The public and elected officials continue to be concerned about the quality of our public schools. With good reason: in the knowledge- based economy of the late 20th century, schools -- and the skills and knowledge they impart -- are crucially important to our national well being.

Interestingly, the idea that schools can be improved and that improving them will help children learn was not widely accepted by researchers and policy makers until recently. Because of a landmark 1964 study directed by sociologist James Coleman, many observers believed that schools themselves didn't have as much impact on student achievement as did the socioeconomic characteristics of the children who attended them.

There is, of course, some truth to this -- advantaged children from intact families do better in school and are easier to teach than poor children from broken homes. But the Coleman Report, as it came to be known, was interpreted to mean that nothing schools do makes a difference, that a child's educational performance is all luck of the socioeconomic draw.

Ironically, it fell largely to Coleman to dispel this grim view. In a recent study, he and his colleagues concluded that schools do make a difference, and they make a big difference. All things being equal, a good school -- characterized by high standards and high expectations, dedicated teachers, intellectual and physical discipline, and shared intellectual values -- will produce much higher levels of academic accomplishment than similar schools that do not share these traits. Indeed, Coleman concluded that these characteristics were most important in schools serving poor children.

None of this, of course, is news to the discerning teacher or parent. Who but an academic researcher would need to prove that some schools are better than others? But research often illuminates, even if it means proving the obvious. The most recent example is a set of findings from the federal government's massive longitudinal study of high school students called "High School and Beyond."

In March 1985, the U.S. Department of Education reported how parental involvement influences student achievement. The opening sentence tells the story: "Those students whose parents are the most involved in their lives tend also to be the students with the highest marks in school." Surprise! But having asserted the obvious, it offers evidence that is both thorough and convincing.

In 1980 a set of high school sophomores was asked the extent to which their parents monitored their activities. The same question was posed just before graduation two years later. Did their parents know where they were and what they were doing? The overwhelming majority of "A" students (88 percent) reported a high degree of parental involvement. By way of contrast, 81 percent of "B" students' parents knew where they were, 72 percent of the "C" students and only 61 percent of the "D" students' parents.

The pattern is repeated in other measures of student and parent involvement. Three- fourths of all "A" students reported that they talked to their mothers or fathers "every day or almost every day." Only 67 percent of "B" students, 59 percent of "C" students and 45 percent of "D" students reported that they talked to their parents at the same rate.

Interestingly, a small but potentially significant difference between parents emerges. Mothers play a more important role than fathers. Ninety-two percent of "A" students reported their mothers kept close track, compared to 85 percent whose fathers did. In the case of "B" students, 89 percent reported that mother kept close track, while only 79 percent reported that father did.

It is abundantly clear that parental involvement is critically important to school success. But does this mean that the school is unimportant? No. Rather, it suggests a powerful synergy between home and school. In the case of advantaged children in good schools, the synergy is strong and positive; in the case of disadvantaged children in bad schools, the synergy is negative and destructive. In the case of disadvantaged children in good schools there is hope, but the school has its work cut out for it.

Improving education then, has two dimensions: expand the efforts to improve the schools and find more ways to involve parents in their children's education. Unfortunately, demographic trends complicate the picture. The nation's poverty rate for children under 18 is climbing. Today it is 22.2 percent, a dramatic and dispiriting increase from the low in 1969 of 13.8 percent. Most disturbing is that nearly half of these youngsters live in female-headed households. Among minority groups the figures are higher: 69 percent of children in families headed by a black female live in poverty. Seventy-one percent of such Hispanic children do.

That means for many poor children there is only one parent available with any regularity. Is it any wonder there are few "A" students among them?

It is a consummate irony that just as research confirms the central role of the family in the education process, many American families have never been in more desperate shape. Indeed, with the evidence about children in poverty, one wonders if the term "family" has any meaning for these youngsters. The breakup of the family is creating the "feminization" of poverty, and it is certain to sow the education whirlwind.

All of this makes for tough sledding. Many educators believe that their jobs are made much more difficult because parents are not interested in their children's education. Many parents believe their children don't learn much because the schools aren't very good. They are both right. But what to do about it is less clear.

Good schools are a delicate combination. They depend heavily on the people who staff them and on the people who send their children to them.

Trying to improve education by concentrating on only one side of the equation overlooks an essential ingredient. Schools must find ways to involve more parents in the educational activities of their children. Parents must demand better schools. To make informed demands they must first involve themselves in the schools' activities. In that, perhaps, lies the hope for long-term improvements.