The child is lively and sweet, in love with music and dancing and all the delights of being 11 years old. And yet she has cost Arlington County nearly $200,000 in legal fees, arising from the day that her mother said she heard her school principal say she did not want that child at her school.

The principal, Holly Hawthorne, of the Arlington Traditional School, denies making the remark. Arlington school officials say they have spent five years doing everything they can to help the girl, who has a moderate form of mental retardation and attention deficit hyperactivity disorder.

That has not kept the child's parents from taking their case through a series of administrative hearings and into the federal courts. They want their daughter in a regular classroom with children her age while she works with a special education teacher. The school system says the girl will learn academic subjects much better in a separate room with just a few other disabled students.

The county's legal costs, $193,845.58 and still climbing, are a record for a special education case in Arlington, and among the highest ever in the Washington area.

Jerome Bruns, former Falls Church student services director, testified for the parents. "For a relatively modest expenditure," he said, "they could have done what the parents wanted and see how that worked," an approach used in other school districts.

"The law requires we provide a free and appropriate public education," said Lisa Farbstein, spokeswoman for Arlington schools. "The student needs to be able to make academic progress, and if the parents are asking us to put the child in a situation where she cannot learn, we need to do what we must to help the child."

Although such extreme and expensive disputes are not common, they happen often enough in the complex world of special education to lead experts to call for mediation. This, they say, is particularly important in the initial meetings, when parents are trying to deal with the shock of learning their child has a disability and teachers are wondering which of a hundred different teaching approaches would be best.

Parents and school officials "need to be able to sit down at a table and talk to each other, so that costly court disputes can be prevented," said Deborah Ziegler, a staff member at the Reston-based Council of Exceptional Children.

In the case of the Arlington child and her parents, who are not identified in their lawsuit (Jane Doe v. Arlington County School Board) and who spoke on condition of anonymity so as not to embarrass their daughter, reconciliation with county school officials seems unlikely.

The parents still think the county has a fine public school system. Their daughter has transferred to another Arlington school and is about to enter the fifth grade.

They say they are pursuing their legal fight, hoping to convince Arlington and other districts that letting disabled children spend as much time as possible in regular classrooms is a good idea.

"We ran into a buzz saw," the father said. "They just refused to put her in a general classroom."

When the child first enrolled at Arlington Traditional, a magnet school with the county's highest test scores, no one knew there was a problem. Admission is by lottery, with no rules against children who need special education. The parents noticed the girl was uncomfortable in some situations and did not always speak clearly, but "the doctor had told us things click in for different kids at different ages," the father said.

Within six weeks, her kindergarten teacher recommended she be tested. She was designated a special education student. Operating under federal rules, the school and the parents agreed to an Individual Education Plan (IEP) that, the parents thought, guaranteed she would spend most of her days in a regular class.

In second grade, the father learned that his daughter was being pulled out of class for special lessons. Her teachers pointed out the girl was still learning to recognize letters. Her math did not extend much beyond 1 plus 1. Her classmates were reading and subtracting multi-digit numbers.

The parents asked why their daughter could not remain in the class, doing her simpler work with the help of an aide or teacher. But when that was tried, said John F. Cafferky, the attorney representing the school system, "she did not want to do her work, she wanted to do the other kids' work."

The parents insisted that if an aide or teacher was with her continually, she would be able to focus on her own work--a much cheaper alternative than fighting a lawsuit.

Cafferky said the school tried that and it did not work. Bruns, who has reviewed all the documents, said there is no evidence that the school ever did what the parents asked.

In the middle of the girl's second-grade year, relations between the school and the parents fell apart.

The parents hired D.C. lawyer John F. Karl Jr., the girl's soccer coach, and sued the system in January 1998, asking not only for a new placement for their daughter but for monetary damages from the system and its special education director, Alvin Crawley. The individual suit against Crawley was later dismissed. U.S. District Judge Claude Hilton ruled against the parents in Alexandria federal court March 18.

The father said school officials were inconsistent and sometimes cruel. The parents had asked if another child might agree to be an official buddy for their daughter, as had been done in some other cases. The child had once said, listening to her sister talk about friends, "I don't have any friends." The request was denied.

The parents say they have spent $30,000 on their case and will stay with it, even though there may not be a decision from the 4th U.S. Circuit Court of Appeals until next year at the earliest.

"It is such a painful experience," the father said. "I just wish the school system had spent more time on education and less on litigation."'