A NEW BABY BOOM is threatening to disrupt American education. More worrisome than the actual classroom crunch is this: The majority of the people who pay most of our public school costs have no children of their own attending them, and those who will be in the classrooms often will be so poor that they pay virtually no taxes that support the schools.

The first increment of a growing wave of 6-year-olds will be marching next fall -- scrubbed faces, sharpened pencils, new book bags and all -- and their tramping feet will rock our society a little. The 1985 crop -- and those who follow for the next several years -- will be more poor and non-white than the nation as a whole. In an overwhelming number of cases, they will go home to mothers only, with little education themselves, subsisting below the poverty line, either in low-paying, menial jobs or on welfare.

Thus, the childless "haves" will be called upon to pay for educating the offspring of the fertile "have-nots."

That sounds democratic enough, a share- the-wealth plan that Huey Long or Robin Hood would be proud of. But, in the realities of today's tough world, it isn't hard to imagine the objections and the lobbying on Capitol Hill and in state legislatures that will follow.

If we are to avoid a political confrontation, public education will have to do a better job of making sure that its graduates can read, write and think.

The truth about the changing composition of the school population came home to me last winter while I was analyzing data for a study of elementary- and secondary-school children. The findings have been substantiated in studies released more recently by the Congressional Research Service and Congressional Budget Office and by the Children's Defense Fund.

The data show, among other things, that the percentage of children in families with incomes below the poverty line increased to 22.2 percent -- up from 15.1 percent in 1970. Ten million of the 69 million children under 18 in 1970 were poor. Today, 13 million of the 62 million children in this nation live below the poverty level.

Yet, there is even more to disturb us about this quiet, persistent problem. Here are some other findings that have implications for education that nobody seems to be addressing as yet:

* The population under 5 years grew three times faster than the general population from 1980 to 1983.

The increase is mostly non-white and disproportionately poor. This overall increase will produce enrollments similar to those in the 1960s when school systems and taxpayers were hard-pressed to meet the needs of the baby-boom generation.

* The fastest growing household populations in this nation are people who aren't married and who don't have children -- known as "nonfamily householders." There were 23.4 million households with one or more unmarried, childless adults in 1984 -- up from 7.9 million in l960 and 11.9 million in 1970. Nearly half of all households added since 1980 have been nonfamily.

* Almost two-thirds (64 percent) of all households today do not have children, compared with a little more than half (54 percent) just 15 years ago. Only 47 percent of married-couple families have children, compared with 57 percent in 1970. Sixty percent of households headed by females, no spouse present, have children with them. Of these children, 56 percent live in poverty. Five times as many women who have never married maintain families with their own children as in 1970.

Of all black children, 57 percent were born out of wedlock in 1982 and half of those had a teen-aged mother. Of all black children who live only with their mother -- 47 percent of the total -- 71 percent live in poverty.

* Private-school enrollments are outstripping public-school enrollments. The number of highly educated, high-income parents is growing, and they are sending their children to private schools. Unless the trend stops, children from well-to-do, better-educated homes will polarize in private schools, the rest in public schools. And those in public schools, by and large, will be the offspring of single, uneducated, low-income, minority parents who are producing the most children today, proportionately.

'A Nation at Risk," the report commissioned by the Department of Education in 1983, pinpointed the weaknesses and failures in our educational system. We have heard over and over since then of how we need 1.2 million new teachers by 1992 and nobody is sure where they are coming from.

But no one has faced who will pay for the teachers, and for the school buildings, textbooks, computers, buses and all the other things that go into providing a free public education. Education from kindergarten through college is a $240-billion business in our country.

Circumstances in recent years have hidden the cost problem in our public schools. During the past decade of decline in the population of school age children, enrollments in private nursery, elementary and secondary schools rose 3.9 percent, but public school enrollments from nursery through high school dropped 11.4 percent. At just the elementary and secondary levels, private schools held steady whereas public school enrollments dropped 15 percent. Clearly, the private schools drained off some students from public schools.

Given these reductions, one might expect that total spending for education declined. Yet, total spending for public elementary and secondary schools remained steady in terms of real dollars. With fewer pupils, the spending-per-pupil actually increased by a staggering 22.5 percent in real dollars. While this increase was occurring, per capita income in real dollars went up only 6.5 percent in the 1973-83 decade.

The decline in school enrollments, reflecting fewer school-age children, will begin to reverse this year, as the population pendulum swings back. What will our schools do then, faced with greater numbers? They will ask taxpayers to dig down for more funds, of course.

A little-noticed omen for the future is this: Nursery school enrollments jumped 83 percent from 1972 to 1983. Thus, one in three 3-and 4-year-olds were enrolled in school in 1983, compared with one in five in 1970 and one in 10 in l965. Significantly, two-thirds of today's nursery enrollees are in private schools, compared with 10 percent of high school students in private schools.

