IF RONALD REAGAN means what he says, the next four years will be a turbulent time for the Washington lobbies and organizations that defend the interests of the nation's 95-billion-a-year public school system.

For all his talk about cutting back the federal government's role in the schools and colleges, Reagan is a radical when it comes to ideas about the future of primary and secondary education. He favors changes that go to the root of the system. If carried out, they could substantially alter the schooling of American children.

At the forefront of his policy are schemes that would give parents a wider range of choices about where to send their children to school, along with the financial wherewithal to shop around. Ironically, considering the president-elect's anti-government biases, several of these schemes would require the federal government to intervene massively. For example, Reagan wants tax credits for parents who are paying private school tuition -- a proposal that a Congress considerably less Republican than the new one almost approved in 1978. And he also favors a plan that would provide children with educational benefits, or "vouchers," which they could use at the public or private school of their choice.

These ideas have already been denounced by Albert Shanker, president of the American Federation of Teachers, as leading to the "destruction" of public education. And it is not at all clear whether Reagan will have the clout to push through even the tuition tax credit plan, once the public school lobby goes to work.

Yet, whatever the outcome, it seems possible that the Reagan presidency will inspire the most far-reaching debate about public education in many years.

For most of the 1960s and 1970s, discussions of the public schools were monopolized by a single burning issue: how to absorb a huge mass of minority children into what was predominantly a middle-class school system. Educational quality was discussed, but usually in the context of civil rights. The thought that led to Head Start, Title I and other innovative programs aimed at blacks and the poor was rooted in the long egalitarian tradition of American public education. It did not question the system itself. Rather, it sought to expand the reach of the system to those that had long been deprived of its full benefits.

At the same time, any serious attempt to discuss the broad pros and cons of public schooling was clouded by emotion and politics. Liberals branded critics of the public schools as racists or elitists, while the zealous activists of the New Right portrayed the schools as hotbeds of liberal experimentation, permissiveness, atheism and "secular humanism." In this atmosphere, it was hard for anyone to rise above the fray to ask a more fundamental question: Is the vast public school bureaucracy that has grown up in the last 140 years flexible and responsive enough for the American democracy of the 1980s?

The coming struggles over tuition tax credits and vouchers are sure to be laden with passion and emotion. But there are signs that the time for a debate over this larger question is propitious.

The crisis of mushrooming enrollments is over, providing something of a breathing spell. Racial segregation is still an issue in dozens of school districts, but many blacks themselves now say that they are more concerned with educational quality than desegration for its own sake.

Teachers and principals, who have been in the trenches of the 1970s, deserve a full airing of the school question. Many of them feel strongly that they and their schools have taken a bum rap. In their view it is not the schools that have failed society, but society that has dumped its problems in the laps of the schools and then withdrawn the financing and support needed to deal with all the recent upheavals in family life, race relations and the U.S. economy.

Finally, there are many indications that the public is looking for new ideas.

Public concern over education can be seen in the trend for private school enrollment to edge up steadily while public school enrollments decline, and in parental pressures for more school discipline and teaching of "the basics," (though defining "the basics" is no easy matter in a society changing as rapidly as the United States).

More dramatic, perhaps is a recent survey of public attitudes toward the voucher plan by pollster George Gallup, in which 47 percent were in favor and only 42 percent opposed. Whether or not all those questioned fully understood the implications and complexities of the voucher plan, the poll demonstrated that a great many Americans are not satisfied with what exists now.

Neither, it should be added, are liberals who have begun to advocate fundamental reforms along with the Reagan conservatives. It is a sign of how much the ideological lines are blurred these days that men such as University of Chicago sociologist James S. Coleman and Harvard sociologist Nathan Glazer, both certified liberals in the Kennedy-Johnson years, are now willing to consider alternative models to the current public school system.

As contemporary reformers point out, this system of free schools financed primarily by the property tax arrived fairly late in the nation's development. Until the 1840s, there was little distinction between private and public schools, and there was no uniform school system. Parents who sent their children to public schools paid a "rate," or fee, from which they could get an exemption for reasons of economic hardship. By mid-century, Horace Mann and fellow reformers (aided, say some revisionist historians, by Northeastern manufacturers motivated by a desire for a trained work force and "social harmony") had begun to create the structure of the public schools as we know them today. But it was another 50 years before the comprehensive public high school came into being. In both periods of reform, there was strong opposition -- first from local communities resentful of paying property taxes to support the grammar schools and later from ethnic communities fearing the loss of their cultural identity once the high schools were established.

Glazer and others maintain that the growth of this system was in the spirit of American egalitarianism, but went against elements in the American character which strive toward pluralism and individuality, and value cultural, ethnic and religious identity above unity and assimilation.

These other elements have enabled the parochial school system to survive, the current reformers maintain. And these same values are spurring a mounting public reaction against the huge bureaucratic superstructure that has grown up around the public schools, stifling efforts toward real local control, accountability, and parental involvement with childrens' education.

"The truth is that the neighborhood school is controlled by a national educational and bureaucratic hierarchy completely insulated from local community pressures and answerable only to itself. Curriculum is determined by remote educational commissions in far-off universities, while national school policies are determined by federal judges and the dispensers of federal funds." So writes Samuel L. Blumenfeld in his book, Is Public Education Necessary? to be published next month by Devin-Adair.

Blumenfeld is a libertarian who would prefer to see the government get out of education entirely and leave it to private enterprise to establish a national network of schools.

Such an extreme outcome is hardly likely. But proponents of vouchers and tuition tax credits maintain that their proposals could add a needed element of competition and force the public system to do a better job of meeting the needs of its "consumers" -- the parents and children it serves.Out of this, they say, would come a more diverse school system, better tailored to differing parental views on what constitutes a good education for their children.

Sociologist Coleman has pointed out that the concept of the government providing benefits, rather than a direct service, is already established in Medicare and in the food stamp program, both of which allow the recipient to use the benefits wherever he or she chooses.

John E. Coons, the self-proclaimed liberal who is leading an effort to get a voucher plan put on the California ballot, likens vouchers to "a full state scholarship, plus admission and transportation to the school of choice." Coons contends that the plan would stimulate "more voluntary integration" because blacks and whites would end up in schools together out of choice.

Doubtless, there would be enormous technical problems. For example, what if a child with low math and verbal scores applied for admission to a school specializing in an academically challenging curriculum? And what kind of safeguards would have to be built in to prevent whites from using the voucher plan to set up their own, segregated schools?

At this point, Reagan himself is on record in favor of more "choice," but he as avoided the difficult specifics. He has complained in his book Call to Action that "in public education we are very near to a monopoly." This is already more than most presidents have said about public education. Understandably. Education is a dangerous and largely untried arena for an American president. But there is a large constituency of Americans who are concerned about the schools. It is doubtful whether Reagan will be able to resist the temptation to portray himself as their moral standard bearer.