U.N. Ambassador Jeane J. Kirkpatrick's strong support for the administration's Central American policy has led to campus heckling and has sparked a national controversy over freedom of speech and the academic tradition of dispassionate discussion of issues.

The latest chapter unfolded today at Barnard College, a quiet cross-Broadway sister of Columbia University. Earlier this week the board of trustees at the 2,500-student women's college announced that it would award a medal of honor to Kirkpatrick, a Barnard graduate, during commencement ceremonies May 17.

While Kirkpatrick will not speak at Barnard, the announcement of her award began an immediate tempest on the small urban campus just five miles up Manhattan Island from the United Nations. The school faculty promptly voted its disapproval, 48 to 18.

Today students started a petition drive calling for withdrawal of the award, and claimed to have collected 1,000 signatures by afternoon. The students delivered the petition to Barnard President Ellen Futter after a meeting of 200 protesters heard several Barnard seniors say they would be "embarrassed" to accept their degrees while Kirkpatrick also was being honored.

Barnard administrators are trying to play down the episode, insisting, as Futter put it, that the award is not an endorsement of Kirkpatrick's views but "a tribute to an alumnus who has achieved in an extraordinary way."

The flurry of activity at Barnard follows a cross-country wave of college heckling incidents, several involving Kirkpatrick, that are reminiscent of the Vietnam protests of the 1960s and 1970s. Much of the new campus militancy involves El Salvador and draft registration.

Kirkpatrick was heckled into silence during a speech at the University of California on Feb. 15. She later finished the address, but canceled a second Berkeley speech the next day.

Kirkpatrick was heckled again at the University of Minnesota. Later, a student and faculty protest forced her to cancel a planned commencement address at Smith College. An aide to Kirkpatrick said that the college could not provide adequate security against demonstrators.

Other speakers, including former Black Panther leader Eldridge Cleaver and Saudi Arabian oil minister Ahmed Zaki Yamani, have been jeered into silence in the past month, Cleaver at the University of Wisconsin and Yamani at Kansas State University.

The new wave of organized heckling has caused deep soul-searching on some campuses, especially at the University of California, where the right to be heard became a burning issue among antiwar students during the Vietnam era.

After Kirkpatrick was hooted down there the university's chancellor, Ira Heyman, issued a statement saying that he was "embarrassed that Berkeley has been advertised around the world as a place which succumbed to mob rule."

The university's Board of Regents also acted, saying it "deplores the incident in the strongest possible terms" and directing that an apology be sent to Kirkpatrick. Berkeley's academic senate called on both students and faculty to allow the school to be a "forum for the free expression of all points of view" and to "protect free speech on campus."

Even the militant group that organized the protest, the Students Against Invtervention in El Salvador, admitted that the heckling went too far. The group said it had no intent to censor the views or the right to expression "of those who disagree with us."

As the Berkeley incident spread to other campuses and other speakers, five national organizations representing college administrators, teachers and students called on the academic community to cooperate in toning down the protests.

The groups--ranging from the American Association of University Professors to the United States Student Association--denounced the use of the "hecklers' veto" and asked faculty and students "to reaffirm our traditional commitment to freedom to speak and to listen."

Still, as a late spring sun began to shine on campuses across the country, the shadow between free speech and dissent seemed murkier than ever.

At Barnard, both supporters and opponents of the award to Kirkpatrick insisted that the issue is not free speech.

Across Broadway at Columbia on Thursday, in an earlier demonstration against the administration's Central American and draft registration policies, an activist Barnard economics professor, Alice Amsden, told several hundred students that the question at Barnard was one of "honoring militaristic ideologies," not freedom of speech. Amsden said she found it ironic that "those who oppose her Kirkpatrick are accused of suppressing human rights and being against freedom of speech," while Kirkpatrick actively supports Reagan administration policies backing "authoritarian regimes" in Central America.

Amsden had to struggle to be heard over a small, booing group waving an American flag and shouting, "Freedom of speech! Freedom of speech!"