What we may be witnessing is the birth of a tradition. We have more families in which both parents work. They are becoming accustomed early to paying tuition to send their children to private schools. The tuition becomes part of their household budget. Are they likely to take their children out of private schools when they reach the first grade? From the little data we have, the answer appears to be probably not.

Action can hardly be postponed much longer. We are in the midst of a baby boomlet -- not nearly as big as the baby booms after World War II and the Korean War, but enough to strain our schools more than they already are for the next 15 years. After 15 years of steady decline in elementary and secondary school enrollments, the curve will go up again for the next decade and a half. Can our schools handle it? Will they be good enough to justify the enormous increases in funds they will seek?

What will be said by the rapidly growing numbers of single householders, childless couples, couples sending their children to private schools, and people who've already raised their families? How pleased will such people be with having to pay taxes to support schools for other people's children? Some frictions are bound to be broad and deep.

This last decade of skyrocketing per-pupil costs for education was also the decade of plummeting achievement test scores, increased dropout rates and teen pregnancies.

The demographic trend also raises the prospect of heightened racial tension as the issue of who will pay for education develops. The new baby boomlet has a greater proportion of non-white children than the rest of society. There were 400,000 fewer white children under five in 1984 than in 1970 -- which had the highest number in a decade -- but there were 280,000 more black children under 5.

These numbers are in line with the general rate of population growth, up 50 percent for blacks of all age groups from 1960 to l983, compared with 26 percent for whites during the period. The Census Bureau's 12 percent growth projection from now to the year 2000 reflects increases of 23 percent among blacks and 9 percent for whites.

Yet, it is not racial discrimination, but the sharp divisiveness of take-home pay that threatens to dichotomize our schools. Available figures show a direct correlation between family income and whether a child goes to public or private school. Only 5 percent of children from families with incomes under $25,000 go to private schools, but 20 percent of those from families earning over $50,000 are privately enrolled.

There are other major factors that bear on whether a child does well in school or founders in a morass of ignorance and confusion, drifting perhaps into serious troubles like teen-age pregnancies and drug abuse. Two big ones are the education level of the child's parents or parent and the home environment -- is it a peaceful, supportive place or does it tear at the child's soul?

In the worst shape, statistically, are children in households headed by a female, no male present. The median income for these in 1983 was $11,790, compared with $27,290 for married-couple families. And there are more than twice as many households in which women are raising children by themselves than in 1970 -- nearly 6 million in l984, compared with 2.8 million fifteen years ago. Fifty-six percent of the 12 million children who live with them are poor.

Amid the welter of such statistics, there is a clear warning. Poverty begets poverty, and ignorance breeds ignorance. The opposite is equally true: The more money one has, the more money one is likely to get, and the more education, and so on and so on, as the generations follow.

For the 6-year-olds toddling off to first grade in September, the cards are already stacked. The vicious cycle goes on, and what these children do while in school -- with varying degrees of help or hindrance from their parents or parent -- will decide much about our country well into the next century.

American teachers are under heavy pressure these days. Rarely have we directed so much critical attention to education, asking why we do not have better teachers everywhere and why so many of our supposedly educated young people can neither read nor write adequately.

We may very well need to spend many more billions to insure that every American gets the best education possible. But whoever leads the crusade had better have some good answers and strong guarantees ready when the childless are asked to foot much of the bill.

American education has too easily embraced "social promotion" that passes students through our school system whether or not they have met minimum standards for promotion to the next grade. And it has allowed too many students to drop out of school as soon as they legally could, still lacking enough education to have a fighting chance for coping with society.

It should not be too much to expect that students emerging from first grade ought to be able to read at first-grade level. Students who get passed on to ninth grade ought to be able to read books on an eighth-grade level and so on to graduation. They should be able to speak and write using correct English by the time they parade down the aisle to pick up a high school diploma that implies that they can. Far too many young people are graduating from high schools today who cannot read and write well enough to fill out a job application form, which requires in most cases that a person be able to read on at least a ninth-grade level.

Last year, two-thirds of colleges and universities offered remedial courses in reading, three-fourths had them in writing and 71 percent had them in mathematics.

Not every student who gets a high school diploma needs to know calculus, but all high school graduates should be able to think logically -- to see cause-and-effect relationships. They should know some history and some literature. They should understand culture and how theirs came to be and why.

These demands may seem excessive to some, given the temper of the time, but why shouldn't we impose some standards on our educational institutions? Why shouldn't the public be able to feel confident that the teachers teaching and the administrators in charge of education are competent for the task?

The public has said it will pay for education. But it wants its money's worth.