Nearly 44 million students start back to a leaner and hungrier school year this week, heading generally for larger classes taught by fewer teachers with older books in shabbier buildings.

Education associations estimate that up to 55,500 teachers could lose their jobs this fall, mainly in the Northeast and Midwest. Federal budget cuts and the sagging economy have finally reached the classrooms.

The "baby bust" of a school-age population that has been in decline since 1971 was expected to ease the schools' financial burden, but it hasn't worked out that way.

Educators see the second wave coming, the children of the post-World War II baby boom generation, and are reluctant to close schools they believe they will need again in five or six years. Meanwhile, they cannot afford to keep everything going.

Widespread unemployment means lower tax income for state and local governments, at the same time that President Reagan's first-year budget cuts are now reaching the schools. "The school districts are using reduction of school employes to balance their budgets," said Gary D. Watts, chief organizer and director of affiliate services at the National Education Association.

He said NEA expects that 50,000 teachers may be laid off this fall, while the American Federation of Teachers put the figure at 55,500. AFT research director Jim Ward said that is "a judgmental figure" based on a survey of all AFT locals, adding that the pinch would be worst in New Jersey, Michigan, Massachusetts and other northeastern and midwestern industrial states.

Sun Belt or energy-rich states can expect to hire more teachers for rising student enrollments, he said, but the net effect is downward.

Although federal funding accounts for only 8 percent of school spending nationwide, it is the specialty 8 percent: math and reading booster courses for disadvantaged children, supplementary money for library books, school lunches and for teaching handicapped youngsters, aid in desegregating and in vocational education, and help for schools near large federal and military installations that pay no property taxes. All these programs have been slashed an average of 20 percent from last year's levels.

States with income-tax rates pegged to the federal rate saw their incomes drop with last year's tax cuts. In addition, states where industrial unemployment is highest have chopped their overall budgets, with education among the hardest-hit areas.

"Overall, the kids can expect to see fewer options," said August W. Steinhilber, associate executive director of the National School Boards Association.

Districts first defer buying new text and library books, he said, and make do with older microscopes and other laboratory equipment.

Then they defer maintenance on their buildings and cut back custodial care, and finally they go after extracurricular activities, especially junior high school sports and after-school clubs and socializing.

"Kids will probably have fewer evening programs and will pay more for their lunches. There'll be fewer teachers, fewer administrators, fewer specialists, especially in science and math," Steinhilber said, because businesses and universities are willing to pay more for experts than the high schools can offer. This comes at a time when business and industry are urging schools to put more emphasis on scientific and technical education, he noted.

Cuts in the Comprehensive Employment and Training Act and in technical training programs will be deeply felt in poor areas, with ominous social consequences, educators agreed. Most school security officers were paid under CETA, and their departure has "very scary implications" in urban ghetto schools, said Ward of the AFT.

The AFT is running more workshops on teacher self-defense and legal rights, said spokesman Scott Widmeyer. Baltimore educators report a rising incidence of weapons found on students, while Miami officials recently held a series of meetings on the issue of violence in the schools after a teacher was killed.

AFT found that school crimes were down 22 percent in New York City last year, "but we're concerned whether that trend will continue with fewer school safety people," Widmeyer said.

He blamed the economy for part of the problem. "When people can't find jobs and have nothing to spend, it makes family life not what it should be. When the kids come to school, those problems are built up in them and they come out sooner or later. Teachers are the ones who have to cope," he said.

In Michigan, where a reeling automobile industry has put $500 million less than last year into the state's coffers, education spending has been slashed 10 percent as part of an overall $626 million state budget cut.

"We're cutting into the meat and in some cases into the bone of some school districts," said Philip Kazmierski, special education assistant to Gov. William Milliken. He noted that in 15 townships, tax hike votes will determine whether their school systems open at all.

A side effect of the situation is fewer teacher strikes. In previous years the NEA, which represents 80 percent of the nation's 2.5 million teachers, has had about 200 walkouts nationwide, but it staged 140 last year and expects fewer this fall, Watts said. The AFT led 25 strikes in 1980 but only 14 last year and expects no more now, Widmeyer said.

In Michigan, for example, salaries are low and teachers are hurting, he said, but "it's pretty hard to fight for a salary increase when a state is on the brink of bankruptcy."