or the schools, is the sense of obligation that many parents feel to help children with their homework. Usually, the schools advise against doing too much, though Gordon said that "a parent should not feel that he is breaking any rule if he gives assistance."

In the international comparisions, Lerner said, parental help was the only aspect of homework that had a negative effect on achievement. She said this showed that parents generally gave more help to children who could not do the work themselves.

"Children have to be responsible and struggle with it themselves," Lerner said.

Dorothy Rich, president of Washington's Home and School Institute, said the way out of this dilemma is for teachers to assign some homework that parents and children should do together. She has prepared hundreds of lessons suggesting how parents might present the material, which the National Education Association recently began to distribute.

"Is it the child's assignment or the family's assignment?" Rich said. "Let's try to be explicit about it."