"I didn't want to be here," Gavin Chaz said as he sat in a small air-conditioned classroom last week in Arlington's Key Elementary School. "But on the first day it seemed better than I thought it would be and then I kind of liked it.

"Some of my friends still think it's sort of dumb to go to summer school," he said. "But I say to them, "Spell America." They can't do it, and now I can."

For about 55,000 students in the Washington area (about 10 percent of the total), school didn't end last June.

Like Gavin, a 12-year-old who will be entering seventh grade in the fall, they are attending summer sessions.

Most are doing remedial work, trying to master subjects - in Gavin's case writing and spelling - that they didn't learn well during the regular school year. If they are in high school, most are trying to pass courses they previously failed.

But an expanding minority, officials said, are going to summer school not to catch up but to get ahead, and even to have some intellectual fun.

At Bethesda's Leland Junior High School, for example, there was a 3 1/2-week institute during July for bright elementary students, centered on the theme "Phocus on Phads."

"We spelled it that way because we wanted to play with the kids," said James McAlphine, the teacher specialist who planned the program.

"This was pure enrichment," McAlphine said. "We wanted to deal with the process of learning rather than give the kids new facts per se. So we invented centers for the kinds to work with. We gave them a problem situation dealing with fads, and let them go to it. They produced some wild things."

The students - in grades three to six - also spent about a quarter of each three-hour 20-minute session playing games, McAlphine said, such as Master Mind, Stratego Chess, Monopoly, bridge and even some poker.

After each game, he said, teachers and students analyzed the play.

By contrast, at Spingarn High School in Northeast Washington there is no playing around in summer school.

Its 575 students attend classes four hours a day, five days a week, starting at 5:30 p.m., so most of them can hold day-time jobs.

LaSaundra Miller, 17, said she works during the day at an aquarium shop in Southeast Washington, then eats supper at her grandmother's house before heading for English class.

"They keep us busy here and we're working hard," she said. "Everybody wants to get out and get a diploma so they make an effort to do the work now, even if they didn't work so hard during the winter."

Miller said she sometimes gets tired during the long classes. Overall, she said, the work "basically is easier than winter school."

The same point was made by William Watts, the summer school principal at Robinson Secondary in Fairfax County.

"It's a 30-day session for which they get a full year's credit," Watts said. "That's what makes it such a good deal. But teachers really have to accelerate...[and] you just can't go into depth. You have to develop the major [points] in the subject area."

"The teacher really has to make the work more organized that it is in the regular term," said Barbara Pitman, who teaches summer classes at Arlington's Key Elementary. "The remedial kids usually aren't able to organize their own work well, and you have to do it for them."

At Spingarn High almost all courses are tightly organized into "learning activity packages." Each one is a mimeographed set of work-sheets and textbook material that teaches a specific topic. Students have to pass a test showing they have had completed each "package" successfully before they can move on to the next one. They have to cover a certain number of packages, teacher Thomas Austin said, in order to pass a course.

The sessions at Spingarn and about 50 other Washington public schools are the first large-scale summer program the city school system has run since 1975. Officials said budget cuts have prohibited the sessions.

This year the $3 million cost of summer classes was paid from money saved because of the teacher's strike in March. When the program was first announced during the strike, officials said they expected 25,000 students would attend, but the projection later was scaled down to 15,000.

At its peak in late June, attendance topped 14,000. It quickly dropped to about 13,000, Marshall said, when the major's summer job program began, paying $2.90 an hour for youths aged 14 to 21.

"We were really rolling before the summer jobs opened up," Marshall said. "It might have been better if these kids stayed in school, but a lot of them did remain with us."

Teachers and officials throughout the area said discipline problems are relatively rare in summer school, and attendance is high.

Part of the explanation for this, they said, is the small size of classes. In Arlington and Washington, for example, most summer classes have just 15 to 20 students compared to 25 to 30 during the regular term.

But the most important reason why summer school lacks some of the usual school problems is motivation, officials said. Students, for their parents, want to pass courses previously failed or they want to push ahead faster. Otherwise, they don't register and they don't come to class. In summer, there's no compulsory attendance law.

"The students know why they're here," said Robert Pruess, who is teaching algebra this summer at Washington-Lee High School in Arlington. "They have a job to do and they do it. Motivation - that really makes all the difference in the world."

"Hey man, I really need that diploma," said Moses Jones, 18, a 12th-grader who takes English in the evening at Spingarn High and a U.S. government class during the morning at another D.C. school, McKinley. "I'm working harder now than I've ever done." Jones said, "If you want to get anywhere you can't fool around"

In addition almost all the high school courses have strict attendance rules - usually a student gets no credit if he is absent more than three times.

Another motivating factor is money. Except for Washington and some programs in Alexandria, students must pay tuition to go to summer school in all local jurisdictions.

The changes range from $15 for a junior high make-up course in Alexandria to $80 for high school courses in Arlington and Fairfax.

Tuition is waived or reduced if students can't afford it, but most jurisdictions require everyone to pay something - except in cases of extreme hardship.

"We try to make everybody pay at least $10," said Eleanor Rotter, summer school director in Prince George's County. "That way they make a commitment. Otherwise, we've found, they often don't take it seriously."

In most jurisdictions, though, tuition covers only about 25 to 35 percent of summer school costs.

Besides remedial work, Washington has a few advanced courses this summer for gifted students. There are much more elaborate programs for the gifted in Maryland and Virginia. Both have state-financed programs, mostly on college campuses where junior and senior high students live for several weeks while taking special courses.

The most rigorous advanced program is at Johns Hopkins University in Baltimore, where bright 7th and 8th graders are selected on the basis of College Board exams. They take college level courses in Mathematics, German, or Greek mythology. Most cover a full term's work in eight all-day sessions spread over eight weeks. Afterward, many skip regular high school work or gain early admission to college.

For students with academic problems in elementary grades the academic gains from summer school are less visible. Privately, some principals are doubtful that the classes amount to much more than "cheap baby-sitting."

"In four weeks it's very difficult to correct a problem that's been developing for four or five years," one principal said. "Sometimes you can teach some specific skills, such as the number facts or some spelling and handwriting. Students from other countries who want to learn English seem to do well. But generally in the remedial work I think the odds are against doing too much good."

Other teachers and principals said they are satisfied if students don't slip farther behind, which often happens to low-achieving youngsters when they don't go to summer school and don't read at home.

"We want to think a lot is accomplished in summer school," said Paul Wire, the principal at Key elementary. "But for many students, if it keeps them from regressing, that's quite an accomplishment." CAPTION: Picture, Youngsters at Barry Farms public pool exultantly demonstrate one of most enjoyable ways of beating the heat in Washington; By Joel Richardson - The Washington Post