Throughout her four years on the Arlington school board, Torill B. Floyd earned a reputation as someone who did her homework. No issue was too small to escape her scrutiny: She spoke out vigorously on matters ranging from the complex school budget to the condition of school bus tires.

The politics of the board seemed to matter little to Floyd, the only Democrat this year, as she independently pursued a point or argued a position.

A Norwegian-born dentist whose four-year term expires today, Floyd did not seek reappointment by the GOP-dominated County Board. When her replacement, Margaret A. Bocek, takes her seat tomorrow, the school board will become all-Republican.

The changes on the board concern Floyd.

For one thing, the new board will have only one member from south Arlington: Evelyn Reid Syphax, who is expected to be named chairman tomorrow. Floyd, who also is from south Arlington, said she fears the "lopsided representation" could lead to a "lack of sensitivity to the problems in south Arlington" where the school and the general populations are increasing.

"I'm also very concerned that the school board does not reflect the composition of the County Board," Floyd said, referring to the last two County Board elections when a Democrat and Democrat-backed independent won handily. "At this time, a different point of view seems to be coming out of the County Board election results. But we're getting a very conservative majority on the school board which may not be in line with what the citizens want."

Her concern about the board's new conservative bent was reflected in her farewell to her colleagues, when she urged them not to drop or reduce dozens of programs created during the 1970s.

In a later interview, she said, "While you always have to look for ways to tighten up the budget, I'm afraid that keeping many programs is going to depend on just the costs, and because it costs more to run some of them, the board is going to try to reduce them."

Among the programs added during the 1970s that Floyd listed as particular concerns were expanded special education, vocational education, remedial skills, special programs for children with English-language deficiencies, extended day care and programs for the gifted and talented.

"I'm concerned that we keep those programs and we expand on them," she said.

One of the major issues facing the new board will be school closings. A special commission studying secondary school consolidations has recommended that H-B Woodlawn Secondary School and the seventh grade at Page Traditional School, both alternative schools, be closed.

Floyd said she was disappointed that the commission did not recommend incorporating some features of the Woodlawn program into the regular schools, but was pleased that the commission--as well as one studying grade school closings--urged redistricting to achieve better racial and ethnic balance.

Floyd said she would have preferred more citizen participation in the grade school study.

Although citizen participation has been "outstanding" in the past, Floyd said she has "seen too many attempts at shortcuts this year" that threatened the "open process" of board deliberations.

One example she cited was the failure of the County Board to invite the entire school board to a meeting at which school budget guidelines were to be discussed--a meeting that was announced at 1 a.m. only a few days beforehand. Another was the board meeting at which she threatened to quit when the board almost adopted a budget spending ceiling--an item that was not on the agenda.

Floyd said she also was disappointed in what she sees as the failure of Superintendent Charles Nunley "to provide instructional leadership in terms of initiatives for new programs and his handling of personnel matters." But, she added, Nunley has been superintendent only one year and has addressed some practical matters, such as the upkeep of building facilities.

Of particular concern to Floyd is the "back-to-basics" trend, as embodied in the alternative program at Page School.

"It concerns me that it's apparently the 'in thing' to have your children in alternative schools when, in fact, the neighborhood schools are very good," she said. "But some parents don't try to find out what is available in the neighborhood schools and work to strengthen them."

Although she believes that alternative programs are important, she says she hopes the new board will not overemphasize Page-type formats, simply because two board members (Bocek and Simone J. Pace) have children at the school.

"In the past decade," she said, "the school board has placed a strong emphasis on basics that has resulted in improving test scores and has tightened up on promotion and attendance policies.

"What we really need to emphasize now are other aspects of the school system: creativity, independence and analytical thinking."