Now they've gone, carrying school lunches and school jitters, Soon they'll have settled into class, and memorized the hours and the corridors, the teachers' names and foibles.

But the children carry something else with them past the crossing guards and playgrounds today: a loaded bookbag of expectations. Their own, their parent's, their society's.

If there's a single message passed down from each generation of American parents to their children, it is a two-word line: Better Yourself. And, if there's a temple of self-betterment in each town, it is the local school. We have worshipped there for some time.

Most of our ancestors left countries where poverty, caste and class were inherited. They came to a country founded on the notion that they were born equal. So they lived, and we still live, not with the reality of an equal society but with the ideal of equal opportunity -- especially for the children.

Americans have, in a sense, always laid their dreams on their children. As long ago as the late 1830s, people like Edward Everett, the governor of Massachusetts, said: "The wheel of fortune is in constant operation, and the poor in one generation furnish the rich of the next." It was the hope for the chances of the "next" that kept the country relatively stable.

Our children's chances have been invested in the schools since Horace Mann, denouncing visions of redistributing wealth instead advocated free and universal education. He was one of the first to give children and schools the job of equalizing America. In 1848, he wrote: "Education, then, beyond all other devices of human origin, is the great equalizer of the conditions of men -- the balance-wheel of the social machinery."

That notion has been behind reformist public policy -- from the schools to the Head Start program to parent education.

It has also formed the outline of the most popular tales of the poor boys who made good through study.

But to a certain extent, the text has now been revised. The relationship between schooling and success, education and equality, classes and class has been scrutinized anew.

It is still true, according to Harvard's Christopher Jencks in "Who Gets Ahead?," that the best indicator of economic success -- among men at least -- is how much education a man has had. A college degree of any kind still makes a great difference. But at the same time, Jencks find that we can tell soon after a child is born whether his chances for success are good or bad "for reasons that have nothing to do with anything he did."

It appears that, to a large extent, the status of the family determines the education of the child, which in turn determines his status.

"Most people, when they speak of school as an equalizer, mean that advantages obtained through schooling will cancel out socially inherited disadvantage as children become adults," writes another "revisionist," Richard DeLone, for the Carnegie Council on Children. But he notes that 1) education hasn't closed the gap between the rich and the poor and 2) only one man in five will succeed in surpassing his father.

While education may be the best, or only, route out of poverty for the individual, on the whole status is inherited today in America not through the genes but through the class structure.

". . . Schooling by itself cannot produce interclass or interracial equality," writes deLone. Even among the immigrant fables, the reality was that most families achieved some economic stability first and then insisted on their children's education.

The point isn't to denigrate school, but to gain perspective on the idea that each child starts with an equal chance and that education itself can solve inequality by lifting the next -- always the next -- generation out of poverty.

If we truly want to reduce poverty or inequality, we may have to start with parents -- not kids and economics, not education.

"I don't think there has ever been any question that a society can narrow its social extremes if it wants to," said Jencks. "The question is one of political will."

Instead, we have thrown the issue of equal opportunity onto the backs of our children, and that's a heavy burden to carry off in a school bag.