THERE IS A MODEST proposal for improving the quality of U.S. schools, upgrading the teaching profession and providing some real community support for working parents: Operate the schools year-round. Put them on a four-quarter year, require all youngsters to attend three quarters, and allow them to attend a fourth. Give teachers the option of teaching year-round and make their pay commensurate with the extra time worked.

The present school year is an anachronism. It was designed for a 19th-century, agricultural nation that needed young people to help with crops and did not have air-conditioning to cool school buildings in the hot months.

A longer school year could help school reformers achieve many of their objectives: higher pay for teachers, opportunities for disadvantaged and slow-learning youngsters to catch up, enrichment programs for the gifted, and simplification of the child-care problems encountered by working parents during the long summer holiday.

Granted, the costs of such a change would be considerable, even if it was phased in gradually, and even if the savings from increased operating efficiencies were factored in. But we believe the American public would be willing to pay for it for one simple reason: it would provide dramatic, tangible benefits as opposed to marginal improvements in U.S. education.

First, consider the advantages that a 48- week year would provide to students of all abilities. From an academic standpoint, there is accumulating evidence that a full year of school produces improved learning, particularly in the case of low-income and socially disadvantaged students. Houston, which has tried a year-round program, has found that the achievement scores of students enrolled in it are markedly higher. As a consequence, the Houston school system has expanded the plan to 13 additional schools this year.

Children do not all learn at the same rate; yet those advocating reforms rightly insist that all students should achieve minimum levels of academic competence. If we do not want a high failure rate among children who have difficulty with academics, we will need to provide them with extra time -- and extra teaching -- to enable them to meet the higher standards.

For the immigrant youngster who needs to know English, extra quarters afford a chance to immerse oneself in language study without subtracting time from arithmetic, geography or science.

For the student with learning difficulties, an extra, non-mandatory school quarter could provide time for work on areas of weakness without the stigma of staying back a whole year.

For the gifted child, an added 12-week quarter would be an opportunity for exploring a new subject, getting requirements out of the way or indulging a special interest in computers, poetry or experimental biology. In some years, such a student might take a break, go to camp, travel or earn money.

In eight years of four quarters, a gifted student could cover as much academic ground as he now does in 11 years of 36 weeks of school. A gifted student could graduate from high school in 9 years and have two years to pursue a special interest or earn money for college.

For the average student, the optional fourth quarter could be a time for pursuing interests for which there is insufficient time the rest of the year: driver's education, typing, studio art, or work programs outside school.

In the early grades, the optional fourth quarter of school might be a time for a student to read books of his or her own own choice, master basic arithmetic that has been giving trouble or work on a science project. At the high-school level, a 48-week year would allow for much more flexible schedules. The varsity basketball player who cannot handle physics during the winter quarter could take the course in the spring, summer or fall quarters.

In some respects, parents would be the principal beneficiaries of a reformed school calendar. As women poured into the workforce in the '60s and '70s, families with two working parents became the rule rather than the exception. This was the genesis of "latchkey" children, who come home to empty houses. Schools have been slow to adjust to this development, which is now a permanent fixture of U.S. society.

For American families, summer is no longer a time of leisurely picnics or putting up tomatoes for winter. Long summer vacations have become a major problem for families that must make child-care arrangements. The wealthy pay for camps, day-care programs or summer schools that charge tuition. But for the less affluent and poor, summer is a time for juggling schedules or allowing children to go unsupervised.

For many children growing up in the '80s, summer has become a ime of round-the- clock television watching and unsupervised outdoor play. A 48-week school year would be a boon to many hard-pressed parents and would still leave time for a family vacation.

Public attitudes toward a longer school year are clearly changing. In 1982, the Gallup Poll found just 36 percent favoring the addition of a month to the school calendar; in 1984, 44 percent did -- including a clear majority of big-city residents, college- educated adults, and, inexplicably, Westerners. Although half of all respondents were still opposed, the poll results would likely be quite different if the fourth quarter were described as an option rather than a requirement.

In addition, there are practical reasons for considering the 48-week school year that make good sense given the problems now facing the teaching profession.

Typically, teachers are in school just under three quarters of the year: 36 working weeks, compared with a 48-week working year for most Americans with full-time jobs. To supplement their incomes, about 30 percent of teachers take summer jobs. Eleven percent "moonlight" during the school year, and one in four does extra work for additional pay in the school system -- coaching, advising student organizations, driving buses. A recent study in New York indicates that one teacher in three holds a second job during the school year, and 53 percent work during the summer. Put another way, teaching is not the sole occupation of many teachers, a fact that has detracted from efforts to make teaching a true profession.

If teachers were paid for a 48-week year at the same rates they are paid today, their salaries would instantly rise by one third, to an average of nearly $30,000 from today's average of $22,000. Even the notoriously low salaries of beginning teachers would rise from today's $11,000-$15,000 to a more respectable $15,000-$20,000.

Not all teachers would welcome additional classroom days, and some would forego extra income to preserve long vacations. But making teaching a full-year vocation could ease the impending problem of a teacher shortage, which is likely to hit the country in two or three years. If all teachers opted to work year-round, while most students continued to attend only three quarters, we would need only three-quarters as many teachers as we employ today. In theory, 1.65 million full-time teachers can do the work of the 2.2 million now employed. Because the nation is expected to need 1 million new teachers in the next six years, more effective utilization of the existing teaching force would be a boon. This would still leave room for the hiring of young, talented new teachers.

