To Eleanor Levi, the smiling blue stick figure tells the whole long story.

Tacked onto her classroom wall at Alexandria's Mount Vernon Elementary School, the drawing shows a child jumping rope. Above it are four sturdy words: "I can do it."

Levi teaches students with learning disabilities, children who only a decade ago many teachers believed could do nothing at all.

"We didn't even have a room for special education," said Harry Burke, who came to Alexandria's public schools in 1973 and is now director of special education programs there. "We had no files, no secretary, no budget. Kids were put in a makeshift program, almost a holding pen. It was gratuitous and degrading."

The situation in Alexandria, where handicapped children were kept in a bungalow that has since been leveled, was not unique. In the District, school officials openly turned their backs on thousands of handicapped children until a federal judge forced a change. And in Montgomery County, where some programs for handicapped children were available, parents had to go to court to win mandatory services for others affected with more serious handicaps. Rules were evaded in dozens of states and millions of handicapped children were hidden, neglected and not trained for anything.

"Parents would shout and plead at school board meetings," Burke recalled. "It was a cry that never changed: 'Why won't you teach our children?' "

Today, that begging is over. Ten years ago, on Nov. 29, 1975, President Ford signed a controversial civil rights law that guaranteed a free public education to every handicapped child in the United States. And despite cries that it would destroy many schools, it has created neither the calamity its critics expected, nor all the solutions its sponsors had sought.

Like any sweeping piece of legislation, PL 94-142, the Education for All Handicapped Children Act, has its critics. People say it is too broad, it bogs school systems down with unnecessary paper work, and its awesome costs are difficult to justify in an era of tighter budgets. But by any measure, both its supporters and opponents agree that the law has had a profound effect on handicapped children and the way they're viewed in school and in society.

Numbers tell part of the story.

In 1974, the year before the act was signed into law, the federal government spent less than $50 million to fund special education. For the coming fiscal year, Congress has appropriated more than $1.3 billion. Almost 4.5 million handicapped children -- 11 percent of America's public school population -- receive some form of special education. Since the law was implemented, the number of handicapped students receiving special education increased by about 25 percent, according to the Department of Education.

In the last decade, as wheelchair ramps and elevators have become part of the design of American schools, the number of special education teachers and support personnel has doubled to more than 500,000.

In the District, Virginia and Maryland, almost 250,000 students received benefits under the law during the 1984-85 school year. In the past, many of those children would have spent their days in idle futility instead of in class.

"Today, the questions are not about whether a kid has a right to be in the building, but about the best way to get him in there," said Frederick J. Weintraub, legislative director of The Council for Exceptional Children and a key figure in the passage of the bill, which was signed into law after five years of furious lobbying.

Alexandria is typical of the complete shift in priorities. It now devotes almost 10 percent of its $53 million school budget to services for special education. Almost one out of every eight Alexandria students participates in the program.

The central purpose of the law was "to assure that all handicapped children have available to them a free appropriate public education." Essentially, the law grants every child the right to be educated in the least restrictive possible environment -- a concept often referred to as "mainstreaming" -- and it is the goal of most special educators to allow any handicapped child who can manage it to study in a regular class.

"It is such a different world now," said Robert Bullock, whose 6-year-old child has Down's syndrome and has attended public schools in Arlington, Fairfax and Alexandria. "If a child can handle a regular school, they are obligated to give it to him. If he needs a special school, they have to provide that, too. When I was in school there was no chance for these kids. Even now we are squeamish. How often do you cross the road and say hello to a guy in a wheelchair?"

Where a decade ago children with physical and mental handicaps were hidden from the sight of the average student, today they walk the halls, share meals and -- in greater numbers each year -- share classrooms.

In many public schools, teachers and parents say the law has given handicapped children a new self-esteem and radically raised the level of tolerance and understanding.

To critics, however, the law is painted with such a broad brush that thousands of children have been classified incorrectly as handicapped and erroneously served at great public expense.

"The people who wrote the law were so understandably desperate not to exclude handicapped students that perhaps they went a bit overboard," said Elizabeth Delaney, a teacher of special education at Sam Houston State University in Texas, at a recent conference in Washington. "We are picking up thousands of slow learners and calling them disabled."

