The Washington area's shrinking public school systems reopen for the fall term this week -- with a renewed commitment to raising academic standards through new tests, textbooks and promotion requirements.

Even with an areawide enrollment drop of about 3.5 percent, some 540,000 students are expected to begin classes throughout the metropolitan area. They start back today in all public school systems except the District of Columbia's, where classes begin on Thursday. In Loudoun County, classes started a week ago.

"We have to try to do more with less," said D.C. School Superintendent Vincent E. Reed, whose school system has undergone the most drastic school layoffs in the area in recent years.

Caught in the District's budget crisis, the city school system has lost 12 percent of its classroom teachers since last year, and 15.6 percent of its administrators. Student enrollment is expected to drop 7 percent, falling below 100,000 for the first time since 1952.

To trim its staff, the D.C. school board has sent layoff notices to about 730 employes, including virtually all teachers under 30 or with less than 10 years' experience.

Elsewhere, substantial drops in enrollment and cuts in staff are taking place in Prince George's, Arlington, and Montgomery counties. But the layoffs there are not as extensive as the District's, partly because staff reductions have been achieved primarily through resignations and retirements.

In Montgomery, 31 teachers have been laid off -- the first ever in that school system. In Arlington, about 30 more teachers have been fired this year.

Even though Prince George's system has the largest drop in its school work force among area suburbs -- about 5 percent -- only one regular employe, the safety director, whose job was abolished, has been laid off. All the other reductions were made through retirements or reductions were made through retirements or resignations, although some administrators were assigned to lower-paying teaching jobs.

After several years of major drops in enrollment, Alexandria expects to lose only about 200 students this fall and has cut its staff only slightly.

The one major suburb that's not cutting back is Fairfax County. Although its enrollment is expected to decline slightly for the fifth year in a row, the number of school employes will increase by almost 2 percent.

When Washington began sending out layoff notices in July, Fairfax conducted job interviews in the D.C. school administration building. It ended up hiring about 25 former D.C. teachers.

"They're young teachers with a lot of energy and enthusiasm," said Richard W. Harley, Fairfax's acting personnel director. "They represent a good group so we went into the city to get them. They were out of a job and we're looking for growth."

As they grow smaller, the school systems -- except Fairfax's -- are moving away from some of the liberalizing innovations they adopted in the 1960s and 1970s.

This fall, as part of the "back-to-basics" trend:

Washington schools will begin to divide the first three grades into two semesters. All students in those grades will be required to master a checklist of skills before they will be promoted to the next semester.

Students in Montgomery County high schools will take the uniform schoolwide final exams in all academic subjects each semester, instead of just taking the tests that are prepared by their own teachers. Despite considerable opposition, the school board decided to develop countywide exams in English and mathematics over the next three years.

In Prince George's County, all elementary teachers will begin using a single series of spelling books. A single series of reading textbooks will be phased in over three years, starting this fall. Elementary teachers already use a single series of math texts.

"We're trying to provide consistency and structure," said Louise F. Waynant, director of instruction for Prince George's County. "Teachers can add a great deal of material they choose themselves to what's given in the textbook. But we felt there should be a single series of texts (in each of the basic skills). Our children move around a lot and they've been dipping in and out of a great many books. There used to be 12 (different) reading series in common use."

But in Fairfaix County, the much-heralded programs that compelled all high school students to write a grammatically correct essay has been quietly dropped this year. School administrators are developing plans for a new, more explicit sex education curriculum. And there is no move at all toward more standard tests on textbooks.

"We've had a stable middle-of-the-road curriculum that proved very successful," said school board chairman Ann P. Kahn. "We feel, 'If it's not broken, don't fix it.' We don't need any violent swings from one thing to another."

Kahn has been very skeptical of the minimum competency tests in reading and mathematics, that all students in the state must pass before they can graduate, starting next June. Maryland will have a similiar requirement in reading starting in June 1982. The District schools will have a required "everyday skills" test for the class that graduates in 1984.

The competency tests have been adopted by more than two dozen states in response to complaints that increasing numbers of students have been graduating without mastering basic skills. are especially helpful . . . The testing itself can be a rather useless exercise. It's very expensive. And when the tests are given in high schools all they do is highlight those who are incompetent."

The testing of this year's Virginia seniors began when they were in 10th grade. Those who failed have had two more chances to pass the exam since then. They can have three more tries while they are seniors.

The exam is pegged to a ninth-grade level of difficulty and by last spring, only 3 percent of the class of 1981 still hadn't passed it. The failure rate for blacks, however, was 8.5 percent, compared with 1.5 percent for whites. The disparity has sparked criticism from black organizations, who have indicated they might sue to block the exam from being a graduating requirement. i

The back-to-basics trend fits in wellat a time of financial retrenchment.

For example by adopting standard textbook series, Prince George's County will provide a common course for all students and save money.

Montgomery County high schools, meanwhile, are cutting the number of class periods from seven to six a day, which will limit electives and give more time to required courses. But that also means that fewer teachers will be needed to staff the periods.

"We're getting more mileage out of the staff," said Paschal Emma, a veteran principal who is now in charge of implementing the new senior high policy. "The seven-period day was a luxury that we can't afford now."

Generally, the cuts in school staffs are not expected to produce larger classes or reduce course offerings because, with the exception of Washington's cutbacks, they are proportionately aboutthe same or smaller than decline in enrollments. Indeed, under the prodding of federal law, the number of small -- and more exensive -- classes for handicapped youngsters is increasing in all local school systems.

In Washington, however, the average size of elementary classes is expected to rise from 26 students to 28. Driver's education will be dropped in D.C. high schools, and prekindergarten classes will be cut from full- to half-day sessions, although the District continues to be the only local school system to offer them.

Because of seniority rules, the layoffs in the District will cause the most upheaval in elementary schools with large numbers of young teachers. This has happened particularly in new open-space buildings, such as Lafayette School in Chevy Chase and Friendshipand Washington Highlands Schools in Anacostia.

"We're losing our new blood," one administrator said. "The teachers who wanted to try the innovative programs. Now we're going to get the older teachers in those buildings, and I bet they'll want to put back the walls."

In Arlington, the walls already havegone back up in some open-space buildings, a move that is applauded by the county's new school board president, O.U. Johansen. Johansen leads a board that for the first time in many years is dominated by persons appointed by a Republican majority on the county board.

When he took office in July, Johansen declared, "As the mantle of leadership is passing to the representatives of a new consensus, there is evidence that much of what was considered sacred just a few years ago is being discarded. Compulsory attendance policies have been strengthened, walls are being placed in our already obsolescent open schools of recent vintage, and increasing attention is being paid to basic education . . . There has been a return to what should never have been abandoned."

In Washington, the pain of this year's staff system had increased its work force in the past two years even though enrollment fell by 14,603 students. Yet this fall, even with thecutbacks, the student-teacher ratio will be better than it was in the 1977-78 school year.

By contrast, in Prince George's County, where enrollment has declined almost as sharply as in the District the staff has been cut in line with the decreased enrollment over the past three years.

"We don't like to do it, but we know what the fiscal necessities are," one Prince George's official said. "So we've tried to cut back gradually, and not be forced into doing it all at once when we can't absorb it, and a lot of people get hurt."