"It's nice going back to school," Mahadi Stevens said carefully, "because you learn some stuff here. The more you learn the faster you get ahead."

For Mahadi, who is 7, and about 350 other youngsters yesterday was the first day back to school at Edmonds-Peabody Elementary on Capitol Hill. Around the city an estimated 115,000 students returned for fall classes.

Despite threats of a slowdown by the Washington Teachers Union, the first day went smoothly, school board president Conrad Smith said.

Other officials cautioned, that the effect of the job action, called a "work to the rule," might not be felt until next week.

At the Peabody building, 5th and C streets NE, some youngsters stood on the sidewalk a bit apprehensively before the school bell rang at 9 a.m. Others ran up the stairs talking to friends. A few held hands tightly with their parents who led the way inside.

Principal Veola Jackson sat in the hallway behind a white table that was somewhat akin to a check-in counter at an airport. As she gave out room assignments and asked parents to sign forms, she said a few children had come to the school last week.

"It was just some of the older ones," she said, "and they wanted to say, 'Hi.! They get impatient, you know, for things to start."

Teddy Carter Jr., a 6-year-old entering first grade yesterday, said he came back to school "to learn how to read." He dressed for the occasion in a gray vest and clean sneakers.

His father, Theodore Carter Sr., said his younger son, Chad, 4, seemed somewhat disappointed to be staying home. Chad is supposed to start prekindergarten at the school, Carter said, but those classes do not begin until next week.

"He sucked his thumb again a lettle," Carter said, "He's frustrated. We've been telling him he's a big boy now because he'll be going to the same school with his brother. He'll have to wait a little and that will be the exciting day."

Under a new school board policy all 4-year-olds in the city will be able to attend free half-day classes this year at their neighborhood schools. The prekindergarten teachers are breaking them in slowly, spending a half-hour in the classroom with each child and his parents before regular sessions begin.

"I want each child to meet me and get to know me a little," said teacher Lois Kauffmann, as she took out her puzzles and games.

"It's sort of a frightening experience to be plunked into a classroom of 20 kids when you've never been there before. So we let them try things around the room when they come here for the interview, and when they come back (for classes), they usually go back to something they know."

"There's virtually no hanging on," Kauffmann added "and no crying."

Around the city, no new schools opened for the first time in five years. Because of declining enrollment five schools were closed at the end of the spring term, and their students went to other buildings yesterday.

At Garrison Elementary School, 12th and S streets NW, there were coffee and donuts, for parents bringing their children from Grimke School, two blocks away, which closed in June.

The school system's most prominent pupil, President Carter's 10-year-old daughter Amy, also moved to a different school. After almost two years at Stevens Elementary, near the White House, she started sixth grade at the Hardy Middle School, Foxhall Road and Volta Place NW.