Matthew Lawrence sat at his desk at the Franklin School Monday morning, struggling over a sentence.

This is no ordinary class he attends -- the students are all adults, and all read below fourth-grade level.

Lawrence says he dropped out of school in the seventh grade to take care of his family. He is just one of more than 100,000 District residents -- 15 percent of the city's population -- who read below fourth-grade level.

At 32 he is considered a "functional illiterate." He cannot read most newspapers, job applications, package directions and road signs. "It's pretty bad," he said, "when you got to ask somebody to read your mail for you. They could tell you anything."

Encouraged by a friend, Lawrence came to the Adult Education Demonstration Center at the Franklin School two years ago. He attends the free basic education classes in the morning, works in the afternoon and hopes someday to pass the General Education Development (GED) exam for a high school equivalency certificate.

Despite its dingy corridors and peeling paint, the AEDC is a place where students are serious and hopes are high. "I know I'm gonna get my GED," said a young man who started classes last month. "It will take a year if I go every day. I'm confident."

For Lawrence and the estimated 200,000 undereducated District residents like him, free adult literacy programs are a ticket to a better job. Lawrence figures he can double his income as a machinist if he earns a GED certificate. "People come here because they want a better job and realize they don't have sufficient basic skills to get one," said the center's director, Delia Pailen.

"Adult illiteracy is tied to poverty and unemployment," said Jane Tomlinson, a volunteer at Literacy Action in Adams Morgan. She said more than half the city's unemployed persons lack high school diplomas.

Several dozen organizations provide instruction in basic skills for the city's illiterates -- most of whom are por, young and black -- but the District school board's Division of Adult and Continuing Education shoulders the major portion of the load.

With a yearly budget of $3.5 million, the division serves 24,000 people each year at four full-time education centers: the Adult Education Demonstration Center at 13th and K streets; the Gordon Multi-Lingual Center at 35th and T streets NW; the Armstrong Center at 1st and O streets NW and the Miner Adult Center at 601 15th Street NE.

The courses at these centers are designed with the special needs of adults in mind, explained Connie Spinner, a programmer at the division. Students range in age from 16 to 80, but most are under 35, she said.

Convenience is the keynote at the centers, and the administrators pride themselves on flexibility. Day and evening courses are offered in everything from accounting to welding, but most of the students are preparing for the GED, she said.

With open enrollment, open classes and a nursery, students are free to come as often as they like. "You can come any day, any time, and they'll start you as soon as possible," explained one student.

Spinner, a former student and teacher in the District's adult education network, explained the needs of adults in school. "If instruction didn't have a direct line to survival, it wouldn't work. We've discovered it's more effective to meet an immediate need while trying to reach an ongoing goal," she said.

Basic reading booklets focus on "life-coping skills -- how to understand income tax forms, insurance, contracts and comparison shopping. "Dick, Jane and Sally just doesn't work for adults," said teacher DeBorah Johnson.

Preparation for the GED can take a few months or as long as four years, depending on the student's starting level. School board officials, however, seem pleased with the success rate. In 1979, more than a third of the students taking the exam passed. "Last year 1,063 people passed the GED, and there were only 6,000 students graduating from high school in the District," said school board official Andrew Weeks.

The driving force behind the division is Assistant Superintendent Mary Turner, a legend in the world of adult education. She built her reputation as the energetic first director of the AEDC, scrounging money when there was none to be had, and pioneering unconventional approaches to adult education.

"Mrs. Turner doesn't know how to say no," said Connie Spinner. "She's never turned down a challenge to work for adult education. I know this sounds like a eulogy, but she's a yes-person in a world where you don't find many of them."

"The problem with adult education," explained Spinner, "is that it has such a low priority. There is no law for compulsory adult education. We are always the ones to cut back first."

With talk of budget cuts throughout the District, the Division of Adult Education is understandably nervous. Although specific targets for cuts have not yet been identified, the D.C. school board will have $27 million less to work with next year and is considering eliminating about 900 staff positions and closing several adult education centers.

"We don't know where we stand," said Spinner. "Hopefully we're mounting a good case to retain our level of funding, but things are very tenuous now. They're still looking at everything. And while we're hoping for the best, we're very much on pins and needles."

But District School Superintendent Vincent Reed, who has been working on the budget for several months, said there is "a very strong feeling for adult education. We should still be able to serve the same number of people. It would just be less convenient for them."

Although adult education now receives only 1 percent of the District's school budget and may be faced with making major cuts, there is still talk of new programs. Spinner is hatching a plan to link the literacy program with a newspaper.

The project caught her eye at a conference last year. "A local newspaper in Vineland, N.J., ran a weekly column for GED preparation. It was very successful and I fell in love with the idea," she said.

Some people were able to pass the high school equivalency exam. Others went to classes for help. "It was great for the homebound and the handicapped, and people who were too embarrassed to attend a class," she said.

She said the newspaper participation provided the public exposure adult-education programs lack. "You either do your programs or you sell them," she said. "And we are so busy doing them that we don't always have time to talk about it."