Because 63 percent of women with school-age children work, and both parents work in four of five families, school systems should establish adequate day care to deal with the "number one problem of the American family," said a Yale professor who was one of the founders of the nation's Head Start program.

Dr. Edward Zigler, speaking yesterday at a conference on the family and education at George Washington University, said schools have been "much too slow in catching up" with these new demographics.

"Perhaps it's time to reinvent the community school," said Zigler, who headed the office of Child Development at the Department of Health, Education and Welfare during the Nixon administration. Previously he had helped develop the government's Head Start program for preschool children from low-income households.

Zigler defined a community school as "a place that is conversant with the problems and needs of the community it serves" and offers care before and after school for the children of working parents.

"Why don't we go to schools and say, "Open up and hour earlier and stay open two hours later?' " Zigler said.

The need for child care programs has grown in the last 10 years as more and more women have entered the work force and the number of single-parent households has risen. Zigler said one in every four white families today is headed by a single parent. That rate is higher among black families, 56 percent of which are headed by a single parent.

Some local jurisdictions have responded to the need for day care. Fairfax County, for example, has had a county-run child care program since 1979 and now has centers in 52 county schools. Parents pay for the program on a sliding fee scale, with the county subsidizing the cost of the program for low-income families.

This year, Prince George's County has launched day-care programs for school age children at six elementary "workplace" schools. The day care is part of a magnet program designed to achieve a better racial balance in the county's schools by attracting white students to schools with high minority enrollments. Prince George's County School Superintendent John Murphy, who attended the conference, said the programs have been so successful that "we could open up twice as many."

Elinor Guggenheimer, president of Child Care Action Campaign, a private group trying to set up child-care programs nationwide, spoke against programs that are "too sterile." She said, "The school buildings belong to the public and should be used, but I would hate to see the local board of education take over the programs."

Jane Delgado, executive director of the National Coalition of Hispanic Mental Health and Human Services Organizations, said she too would prefer specific programs tailored to special groups of children and run by community or religious groups.

Fairfax County School Board President Mary E. Collier said she does not think schools will have space for large-scale day-care programs because of recent increases in the number of elementary school students. "The schools are full," she said.

Zigler admitted it will be hard to convince state and federal policy makers of the need for the programs.

He began trying to sell the idea of a national day care program 10 years ago. He said a high-level U.S. education official "recalled when he was a school superintendent in Utah, they had terrible winters, and the children would huddle outside the school doors waiting for the bell to ring. He said he tried to get the custodians to open the doors ahead of time so the children could wait inside, but he could not . . . .

"He said, 'If I couldn't get them to open the doors to children in a blizzard, how do you expect me to get them to open them for a day care program?' "