At a few minutes before 9 o'clock yesterday morning, principal Shirley Hammond walked through the corridors of her school in a cloud of authority and perfume, ringing her big copper bell. By name she greeted the children, who looked handsome in their new clothes and carried the latest in lunchboxes -- Smurfs, Pac-Man, Peanuts. The principal stopped at the back door, where a group of eighth-grade girls lingered.

Hammond has been a principal for 15 years and an educator for 29; the girls at the back door were just another part of the routine. "All right, girls, you're not supposed to be here," she said in the commanding tone of voice that all principals must master. The loiterers giggled guiltily and hurried off to class.

And so began the ritual of another first day of school at Brookland School in Northeast Washington, an open-space facility where 360 students began grades prekingergarten through eighth. It was a ritual repeated all over the city yesterday as the District's 180 schools, with an officially projected 91,700 students and 5,300 teachers, opened their doors once more.

As the new year began, the D.C. school system awaited approval from Congress of a $306 million budget, which represents a 16 percent increase over last year. The budget, if approved, will reduce class size in the elementary grades from 28 to 25, according to Janis Cromer, spokeswoman for the public schools.

The new year brings with it new programs -- computers to teach reading and writing to kindergartners and first graders in 15 elementary schools, career programs for high school students in such areas as engineering, health, communication, banking and finance, hotel management and culinary arts. It also brings new goals, one of them to improve attendance at the high schools, where the absenteeism rate last year was between 16 and 19 percent daily, according to Cromer.

It was Janise Mead's 14th first day of school as a teacher, but she still had trouble sleeping the night before her first-grade class was to commence. "I was thinking, 'Now, what am I going to do today? What did I do last year?' "

Her touch of nervousness was nothing compared to that of the boy -- new at Brookland -- who came to her class close to tears. "He said, 'I'm scared because I'm not gonna know what you're talking about.' I hugged him and said, 'Oh, come on, now, things aren't going to be that bad. Give me a chance before you start crying.' " He was smiling by lunchtime, at which point his class had already sung "Thumpkin," recited a poem about September and learned about the numbers O, 1, 2 and 3.

Mead, who was in the third grade when she made up her mind to be a teacher and has never once considered another profession, was already dreaming of February. "Around February everyone starts blooming. They start reading. They become a lot more independent. . . . It's like a miracle." On the first day of school, she felt expectant. "If you can teach these children to read, and do a good job, and if you can teach them math, and do a good job, then they'll be able to fly."

She had made her classroom a cheerful place, with potted plants on all the tables and colored construction-paper signs that offer such encouragement and comfort as: "Emotions are what we feel. Everyone has them. It's okay to feel many different ways;" "I am me!" "Look at us! We are watching our progress. We get better every day!"

Mead, the wife of an art teacher and the mother of two girls, said it would take her a week to learn the names of her 23 students, much longer to learn about their lives. She remembered how sad she felt last year when she asked the boys and girls in her class about their families.

"Out of 32 children, only five lived with both parents," she said. "I'm really down on people who separate and divorce . . . . It really messes up the children. I know that's the way things are, and that's the way the world is today, and sometimes I've felt like packing up myself, but you really need to stay together for the children."

Mead's daughter Shelli was in a classroom on the second floor, starting her first day of fourth grade with Mary Cooke, who was marking her 18th year of teaching. "I love the first day," Cooke said. "It's like being born again. It's fun. I wouldn't want to do anything else." She began the class with that age-old first-day-of-school question: "What did you do this summer?"

Some of the replies: "I went to Wide World, I went to North Carolina. I was riding my dirt bike. I saw 'Poltergeist,' and I saw 'Tron.' "

"This summer I went to Atlantic City, and I saw 'Chinese Connection.' "

"I went to Fort Lauderdale, Fla."

"I went skating."

Around the corner, third-grade teacher Lillian Harris -- the only third-grade teacher at Brookland as of yesterday, with an oversized class of 36 that the principal promises to trim by combining some grades--passed out questionnaires headed, "My Personal Inventory." The students were to complete such sentences as "I like to . . . , I am glad school started because . . . , I am not glad school started because . . . ."

This was one way for Harris to evaluate her students. Judging from some of the responses, she has a lot of work ahead. One boy wrote he was glad school was starting "cuz I what to learn and do not be dum." Another boy completed the "I am not glad school has started because" sentence like this: "I am gaitroeprhntoresirtasdloohrsyoe." When Harris took the boy aside and gently asked him to decipher it, he could neither read what he had written nor remember what he had meant to write.

In the class next to Harris, one girl asked second-grade teacher Cecelia Wilbert, in her 16th year of teaching, a practical question: "Is we having lunch today?"

The teacher answered with a question: "Are we having lunch today?"