Hers is a common sentiment among educators. Today almost half of the handicapped children served by PL 94-142 are considered to be learning disabled children. This compares with 23 percent in the year before the law was put into effect.

The rate of increase in such children served slowed last year, but it still accounts for the lion's share of students who benefit from the act.

"Getting kids back into the middle of society is the whole point of this law," said Diane Duff, an Alexandria special education teacher who is part of the surge in specially trained teachers made possible by the legislation. "We should never forget that our goal is to prepare these children to lead productive, meaningful lives after they are done with school. We are not trying just to keep them occupied, we want them to feel good about themselves."

Most educators say that without a commitment to mainstreaming as many handicapped children as possible, the costly education -- on the average it is twice that for a regular student -- would be money spent in vain. They say that fancy gimmicks to keep them away from the other children would defeat the purpose of the law.

Integration in schools, the blending of handicapped children with those who are not, has been vast in its scope.

Today, more than 93 percent of the country's handicapped students receive their education in settings that include nonhandicapped children. More than two-thirds study in regular classrooms.

In Duff's classroom, some children play with audiotronics games that match sounds to sights, while their more advanced classmates learn to read on an Apple computer. There are talking toys and headphones, cloth cartoon characters and dictionaries worn with wear.

"I'm not sure about the point of the class," said one 11-year-old in fifth grade. "But it's a special education. That means we get to use special things. I always want to be in school."

"It's been such a huge success," said Madeline Will, assistant secretary for the U.S. Office of Special Education and Rehabilitative Services, who is responsible for administering Public Law 94-142. "To have accomplished so much in such a span of time is really quite remarkable."

Most people are aware, however, that protection under the law ends at the age of 21. Increasingly, there is concern for those who have had the benefit of a decent education and have the expectations that creates. Often, the battle begins anew the day handicapped children become adults.

Department of Education officials have acknowledged the classification problem and said they realize that the transition from school to society is the most difficult stage for those covered by the law.

"In the adult world of work we are finding concern that these children have never managed an eight-hour day," said Will. "It is a very skeletal adult service system that we have in place."

Perhaps the vehicle that helps best to ensure the rights of handicapped students -- and is most responsible for the blizzard of paperwork that accompanies any special education recipient through school -- is the individual education plan, or IEP.

The IEP is a plan that every school must use to define the needs of each child who receives special education. IEPs are not uniform, but they always include evaluations, an assessment of goals and a specific list of services each child needs. The plan is totally revised at least every three years and it is a document that parents can use in any way they wish.

"The IEP is like a bill of rights for these students and for their parents," said Lisa Walker, who spent five years helping to get the law through Congress and is now vice president of a Washington firm, the Institute For Educational Leadership. "The law is far-reaching and that is the strongest thing about it."

The costs, however, can be staggering. "For some school systems the additional expenses are only a minor problem," said Michael A. Resnick, associate executive director of the National School Boards Association. "But if a tiny town in Vermont has to find $50,000 to send one of its students to a special school, the burden can be heavy."

Resnick and other educators and administrators said that the Reagan administration, which at one time proposed dismantling the law, has little commitment to educating handicapped children.

"The federal government has never kept its promise," said Paul Marchand, a lobbyist for the Association for Retarded Citizens, speaking at a recent conference. "We fought bitterly for what we have. There have been gigantic problems with money, and the Gramm-Rudman amendment is another potential disaster."

Though the amendment, which would force the government to balance the budget by 1991, would exempt many programs from being cut, PL 94-142 is not one of them.

Educators and supporters of the program are quick to point out that, although the legislation called for the federal government to provide 40 percent of the costs of the act, the government has never contributed more than 12 percent. Currently, state and local governments pick up more than 90 percent of the $5 billion in annual costs.

"I know the costs are huge and so is the amount of time we all spend in meetings and filling out papers." said Levi, whose classroom is cluttered with diagnostic games and audiovisual equipment for the 18 to 20 disabled students she teaches. "But have you ever seen a handicapped child start to feel like a valuable human being? I hate to seem old-fashioned, but can you put a price on that?"