It was the first day of classes at Richardson Elementary School in Northeast Washington, but third-grade teacher Johnny Brinson was not handing out name tags or struggling to match unfamiliar faces with names on his attendance sheet.

Instead, Brinson, 37, greeted his students yesterday morning with a triumphant announcement. "I got you all back!" he said. "Do you know why I wanted you back?"

The youngsters waved their hands in the air and shouted rapid-fire answers.

"Because we're smart."

"Because you're our friend."

Brinson nodded in animated agreement. "It's so good to see you all again," he said.

As students in the Washington area sized up new teachers on what was the first day of public school in almost every jurisdiction, the 16 boys and seven girls in Brinson's class had a reunion of sorts. Brinson taught all but two of the youngsters for either first or second grade; 19 of them were with him both years.

Now Brinson and his students are venturing together into the third-grade world of multiplication, cursive handwriting and punctuation. If all goes well, he may stay with them through the spring of 1994.

"At the end of first grade, I said to {Principal} Marlene Guy, 'You know, I would really like to follow these children all the way to sixth grade,' " Brinson said. "And she said, 'Why don't you?' And that's exactly how it started."

The purpose of the experiment, Guy said, is to provide continuity and an enduring role model for youngsters whose lives outside school have many uncertainties. Nearly three out of four Richardson students come from families who qualify for welfare programs; many live in the Lincoln Heights public housing development directly behind the school. Most of Brinson's students live with only one parent or grandparent, and all but a handful receive free or subsidized school lunches.

"The children need consistency in their lives. They've had so many disappointments," Guy said. "And teachers can have a very, very strong impact."

Education experts say that matching teachers with students for several years cuts down on diagnostic tests and eliminates needless repetition that can take up to 40 percent of classroom time. Although West Germany, Italy and other European countries use similar setups, the experts said, schools in the United States traditionally do not.

"It gives a tremendous amount of stability," said Lillian G. Katz, an authority on elementary education from the University of Illinois. "The children grow together; the teacher can build on their history."

In Brinson's classroom, the system seems to be working. His students led other Richardson classes in national test scores last spring and placed above their grade level in reading, spelling and language skills. Their cumulative test score was 3.0, compared with a national second-grade average of 2.8.

Brinson "can get more out of my son than I can," said Bernell Nickens, a George Washington University security guard whose son, Emory Kosh, 8, started his third year with Brinson yesterday. "I know he is well taken care of and he will learn."

Brinson got right down to business in class yesterday, jumping from one student to another in search of antonyms, synonyms and compound words. He applauded each correct response and reminded the youngsters of lessons taught last year when answers were too long in coming.

But there was time for fun, too. On the playground before the school bell rang, Brinson crushed his students in bear hugs and gave warm welcomes to the parents who had tagged along for opening day.

"I try to do a lot of touching . . . . They need that," said Brinson, who is not married and has no children. "I hug them all the time."

Guy said she will stick with the extended-teaching formula as long as it is successful, and she is encouraging other Richardson teachers to follow Brinson's lead.

Throughout the District and elsewhere in the region, the first day of classes went relatively smoothly.

But school officials in Montgomery County were startled by the number of students who showed up. The unofficial count indicated that 103,509 attended classes yesterday, nearly 1,000 more than the school system had expected.

Brian J. Porter, the school system's spokesman, said high school students accounted for 650 of the unexpected pupils, while middle-school youngsters made up the rest. None of the schools reported any severe strains.

Montgomery schools will not take an official count until the end of the month. If the high enrollment number remains, Porter said, the school system may hire additional teachers.

While the District has shut several schools because of declining enrollments, new buildings were being opened in Maryland and Northern Virginia. Montgomery, for example, is using four new schools and three remodeled ones this year. Fairfax, the area's largest school system, with 128,000 students, opened three elementary schools. Prince William, the second largest school system in Northern Virginia, opened three more.

Staff writers Amy Goldstein and Peter Baker and special correspondent Camille Ross contributed to this report.