Children whose mothers work and children from single-parent homes score lower on school achievement tests, according to a new national study funded by the Department of Education.

The study contradicts a recent review of research by the National Institute of Education, which found that children of working mothers did about as well as children whose mothers stayed at home.

The new study found, for example, that in white, two-parent homes, high school students whose mothers worked full time during their school years scored up to 9 percentile points lower on tests than students whose mothers never worked. The magnitude of the effect was directly related to how much the mother worked, the study found. Students whose mothers work only part time do not do as poorly, it said.

"For two-parent families, which typically have higher incomes, the positive effects of the working mother's income are apparently offset by the negative impact of her time away from the home," the study said.

It also found that test scores were lower for elementary school children with one parent, especially blacks. They scored up to 9 percentile points lower than black children with two parents. On the other hand, the same group of single-parent black children do better in school if the mother is working than if she is not, the study added. This is because her added income helps create a better educational atmosphere in the home.

The study also touched on the effects of homework and television on achievement and found that elementary school children seemed to learn as much from television as they lost from not doing homework. But high school students scored better if they did more homework and watched less television.

"Given increases in the prevalence of single-parent families and of mothers in the work force, these results cause considerable concern," the study said. In 1980, 57 percent of mothers worked, up from 42 percent in 1970. About 43 percent of them work part time.

Children in single parent households jumped from 7.4 million to 11 million, 19 percent of the total, in the last decade, and the number of black children living with a single parent increased from 34 percent to 50 percent.

The study was written by Alan Ginsburg of the Department of Education's office of planning and evaluation, and two consultants. It suggests that more attention be paid to work-sharing for women and to better enforcement of child-support payments for single mothers as partial solutions to the problem. Ginsburg said the study began after the Reagan administration came to power, but was not ordered by Reagan appointees. It cost about $100,000 and used as its data bases two multimillion-dollar studies of elementary and high school students.

NIE's Dr. Oliver Moles, who reviewed both the Ginsburg and the recent NIE studies, said the new work "is significant because it is recent and it is a national data base." He also said he respected the work and the scientific qualifications of Ginsburg and his researchers.

Moles termed the new results "puzzling" because they contradicted NIE, but said, "I'm not quite ready to throw out the other evidence." He said more research is needed.

Cheri Hayes, who worked on the NIE survey for the National Academy of Sciences, said she has not seen Ginsburg's study, but cautioned that other factors, such as the family's attitude toward a mother's work could affect test scores.

Ginsburg noted that recent studies on the subject had inconsistent findings and were limited by small sample sizes and difficulties in controlling variables such as income and education. The new study was able to distinguish full-time from part-time work and trace the mother's work history. It could not measure how long the children had been in single-parent families.

The study noted that a mother's educational background and the number of books in the home were positive factors in her child's test scores. Lack of income had a major negative effect. "It is clear that the single most salient aspect of one-parent families is their relative lack of financial resources," the study on elementary school students said.

But it found that for families at the bottom of the income scale--single, black parents--"the income earned by the mother's employment more than offsets her loss of time at home, perhaps pulling the family out of poverty and making real contributions to the children's achievement."

At the highest income levels--two-parent white families--"the marginal contribution of the mother's income apparently is not sufficient to offset the negative direct effect of her not working and thus of her disminished time at home." These mothers are the most highly educated and work less.

While elementary school students spend three times as much time watching television as doing homework, their scores are not affected, the study found. In high school, doing more homework helps achievement. "It may be that homework time is more productively spent in high school," because it is more specific and difficult, it added.

Ginsburg said he expected the study to be attacked because of its findings about the negative effects of working mothers on achievment. But he said the fact that the findings were consistent across both elementary and high school age groups "give us confidence in our results."