The surge of women into business, law and other professions has "drained away" many of the brightest women from teaching in American schools and is one of the prime reasons for an alarming drop in the academic quality of new teachers, according to a report issued yesterday.

"Many high-caliber young women students are choosing other professions which used to be open to only a few of them," said Emily Feistritzer, director of the study.

During the 1970s, the report said, the College Board test scores of education majors dropped far more rapidly than those of students in other fields, while the number of women earning education degrees dropped by more than a third.

Meanwhile, women being graduated from college with degrees in business rose from just over 9,000 in 1970 to almost 63,000 in 1980, those with a law degree surged from 801 to 10,761, and those getting engineering degrees increased from 526 to 7,669.

Women continue to make up almost 70 percent of the teaching force in U.S. public schools, Feistritzer said. "But a lot of the cream is being skimmed off."

Unless major steps are taken to reverse it, Feistritzer said, the slide in teacher quality "will accelerate within the the next few years," undermining the quality of schools and threatening America's "postwar role as a world leader."

Feistritzer, who holds a doctorate in education from Indiana University, publishes a group of education newsletters in Washington. Her 63-page report pulls together and analyzes a range of data on education from government agencies and teacher organizations.

The report also shows:

* A severe shortage of qualified mathematics and science teachers.

* Widespread dissatisfaction among current teachers with their status and jobs.

* Teacher salary levels that are relatively low and have lagged behind inflation, though the biggest salary problem, Feistritzer said, is not for beginners but experienced teachers, whose pay raises are much less than in other white-collar fields.

Based on population trends, Feistritzer said, in the late 1980s there will be a shortage of teachers in pre-primary and elementary grades because of the increase in births since 1978. But the demand for junior and senior high school teachers will continue to decline into the 1990s, she said.

The average pay of teachers traditionally has been low, Feistritzer noted. But until the 1970s a large proportion of high-ability women went into teaching anyway, because there were few opportunities in other fields.

"Women, like men, go now to money and prestige," she wrote. "That means they go elsewhere than into teaching."

A study issued late last year by the National Center for Education Statistics shows that the average achievement level of female high school seniors going into teaching fell much more sharply from 1972 to 1980 than that of female students heading for other fields.

The achievement of the relatively few males headed for teaching also fell, the study said, but at about the same rate as other male students.

Several other reports, prepared by Phillip C. Schlecty and Victor S. Vance for the National Institute of Education, show that of students who begin a major in teaching, the ones who switch to another field have higher College Board scores than those who complete their teaching degree.

The teachers who quit after a few years on the job also have higher test scores than those who stay in the classroom.

The NIE reports say the proportion of high-ability women who drop out of teaching has been greater in recent years than of high-ability men, reversing the traditional pattern.

Feistritzer suggested that the drop in teacher quality might be halted by making the pay structure of teaching more comparable to that of other professions. This could be done by offering substantially higher pay to experienced teachers who demonstrate quality performance, rather than basing all teacher salaries on longevity and academic degrees.

She also proposed more rigorous requirements for new teachers, including a national licensing exam similar to the one required for accountants.

Any improvements will come about through "slow, patient, upward steps," she said. "Massive infusions of government and private capital . . . can help, but they cannot reverse [the] decline."