More money for teachers and a chance to upgrade the quality of the teaching profession are not the only potential benefits of running the schools year round. It would be easier for teachers to arrange sabbaticals -- simpler for them to take time off to travel or study.

Could school systems handle the intricacies of scheduling and administration?

Some already do. More than 90 of the 600 public schools in Los Angeles operate year-round, as a respone to what otherwise would be unmanageable overcrowding. A building with a capacity of 1,500 students accommodates 2,000 on a year-round schedule. Even if many students availed themselves of a fourth quarter of school, it would still greatly reduce overcrowding.

At the same time, year-round operation would make much more efficient use of school facilities and staff. Buses and bus drivers could be utilized full time. The extra classroom capacity created by the plan would allow school systems to close old, inefficient or unsafe buildings and temporary facilities.

Also, a 48-week year would bring the U.S. education system more into line with those of our major economic competitors. International education comparisons reveal that young Americans who go to school 180 days a year know much less than their Japanese age-mates, who attend school for 240 days, and less than other industrial democracies with longer school years. Some studies even show American high-school students lagging behind high-school students in developing countries in some areas of achievement.

How many would avail themselves of year- round school? At the outset, perhaps not as many as we might wish.

Many school systems already offer summer school. But attendance tends to be thin. In 1982, for example, less than 4 percent of New York State's students attended summer school, and only one school building in eight was used for this purpose.

When the Los Angeles schools last summer took advantage of additional funds to offer "core academic courses," only 10,000 secondary students turned up, though there were funds available for 27,000. Even the remedial summer school for youngsters who had failed the statewide proficiency test had 7,000 fewer students in 1984 than in 1983.

During the past decade, financial pressures forced many school systems to curtail their summer offerings, often limiting them to seniors who otherwise would not graduate, youngsters with learning problems and those eligible for various federal programs. Chicago enrolled 200,000 children in the summer of 1975, and just 24,000 in 1982. Dade County, Fla., is one of the few urban systems to operate a large- scale summer program -- and it receives special state funds for that purpose.

But year-round operation is not the same as adding a slowed-down summer school program. High school students may scoff, preferring to adhere to the familiar pattern. But young working parents with 6- and 8-year-olds in the primary grades would try four quarters. As these children moved up into higher grades, they would increasingly view 48 weeks of school as normal, and the 36-week system of their older brothers and sisters as an odd thing of the past.

Many new teachers would like to boost their salaries by a third, not every year, perhaps, but more often than not.

A number of states have been establishing "career ladders" for teachers, under which senior teachers with added responsibilities would receive significant pay increases. In a year-round school setting, the increases would be even larger for these teachers. In time, teaching will be seen as a decently paid occupation with greater appeal to able young people -- and to older people who might be willing to try but cannot imagine why they would move to a part-time classroom post.

Albert Shanker, president of the American Federation of Teachers, says that the "market" should determine teachers' salaries -- that math or science teachers should be paid enough to keep them from entering private industry. But teachers must understand that no job market pays a 12-month salary for nine months' work. Teachers who say their work is so draining that it requires weeks of rest and recuperation should try that argument on nurses in intensive care units of hospitals, policemen and coal miners.

There is a parallel message for students and their parents. The National Commission on Excellence in Education, which last year issued a report highly critical of the schools, was right to assert that American youngsters do not spend enough hours on academics. The main substitute for active study has become passive watching of television, and spare-time jobs that pay for more leisure- time entertainment, or just hanging out. The United States has considered year-round schooling in the past. There was a flurry of interest in the idea between 1965 and 1975, when education funds seemed plentiful, facilities were crowded, and the possibility of using school buildings as year-round community resources were in vogue.

An extensive experiment with year-round education was undertaken in Newark, N.J., from 1912 to 1931, when schools were open for 10 months a year for one set of children and for another group, 12 months. The 12- month school program was designed for working-class youngsters and the children of recently arrived immigrants in need of special help.

George Brinkerhoff, an education scholar, reported in the '30s that "The all-year schools graduate a higher percentage of their pupils; they show a lower grade age (because fewer students failed even when standards were maintained); they have less retardation; they lose fewer pupils before graduating." What is more, he saw no evidence of "brain fatigue," "loss of mental health" or impaired physical development among those attending the 12-month schools.

The Newark program was curbed as a Depression-era economy measure, much as the ambitious summer programs of the early 1970s were cut for financial reasons. But the United States is again pumping resources into its schools, as governors, business leaders and the general public come to recognize the importance of educational excellence. States have been raising taxes to finance better schools, and public-opinion polls indicate that this is acceptable to the electorate -- so long as it yields results.

We cannot be certain that a full-fledged experiment of this sort would work in the 1980s. But the potential benefits make it worth trying. At a time when the nation is passionately interested in boosting student achievement, providing better care for the children of working parents and enhancing the appeal of the teaching profession, it makes no sense to allow our schools to stand idle 16 weeks a year.