The audience was a group of high school students in Cleveland, and Education Secretary William J. Bennett leaned forward in his chair, eagerly waiting for someone to take up his challenge.

A 17-year-old high school senior spoke up, questioning Bennett's assertion that America's schools must teach young people that the United States is "morally superior" to the Soviet Union. "I wouldn't say that one is morally better than the other," said the student, Rupa Datta, from Cleveland Heights.

"How about free speech?" Bennett fired back. "I think this is a fundamental freedom."

The teen-ager tried again: "In the Soviet Union, there is more equality."

"Sure," Bennett said. "Equality of slavery -- all equally a slave to the state."

That spontaneous exchange was a footnote to Bennett's whirlwind day-long trip to the city on the Cuyahoga River, a seven-hour road show that included teaching stints in two elementary school classrooms, an impromptu hallway news conference for local reporters, an interview with the editorial board of The (Cleveland) Plain Dealer, a luncheon speech to the Cleveland City Club, the session with high school students and a courtesy call on Republican Mayor George V. Voinovich.

But it was an encounter Bennett clearly relished, another chance to use what he calls "irreducible facts" to score another point for the Free World in the global struggle between democracy and "communist tyranny."

It was a typical day on the road for the man who has become one of the Reagan administration's key spokesmen for traditional values and the American way of life.

A linebacker (Williams College) turned scholar, Bennett maintains an informal, no-frills style, despite his former academic career and his membership in the Cabinet. He is a street kid from Brooklyn, but also a student of Jesuit training at Washington's Gonzaga High. He is a beer-drinking locker room backslapper, but also a Harvard-trained lawyer and a philosophy professor with a PhD from the University of Texas.

Bennett rails against "beltway myopia" like the quintessential Washington outsider, but he is also the political insider who knows how to court favor with the White House and conservatives of the New Right.

On airplanes and in the sanctuary of his office, he usually appears rumpled with his shirttail dangling conspicuously out of pin-striped trousers. Scarfing down a hot dog and a draft beer before ripping into a bag of potato sticks, Bennett seems equally comfortable at the bar in the airport lounge as at the head table of an exclusive banquet.

"This guy grew up in Brooklyn -- he's not into pretense and trappings," said Heritage Foundation Vice President Burton Pines. "He is a model of the new conservative. Bill Bennett is at ease with the American people."

It is his political agenda -- promoting traditional values, private school aid and the exportation of American democracy -- that has defined Bennett's first 11 months as Education secretary. It gives consistency to a tenure that at time seems marked by a short attention span. It is the common thread linking what critics call an often unfocused educational agenda that has lurched fitfully from student aid cuts to school prayer to bilingual education to private school vouchers.

"He's the first secretary of Education who goes around giving speeches on foreign policy," said Anthony Podesta of the liberal People For The American Way. "He continues to court the right and sing their music . . . . I think he is an ideologue first and an educator second."

"He gets his politics confused with educational philosophy . . . . What we have is a department of Education run by ideology," said Arnold Fege of the National Parents-Teachers Association

But Bennett's unwavering political agenda has endeared him to the New Right, and made him one of the Republican Party's most popular speakers. A poll in Change recently rated Bennett, 42, and a registered Democrat, the most sought and the most controversial speaker on the lecture circuit. He has been compared to former U.N. ambassador Jeane J. Kirkpatrick, another blunt-speaking neo-conservative, who recently switched to the GOP.

He has also been called a solid White House team player, staunchly supporting the president's budget cuts in education programs, while assiduously building bridges to the Christian Right. He spoke to Phyllis Schlafly's Eagle Forum in September and has appeared on evangelist Pat Robertson's "700 Club" television show.

Speculation that Bennett's ambition extends beyond his current job has been fueled by his intense interest in news coverage -- he is said to telephone his office when on the road to hear what the papers are saying -- and the way he has plunged into a job that he still says should be abolished.

"When you talk about things in a way that is understandable," he said, "and the things that you talk about are things that matter to the American people, like their childen and what they're learning, you're bound to get notoriety."

Bennett refers to his underlying agenda as the "Three Cs," for content, character and choice. He first spelled them out in a speech to the National Press Club in March, one month after he took office, and he has clung steadfastly to them.

"A lot of these issues are tied together by larger background themes -- content, character and choice," Bennett said in an inter- view.

"They can all be brought back to those themes. There's been a consistency, I think, in what we've said."

He blames criticism that he is unfocused on the Washington insiders' syndrome, which measures success in terms of legislative victories on Capitol Hill. "We're not unfocused," he said. "We're focused on many things."

