When public schools open in the Washington area this week and next, students working toward high school diplomas will face tougher academic requirements than many of their peers across the nation.

While some high school students in states such as Missouri and Alaska may take as few as four courses in the basic academic subjects to graduate, freshmen entering high school this year in Maryland, Virginia and the District will be required to complete 20 units of course work. At least 11 or 12 of those will be in English, mathematics, science and social studies.

District high school students are already among the few students nationwide required to study a foreign language to receive a diploma. And the District school system was the first locally to set a graduation requirement in computer literacy, effective for the high school class of 1988.

For the most part, the area school districts began to adopt more rigorous academic standards for high school graduation long before the National Commission on Excellence appointed by Education Secretary T.H. Bell issued its highly publicized recommendations in May.

This was possible, local officials say, because the Washington area is blessed with an abundance of concerned parents, healthy tax bases to support the schools, and long-term, well-paid teachers who are willing to be tough on students.

"When they talk about a rigorous program, we found we already had it," said Lois Martin, associate superintendent of schools in Montgomery County. "We are not doing anything differently because when we analyzed our curriculum we found we were doing pretty well."

Though they say many of the commission's recommendations are impractical to implement fully, most area school officials agree that the commission's report and the political attention now paid to education have provided an impetus for dramatic changes that already were proposed for the local high schools' curricula.

The most visible example is in Virginia, where the state Board of Education last month approved stringent new graduation requirements and a controversial "advanced studies" diploma for students planning to attend college.

These changes will force students entering Fairfax County high schools to take 20 units overall, instead of the previous 18, in the four years before graduation. All Virginia high school freshmen will have to complete at least one additional unit in both math and science to graduate, and the college-bound will have to take two extra years of both, three years of foreign language, and 22 units overall to qualify for the "advanced studies" diploma.

In Maryland, equally dramatic changes have been under consideration for five years.

This fall, a state task force on high school education is expected to recommend that the requirements be increased from two units to three in both math and science. There is also speculation that Maryland, which once offered four types of high-school diploma--academic, general, business and vocational--will follow Virginia's lead and create a special academic diploma for college-bound students.

Maryland's Board of Education already has approved a program called "Project Basic," which will require this year's high school freshmen to pass functional competency tests in reading, writing, math and citizenship before they graduate. By 1985, Maryland's 24 school districts also must have in place a two-year program called "World of Work," which, among other things, will teach students how to write re'sume's and conduct themselves in job interviews. "Survival," another program to be instituted by 1985, will provide students with knowledge of consumer and health matters.

"It's a good idea to make sure that students can be functional adults in our society," said Larry N. Chamblin, a spokesman for Maryland's Board of Education. He said the tests will require students to be able to read, write, compute mathematically and understand the branches of government, the court system, basic constitutional rights and voting procedures.

In keeping with the trend toward tougher standards, local school officials also are beginning to expand computer literacy courses, and newly hired teachers in the District must demonstrate computer literacy to qualify for tenure.

There also have been changes outside the academic areas.

In recent years, for example, Montgomery, Fairfax and Arlington counties have reduced the number of unexcused absences--or "cuts"--that students are permitted before losing course credit. In D.C., where there is no policy, Superintendent Floretta McKenzie is forwarding a proposal to the school board this fall that would set a limit on the number of allowed unexcused absences.

Despite the consensus that students should be required to take more basic courses to graduate from high school and that attendance policies should be stricter, area educators are concerned that there may be a negative trade-off if school systems rush to implement all the commission's recommendations.

The Montgomery County school board, for example, earlier this month tabled one member's motion to adopt the commission's entire program. Some members questioned whether mandating more courses would simply limit the student's ability to explore different subject areas.

And there has been considerable displeasure in Fairfax County over the state's new graduation policies, which are modeled partly on the commission's report. County school officials have charged that Virginia's students will be forced to give up valuable arts and vocational courses to meet the increased load of basic requirements, and that the idea of a special diploma is elitist.

As for the other commission recommendations, most area educators say that some are simply impractical. For example, none of the area school systems can afford to lengthen the school calendar, which ranges from 180 to 184 days locally, to 200 or 220 days, as the commission suggests. And imposing a seven-period day in high schools, which Fairfax County is likely to do to ensure students still take some nonacademic electives, is a costly proposition. Fairfax school Superintendent William J. Burkholder estimates the county will have to spend as much as $10 million to add a seventh period and to hire teachers to meet new requirements for more academic courses.

Even the issue of whether school systems should have homework policies, as the commission recommends, provokes debate.

"I don't think you legislate homework," Burkholder said of the commission's suggestion that school systems assign more homework for students. "Homework will increase automatically because students will be taking more academic courses."

"Our schools have been operating educational programs above the national norm and achieving very well," said Arlington County Superintendent Charles Nunley. "And we beefed everything up before any of the reports came out."