"Being the greedy little creatures that you are, you'd like more than half a pizza " said Peter Brown, as he turns his embroidered work-shirred back to write fractions on the blackboard.

Several of his fifth and sixth grade students at Arlington's Drew Elementary School giggle appreciatively. Others talk loudly to each other about the assignment or shout answers at Brown. One girl lies on a countertop looking bored. A boy gets up from his seat and crosses the room to sit on a sofa. Despite the noise, most students seem to focus their attention on the math problem Brown poses.

"Where should I stop?" Brown says, as he asks the class for the lowest common multiple.

"Actually, Mr. Brown, you could have stopped before you started," said one girl, glancing at her friends for their reaction. There is none. Most of the class is vying to answer Brown's questions.

Donna Paleen's class of fifth graders at the Page Traditional School is very quiet. Students, who sit in neat rows behind their desks, raise their hands to answer questions and are called to the blackboard to translate Roman numerals into whole numbers.

In addition to the usual profusion of brightly colored construction paper cutouts on the wall - the hallmark of American elementary education - there are classroom rules. They include "Respect another person's property" and "Try to obey school rules." Prominently displayed is Munro Leaf's classic 1946 children's book, "How To Behave and Why."

Besides representing two ends of Arlington's educational spectrum, Page and Drew schools are symbols of a long-standing and frequently bitter debate about the quality of Arlington's public school system, which has among the highest per pupil expenditures in the state. Arlington's controversy reflects the national back-to-basics trend with its emphassis on discipline, minimum competency tests, promotional policies and even dress codes.

Last January, as a result of substantial parental demand and despite the reservations of some of its members who said Arlington schools were already traditional, the school board created Page Traditional School. Page, which opened in September, had been receiving enthusiatic responses from parents. The school, which features enclosed classrooms, traditional teaching methods and textbook instruction, stresses disciplined behavior in its students.

Superintendent Larry Cuban and school board members say that Page differs only in style from other Arlington schools. Other schools, they say, teach basic academic skills in different ways.

"We're trying to create a quiet, studious environment here," said principal Frank Miller, who is described by one mother as resembling a "stern but loving parent."

Drew Elementary School, near the Shirlington Shopping Center in a predominately black section of Arlington, was created in 1971 as part of a court-ordered desegregration plan. An outgrowth of the less structured educational innovations of the '60s, Drew offers an alternative to regular elementary schools. Students from anywhere in the county may apply and are screened by the school staff before they are accepted. Like Page, the school is racially and economically mixed. Each school has about 50 students on its waiting list.

"Adaption is one of the key words of Drew," according to a brochure. "The relationship is one that encourages informality and responsiveness." There are rules ("No running in the hall unless you're being chased by a dinosaur") as well as an emphasis on "children's choice." There is, in fact, a regular Thursday afternoon program by the same name, which is much beloved by the students. Drew pupils select from courses taught by parents, which include "Living Together" (preparation for an overnight camping trip), "Look Like A Model," "Learn To Speak French," basketmaking and square dancing.

The demand for Page, according to parents, teachers and administrators was fueled by parental dissatisfaction with currently accepted teaching methods that feature less structured open classrooms and team teaching. Five of the newest of Arlington's 25 elementary schools have only open classrooms, where as many as three teachers and 90 students share a large room.

"I'm not sure I could teach in an open classroom," said Jan Leman, principal of Jamestown School which has only closed classrooms and is described by parents, teachers and Leman as fairly traditional. "I wouldn't want my 25 students laughing at something I'd said and the others all turning around, wondering what was so funny."

Elaine Arquette, whose seven children have attended a variety of Arlington public and parochial schools, agrees.

"I think we adults tend to fantasize about how nice open classrooms would be and about the freedom we wish we had," said Arquette, who has two children, former Drew students, now at Page. "My own children started telling us that they needed more direction at an earlier age."

"You learn to concentrate," said Sharyn Gardner, a Drew sixth grader, who says she loves the school. "We're used to it. It's always noisy here, but it's noisy in most of the schools."

John Phillips is a former school psychologist and teacher at Drew who is now at Page.

"I think anybody who's in a noisy situation for a number of hours feels a drain," Phillips said. "It's more difficult to feel that things are running smoothly. As a teacher, your anxiety is probably less in a quiet classroom, but I'm not ready to make a judgment that there's more learning going on, just because it's more orderly."

Some of the things Page students say they like - staying in one classroom, having the same teacher for all subjects - are the things Drew students would just as soon do without.

"You stay in one classroom all day and you're stuck there," said Michelle Nomina, a Drew sixth grader who transferred from Abingdon School. "It's so boring, you always know what's going to happen. Here it's much more exciting and youl feel free."

Drew principal Ray O'Neill stresses that his school's curriculum emphasizes basic skills as much as any school, including Page. Last year, 5 percent of Drew sixth graders were reading two or more years below grade level. The countywide average was 11 percent.

"I think we've given more conscious attention to the basics," said O'Neill in a rapid-fire manner that complements the way he strides around the school, ducking into classrooms.

"A very bright child does exceptionally well at Drew," Phillips said. "But I think at lot of kids there need a more structured situation. They were having problems adjusting to their neighborhood schools, and their existence at Drew is more comfortable. Their parents aren't getting nearly as much grief about if so they stay.

"At Page, we're finding kids who transferred from open classroom schools and were able to do little or no work and get by," Phillips said.

"I think some kids night get something at Page that because of the environment at other schools they don't have," said Miller. "We're very concerned about a child's academic progress. We emphasize good study skills. We've had the opportunity to pick and choose various types of school programs, but I think this kind of school is good for every child."

"Part of the problem in many Arlington schools is that things are not stated," said Paleen, who left Abington after seven years to come to Page. "We've tried to make it very clear what our expectations are here.

"The first day of school," she recalled, "I gave all the kids small spiral notebooks for their homework assignments. When I first told them to take them out and write down their assignments, they had no idea what I was talking about."