The new U.S. Department of Education began functioning this week, but yesterday there was still debate over what its role should be.

Education Secretary Shirley M. Hufstedler, who is scheduled to be sworn in at the White House today, listened carefully for two hours to some of the leading protagonists in the argument at a form at the Brookings Institution.

At the end, Hufstedler did not spell out her own views. But Steven A. Minter, who has been nominated as undersecretary, declared that the new secretary "did not come to preside over the continuation of the status quo."

He said the new department's power and visibility would be used to promote "excellence, racial equality, and social justice in education." But Minter didn't say how this would be done.

Some of the speakers at the forum were considerably more cautious. But still others listed strong actions they wanted the new department to take.

On the cautious side, Carolyn Warner, state school superintendent in Arizona, declared that while education is a "federal concern, it is a state responsibility, and a local school district function."

It is "perilously close to immoral," Warner said, for the federal government to "coerce or cajole [other levels of government to offer] programs without providing the funding for same."

"The schools should stop trying to be all things to all people," she declared. "Let the schools do what they do best -- provide education and training."

On the other hand, Harold Howe II, a vice president of the Ford Foundation, said the federal government should use its aid to education to reduce inequalities in spending between rich and poor states and also to press strongly for an end to discrimination based on either race or sex.

The federal role in this area is "unique, needed and unpopular," declared Howe, who was U.S. commissioner of education under President Johnson.

"Vigorous action to counter discrimination is going to raise hackles around the land politically," he said. "Unless there is strong support from the White House . . . as Lydon Johnson provided in the late 1960s, it would be difficult for the department to do it alone."

"The old order is rapidly passing," said another participant, Frances (Sissy) Farenthold, an unsuccessful liberal candidate for governor of Texas several years ago who now is president of Wells College in New York. t

"One makes important choices," she continued "of going with the future or hoping for the past."

The future, she said, should include new educational institutions based on "the ideology of equality." It should also bring an end, she suggested to "the arbitrary standards [for credentials in different fields] established by a few private groups that want to reproduce leaders in their own image: an Ivy League White male in a three piece suit."

David Breneman, a senior fellow at Brookings, took a less sweeping view. He said the federal government already has more than 70 categorical aid programs for education, most aimed at helping students with one type of disadvantage or another.

"We are close to completing the agenda set in motion in the 1960s," he declared, adding that while there could be new federal goals, such as promoting finance equalization, there was "a need to maintain local and state responsibility."

The only speaker to talk in detail about academic achievement was Sen. Abraham A. Ribicoff (D-Conn.), who served as health, education and welfare secretary under President Kennedy.

Ribicoff said he was troubled that "many schools are graduating students who can't read and can't fill out employment forms" and said the new Education Department "can try to find out what went wrong."

But, Ribicoff added: "The federal role in education is not to dominate or dictate to local schools but to assist."