U.S. Secretary of Education William J. Bennett helped the District public schools start a new year of classes yesterday by serving as a "substitute teacher" at Benjamin Banneker High School where he lectured about the historic Federalist papers.

With a gleam in his eyes, a piece of chalk in one hand and a finger raised in midair, Bennett appeared at ease, but excited as he faced the 26 11th graders in a first-period class.

He frequently wrote notes on the blackboard behind him, posed questions and appeared to be preaching as much as he was teaching as he talked about the foundations of "our free and democratic" country.

Meanwhile, at more than 120 other schools across the city, about 88,300 students and 4,500 teachers returned to classes that had their own kinds of newness, drama and, occasionally, chaos.

Few new academic programs will be started this year, officials said.

Management seminars and other programs designed to enhance principals' skills will be started, officials said. And stubborn problems such as poor attendance and low test scores have been targeted for attack.

At Banneker, the city's academic high school at 800 Euclid St. NW, where students were required to report to school last Friday for orientation, Bennett spoke of how "man's fallibility" and human nature constantly threaten the orderly processes of government.

The 10th installment of the Federalist papers -- a series of 88 essays in support of adoption of the Constitution that were written by leading political theorists such as James Madison and Alexander Hamilton -- addressed the theme of human nature, Bennett said.

"The Federalist paper No. 10" spoke to the issue of preserving a democracy without outlawing the inherent formation of factional groups that try to exert their influence over others, he said.

"I think Madison says factions are going to be a problem anytime you have liberty," Bennett continued. "Why? Why? Why? . . . Liberty is what it's all about. How do you get rid of factions?" Bennett asked.

Take away liberty for all, several students said.

"The removal of liberty would kill factions, yes, but you can't get rid of liberty and have a country that's worth having. This is the heart of it . . . . This is the heart, the heart, the heart . . . . The Constitution is essential," he said.

Bennett will repeat his lecture at six public and private schools across the country this month.

After Bennett left, several students said they were disappointed that he had avoided any in-depth discussion on slavery, although slave owners helped craft the Federalist papers and the Constitution.

"He didn't go into slavery in depth. He could've expressed his opinions on it," said Almaz Adair, 16, who was class president last year. "The laws were not written for all the people . . . . blacks being considered three-fifths human back then."

Meanwhile, across town at Anacostia High School in Southeast, a new principal grappled with less theoretical isssues: a cafeteria with incomplete repairs and students with incorrect class schedules.

Walton Breckenridge, formerly an assistant principal at Woodson High School in Northeast, said the cafeteria, which was destroyed by fire last year, was still in disrepair. Renovation of a basement-level multipurpose room, intended to be used for several classes, also was not yet completed.

Throughout the day students approached him complaining about their schedules.

Charles McDowell, 17, came up to Breckenridge holding his computer-printed schedule in his right hand, and said angrily, "All these are 10th-grade classes. I'm supposed to be in the 11th grade."

Breckenridge assured McDowell and others that any mistakes would be remedied within the week.

In the main office, Breckenridge was confronted with other problem: rodents. A mouse ran across the floor. A secretary squealed. But Breckenridge remained calm.

"Well, don't scare him," he said.

In an interview later, he said, "I've been a little busy today, but I'm very excited to be here. We've got some fine students here and we've got high expectations for them." He described the glitches of first day as "normal" problems.

Blair Jackson, an Anacostia assistant principal for five years, shared Breckenridge's optimism. "We're doing all we can to hold things together here. We've made adjustments -- food is prepared and carted here from a junior high school down the street. We're using science labs as classrooms.

"We expect things to run smoothly after a few more days," he said. "You have to be resilient and stay positive."