Alexandria school officials have struggled for years with a simple fact about children--some are more expensive to educate than others. A child with a disability or a child whose parents rarely read to him may need more time to learn. More time means more money for more teachers.

Federal programs provide some extra funds for such students, but that has not been enough. This year, Alexandria School Board members say, they are giving top priority to finding a way to routinely give more funds to schools that have more children needing extra help.

Few school districts with Alexandria's broad range of family incomes have taken such a step. Even when more money is allotted to schools with more disadvantaged children, there is no guarantee that will improve achievement.

But many board members say they are determined to try. "I think we are overdue getting to it," said board member Mark R. Eaton. "I have never understood this one-size-fits-all premise for funding."

"We've got to do it," board member Sally Ann Baynard said. "It simply doesn't cost as much to educate a non-special-education, English-speaking, middle-class child."

At the annual School Board retreat in late August where this issue was discussed, the agenda referred to it as "differentiated resources," a bureaucratic way of saying more money for poorer children. In a district where half the students come from families with incomes low enough for the students to be eligible for free and reduced-price lunches, the need is great, school officials say. But they wonder how much they can afford to give disadvantaged schools without shortchanging those in more affluent areas.

"We don't want to rob Peter to pay Paul," said school spokeswoman Barbara Hunter. "We want to increase the pot for all and funnel the extra dollars to those schools that have challenges."

School Board Chairman Stephen J. Kenealy said it will take time to work out the best method and find the extra money. School Board members already are complaining about what they call a City Council failure to provide funds to build new sixth-grade centers in the city's crowded middle schools. Allotting more to some schools will cut even deeper into the budget.

Kenealy said that about 3,000 elementary school children come from low-income homes and could use the smaller class sizes and longer school days that more money could buy. "If you use a round number of 500 extra dollars per kid," he said, "and you have 3,000 kids, that's $1.5 million."

Opinions on the severity of the problem and how to solve it vary on the board. "I think we have already differentiated our resources substantially," said Vice Chairman Claire M. Eberwein. "Most of our new programs are already oriented towards children who are most critically in need of being able to pass the new exams and read on grade level."

There are other money issues that board members say will go high on their agenda. The loss of Polk Elementary School Principal Mildred Cruz-Fridman to the neighboring Arlington school system has disturbed many parents and school officials. Board member V. Rodger Digilio has noted that administrative salaries in Alexandria are below those of other jurisdictions and has proposed a $10,000 increase in principal salaries, now about $80,000 at elementary schools.

Eaton said he thinks such pay raises are in order. "The principal is absolutely critical to the success of a school," he said.

Baynard said principals' salaries should be raised $20,000. "We are going to have a hemorrhage of principals if we don't," she said. She mentioned John Porter, the highly regarded principal of the district's only high school, and Margaret Walsh, head of the Minnie Howard ninth-grade school and a recent Virginia principal of the year, as likely targets of the next raid on the district's administrative talent.

Earlier in the year, board members and staff had discussed a plan to reward principals whose schools showed improvement on state tests and other measures, but principals themselves opposed that idea, saying it ignored the contributions of teachers and staff. Eaton said that should not end the discussion. "I have not abandoned the idea that we can compensate people on the basis of more than just credentials and seniority," he said.

Much of the focus in the coming school year will remain on new school boundaries, new magnet programs in at least three elementary schools and the construction of an elementary school at the western corner of the city, officials said.

A committee is now collecting suggestions for a name for the school, scheduled to open in fall 2000. Kenealy said lobbying by admirers of various people, living and dead, already has begun, with several military heroes frequently mentioned.

"For many districts this is not a problem," Kenealy said, "but when you only name a school once every 30 years, you have to be careful." School officials celebrated significant increases in scores on the Standards of Learning tests this spring, but unlike its neighboring districts, Arlington and Fairfax, Alexandria has not had a single school yet reach the state SOL targets. Schools that do not have 70 percent of their students passing most of the tests by 2007 risk losing state accreditation.

Hunter said the district will continue to pursue Superintendent Herbert M. Berg's Primary Initiative, which focuses on reading skills in early grades. She said school officials also are studying the large number of students who frequently transfer in and out of the system, making it difficult to bring them to the level where they can pass the SOL tests.

"The demographer said half of the city's population turns over every five years," Eaton said. "We have to have thorough discussions of how we can deal with such mobility."