He has proposed a voucher plan that would allow federal funds to pay private school tuition. He said he wants the federal government to begin supporting new ways to teach English to limited-English children. He said he thinks prayer and religion should be put back in public schools. He backs merit pay and competency tests for teachers. And he said he thinks schools should foster a national consensus in support of the Reagan administration's policy in Central America.

In the process of speaking out, Bennett has burned bridges to some members of the education establishment, from the Hispanic lobby to the higher education community to civil libertarians who are concerned about church and state separation.

Bennett attributes the adverse reaction in part to his plain-speaking manner. "I'd rather have people alert and disagreeing than asleep," he said.

He is an avid follower of Gallup polls that he typically uses to punctuate his ad lib speeches, and he seems to believe that the American people are on his side.

He typically speaks from notes scribbled on the back of a briefing paper, as he denounces incompetent teachers ("Bad teachers should get nothing. Zero. They should be fired.") and liberal education innovators ("There was a conspiracy against common sense in the 1960s and early 1970s.") with equal vig- or.

But even his most candid words are typically wrapped in quotationsfrom Socrates and Thomas Jefferson, from Plato and James Madison and Karl Popper and Horatius.

Long passages from the Federalist Papers and Plato's Republic drip from his tongue like Carolina molasses, usually leaving his opponents to sort through the oozing prose before realizing that they have been verbally finessed.

His outspokenness brought him early trouble, after a string of candid remarks drew unflattering comparisons to former cabinet secretary of the Interior James G. Watt. In his first news conference as Education secretary in February, Bennett defended the administration's proposed cuts in student loans by declaring that those hurt by them should consider "divestiture" of their stereos, cars and beach vacations.

When Bennett said that families with several college-age children should consider better "family planning"to cope with federal student aid cuts, an aide later hastily explained that Bennett meant "family financial planning."

Those remarks elicited sharp criticism while alienating some potential allies.

Sen. Robert T. Stafford (R-Vt.), who chairs the Senate Education subcommittee, said Bennett "would not be the secretary of Education" had he made the student "divestiture" remarks before his confirmation.

And American Federation of Teachers President Albert Shanker said in May that Bennett "has made a lot of headlines and almost all of the headlines have been blunders."

Bennett's stormy early days also saw staff difficulties and further embarrassments.

At a hearing on Capitol Hill, Bennett found himself ambushed by Sen. Lowell P. Weicker Jr. (R-Conn.) who chastised him for hiring two assistants who were critical of federal aid to the handicapped. At first Bennett balked and backed his appointees, then tried to distance himself from the two, and later asked both to resign.

That episode saw Bennett come under attack from a new and unexpected quarter -- his friends on the New Right, who accused him of "caving in" to Weicker.

It was particularly stinging because Bennett had wooed that group since his days as chairman of the National Endowment for the Humanities, and they in turn backed him for the Education position.

Some observers attributed his early problems with the job to insufficient savvy for his new, high-profile position, after coming from the National Endowment where he espoused the same views but lacked the media attention.

Others blamed the early gaffes on Bennett's reliance on his instincts, and on a trusted clique of like-minded neoconservatives -- derisively called "the inner-clones" by some department insiders -- who share his political agenda and want to translate it into educational practice.

Now, as he nears the end of the first year of what he expects to be a four-year term of office, Bennett appears to have tackled some of those early problems.

Senate approval this month of some key department appointees means Bennett finally has his own management team in place, adding an air of permanence to a department that seemed disjointed.

The appointment of a professional newspaperman as press secretary, and the addition of a trusted longtime aide from NEH, have dramatically improved his public image.

Relations with Congress have also improved.

Conservatives generally have forgiven him for firing the two aides, although he did ruffle a few feathers on the right recently by denouncing a new group, Accuracy in Academia, that was set up to monitor leftism on college campuses.

Even Bennett's rhetoric seems to have mellowed, in the opinion of his folowers, although the Education secretary insists that he has not toned down his speaking style. Said Denis Doyle of the American Enterprise Institute, "He has learned his lessons, he has moderated his rhetoric and he has mellowed."

Bennett's staying power and his ability to seize control of the national debate has even his staunchest critics moderating their attacks on him, which is a significant turnaround in just six months.

"I think he's pretty good now," AFT president Shanker said.

"We are going to have to work with him," said National Education Association President Mary Hatwood Futrell, who said that she still disagrees with his position advocating public aid to private schools.