A national study with far-reaching implications for American families and schools has concluded that children living with only one parent have significantly more academic and disciplinary problems than their peers.

The study, believed to be the first extensive research of its kind to date, already has caused controversy and promises to be a basic document for reformers pressing schools to become more responsive to the changed needs of families.

About one school child in five now lives with only one parent, and the government estimates that nearly half of the children born this year will spend at least one year of their childhood with only a father or mother. In some U.S. schools, nine out of 10 chldren already live in such homes.

As a group, these children have lower academic achievement ratings, are late to school more often, miss more days and are more likely to drop out or be expelled than children residing with both their parents, the survey reported.

The study sampled 18,000 children at 26 schools in 14 states, representing a cross section of the rural suburban and inner-city populations. It was sponsored by the National Association of Elementary School Principals and the Institute for Development of Educational Activities, a division of the Kettering Foundation.

Since its initial release last week, the survey has won support and engendered controversy.

Ann Parks, a representative of the Parents Without Partners organization, expressed concern that the study could contribute to a "negative image" of single parents.

"Schools already relegate the difficulties of these children to the 'this often happens in single homes' department -- it could be a copout," she said.

However, Deborah Ziska of the National Commission on Working Women said she was "glad these figures are being brought out. This doesn't sound like something you can argue with. We have to deal with reality. The system has to change. It has to become more supportive."

"We're as concerned about stigmatizing these families as anyone," said Paul L. Houts, editor of National Elementary Principal magazine. "What we're saying is that the emotional trauma of divorce and separation shows up in school. We're not making any sort of pejorative judgment. The purpose is to sensitize schools to the fact that a significant part of the population now comes from one-parent households."

A number of recent, polls and surveys suggest that, increasingly, parents are loooking to the schools to provide broader support for families than they have in the past.

For example, the 1980 Gallup poll of attitudes toward public schools produced an overwhelming response in favor of expanded help for single parents. p

Eighty-six percent of those questioned by Gallup favored making school personnel available for evening counseling with single parents who work. And 45 percent felt that a major task of the new Department of Education should be to get parents more involved in the education of their children.

In the view of some parent activists, the schools have not adjusted adequately to the massive shifts that have occurred in family structures in the last two decades.

Of 1,100 single parents surveyed recently by the National Committee for Citizens in Education, nearly one out of three said they felt school personnel showed a "negative attitude" toward one-parent families. And half of those questioned said no evening consultation was available for working single parents.

According to experts knowledgeable about the National Association of Elementary School Principals data, the school problems of single-parent children held true -- in relative terms -- for all groups surveyed.

By far the largest percentage of single family households are in black communities -- an average of one out of two. But one source said that the performance of these black children in relation to their schoolmates was not markedly different from the showing of rural and suburban children when compared with their counterparts, and in some categories it was better.

In comparing the academic performance of the two groups, schools ranked children as high achievers (A or B), average (C) or low (D or F).

Of all the elementary and secondary school children sampled, 40 percent of those living with one parent were low achievers compared with 24 percent of those living with mother and father. At the other end of the performance scale, 30 percent of the two-parent children were ranked as high achievers compared with only 17 percent of the single-parent ones.

One finding of the study was that almost half of the children living with one parent qualified for a free or subsidized lunch -- suggesting they came from low income families.

Because some studies have correlated low achievement and low income, one interpretation is that the economic background of these children rather than their family status explained their poor showing.

However, another interpretation was that the family income was low precisely because the parents had separated.

In a long list of other categories, the single-parent children also fared badly in comparison with others.

"We were disturbed to find that one-parent students are consistently more likely to be late, truant and subject to disciplinary action by every criterion we examined, and at both the elementary and secondary levels," the study concluded.

For example, in secondary schools three times as many one-parent students were expelled and twice as many dropped out during the 1979-1980 year, in which the survey was done. While the secondary school dropout rate of all children combined came to a relatively small 4.9 percent of the total, the numbers were seen as significant when projected against the national total of some 20 million secondary school pupils.

While the survey said the reasons why these children do not fare as well in school can only be guessed at, it concluded: "Clearly, children of single parents need help."

"When parents separate, school remains the most important part of the child's life that stays relatively contant. If extra support and reassurance do not come from the school, the child may not be able to find them anywhere else."

Some schools already have begun to provide additional support, ranging from afterschool programs to night counseling of parents and students.

The study urged that teacher training and counseling be stepped up, that "rap groups" be established for single-parent families and that car pools and other logistical support be provided.