Beverly Mattox, an assistant principal in Fairfax County, suggested that when Mother's Day comes, teachers should not ask young children to make cards solely for their mothers, but for "any special person" instead. Many children, she explained, no longer live with both parents.

Dr. Benjamin Spock, author of the world's best-selling baby book, said that schools should become places where children are "appreciated and loved," especially when the "need for reassurance" is not met at home.

As divorce and out-of-wedlock births have increased, the percentage of American children living with only one parent has soared from 12 to 20 percent since 1970. In Washington, according to the 1980 census, 60 percent of children under age 18 do not live with both parents, compared to about 40 percent in such homes ten years earlier.

What schools might do about this breakdown in traditional families, and what effect it has had on children and schools were topics of lively debate at a two-day conference here sponsored by the Home and School Institute.

The meeting, which attracted more than 200 people, mostly teachers, concluded yesterday at the headquarters of the National Education Association on 16th Street NW.

Dorothy Rich, president of the institute, which tries to help parents improve their children's academic skills, said that the schools should make two principal responses to the upsurge in single-parent families. One is that school buildings should be kept open for child-care from early morning to late afternoon, Rich said, and not just during the regular school hours.

Schools also should "readjust how they communicate with parents," she said, by scheduling conferences that do not conflict with the parent's work or by having teachers available to take telephone calls in the evening.

"But the schools cannot take the family's place," Rich stressed. "A single-parent family is a family."

Nationally, about 90 percent of the 6.8 million single-parent families are headed by women, according to census data. About half of these female-headed households are at or below the poverty level.

"The schools owe it to single parents to provide firm discipline," said Connie Marshner, chairman of the National Pro-Family Coalition. "Setting and maintaining certain standards of conduct is one support schools can give to single-parent homes."

Because single parents often have more difficulty finding time to make up any deficiencies of the schools, Marshner said, schools have an obligation to provide a strong education. She said that they also should be flexible in allowing children to attend classes near to where the parent works.

Spock said that the problems of single-parent children are different from those living with both parents "only in quantity, not quality."

"All children need things that are very different from what they're getting in the schools now," said Spock, 79. "The schools' job should not be to set standards and demand that children meet standards . . . . All you need are friendly teachers who respect children and have been trained to allow children to develop their own abilities."

Two years ago, a widely publicized study sponsored by the National Asscociation of Elementary School Principals reported that children living with one parent have significantly more academic and discipline problems than those who live with two.

Rich said a review of more recent studies shows that most of the difference disappears when socio-economic status is taken into account. But she said that regardless of class, the research indicates that children from single-parent households "tend to receive lower grades, display more disruptive behavior in school, and have poorer attendance."

Besides not sending Mother's Day cards just to mothers, Mattox said, the schools should try to avoid purchasing textbooks that feature mostly pictures of children with both parents, which might embarrass children from single-parent homes.

She said that schools also should teach such "survival skills" as how to answer the front door when no parent is home, and should train their staffs to "be aware of the problem of parental kidnapping," where one of a student's divorced parents may try to spirit the youngster away from the parent who has legal custody.