IT'S a quandary that school districts across the country increasingly face - how to handle the vastly different demands of city and county children in one district. So when the often awkward process of merging city and county schools presented itself to Chattanooga, Tenn., last year, district officials responded with a one-of-kind solution: Wipe the blackboard clean and start from scratch. ''They could have easily said we will absorb the city school system and move on,'' says Steven Prigohzy, president of the Public Education Foundation, a group helping to steer Chattanooga in building a new system. Instead, the county saw an opportunity to move closer to an ideal school system: ''A system that serves both inner-city and suburban children, where the vast majority of kids are high achievers, and where all schools are equitably funded and attract the best teachers,'' says Edna Varner, the energetic principal of Chattanooga Middle School, Phoenix II. The reform effort was sparked by the city's decision to bail out of the school business and consolidate with Hamilton County. Educators say the decision to form a new district instead of merge two existing systems is a first. ''I can't think of one situation where consolidation has been a catalyst for the community to say let's rethink things,'' says Tony Cipollone, associate director of the Annie E. Casey Foundation, a Baltimore-based think tank on children's issues. ''There is a potential to make some real change here.'' Many school consolidations over the last decade have occurred after rural counties across the United States brought financial equity lawsuits against a state. Most counties have won these suits, a trend suggesting more will follow. The Chattanooga model In Chattanooga's case, declining enrollments and dwindling dollars spurred city residents last November to vote to unify the systems. Since Tennessee law requires counties to furnish education, the county had no choice but to pick up the ball. It could, however, decide how the consolidation should work. The county school board, prompted by local leaders and educators, voted to create a new system by July 1997. The challenge is a daunting one because the two systems serve polar populations and have chosen different administrative models. Sixty percent of the 21,000 students in Chattanooga's city schools are black; many come from poor households. The school board is elected, and the superintendent is an educator who was plucked from a California school district. In contrast, 95 percent of the 24,000 students in county schools are white children from middle-class backgrounds. Until recently, county commissioners appointed the school board, and the superintendent has always come from within the community. The county tends to operate more traditional classrooms, while the city has been aggressive in getting grants and experimenting with reform efforts. County students, however, consistently score higher on standardized tests. It's not surprising then, many here say, that deciding how to meld the two systems has become a contentious process. ''It's been boiling along,'' says Don Loftis, retiring superintendent of the Hamilton County schools. ''Everyone has an agenda.'' The Public Education Foundation, which is heading the planning effort, is doing so with grants from other foundations and money from the Chattanooga community. A committee of teachers, parents, and principals from the city and county is crafting a framework of how the new system might look. The county school board plans to receive the proposal in December. Planning committee members say it is too early to give specifics. Some people talk about combining the best of city and county. Others talk of focusing on new standards and ways of assessing standards. Both city and county residents have their own concerns. County teachers are worried they'll be moved and parents don't want their children bused, says Betty Heffington, a grandmother in the Hamilton County Parent-Teacher Association. In the city, Chattanooga residents are worried that the county will not implement a new system, despite going through the exercise. ''Our system is at the mercy of what the county decides is best for us,'' says Rosina Heyword, counselor at Phoenix II. ''I don't want to be overtaken by the philosophy of the county, which I don't feel will utilize reform-minded strategies.'' Secret of success But Ms. Heffington, who serves on the planning board, is confident the county school board is dedicated to the effort's success. ''I truly believe each member cares about children, not just our county kids. I think they will be just as interested in serving the needs of all children. The problem lies in politics, in the attitude of adults who say, 'Don't get on my turf.' '' Chattanooga superintendent Harry Reynolds, also retiring, is cautious about the outcome. The first step is for the county board to conduct a nationwide search for a superintendent, instead of hiring from inside. ''If that happens, my confidence level will soar,'' he says. Says Mr. Prigohzy: ''I would be lying if I said this is simply going to fly. But Chattanooga has made major change over the past 10 years over a fairly wide spectrum. That gives me a sense of optimism that this will happen.''