When Prince William County's 61 schools open Tuesday, one of the most fundamental changes parents, students and school staff will notice is that there is more decision-making power based in their local schools.

The management technique, called school-based management, transfers increased authority from central office administrators to schools themselves. There committees of principals, staff and parents make decisions about funding and academic programs.

Prince William is the first local school district to extend school-based management throughout all its schools. The policy, which is growing in popularity across the nation, has been a crusade of School Superintendent Edward L. Kelly since he came to the county three years ago.

"We have challenges and opportunities," Kelly said in a recent interview. "Teachers and principals will have an opportunity to really make a difference to children. The challenge is to make it work."

Also on the agenda this academic year will be:A full-scale curriculum audit of the county school system, to be performed by an Arlington-based consultant. The audit, budgeted for $41,000, will determine if the schools teach what they purport to teach and how well they teach it.

The process is expected to get under way very soon and auditors will present a report to the county School Board in about three months. The extension of the seven-period day from three high schools to six. Putting the three east county high schools on the seven-period day will enable all students to take advantage of more courses and electives, Kelly said. Three new elementary schools, which will open "on time and under budget," according to school officials. The new buildings are Antietam Elementary, 12000 Antietam Rd. in Lake Ridge; River Oaks Elementary, 16950 McGuffey's Trail, just north of Dumfries; and Mullen Elementary, 8000 Rodes Dr., west of Manassas. The School Board redrew elementary school boundaries to accommodate the new schools last spring. A lecture series to be run by the Prince William Education Foundation in conjunction with the schools. In the after-school and evening lectures at Woodbridge High, speakers will explore topics ranging from the environment to Eastern Europe to help "provide more comprehensive educational experience for students," Kelly said. With school-based management has come a reorganization of the school administration. Last spring the School Board added three associate superintendents, each of whom will be responsible for about 20 schools.

The reorganization is better, Kelly has said, because it puts only one level of management between the superintendent and the principals instead of two or more under the previous organization.

County school personnel have been preparing for school-based management since early 1988, when school officials visited Edmonton, Alberta, to observe how schools there used the technique.

During the past two years, five schools in Prince William have experimented with school-based management. Principals have attended numerous workshops on budgeting and decision-making, and for the past year advisory councils of parents, staff and principals have been developing programs their schools will implement this year. The advisory groups will now reconvene to begin working on programs for the 1991-92 academic year.

The plans for this year are "rather cautious," Kelly said. But he predicted that schools will become increasingly inventive.

One of the biggest hurdles of school-based management for many principals has been budgeting. Having control over an entire school's personnel budget plus funds for equipment and materials presents headaches as well as advantages.

"We spend a bit more time on the budget," said Stonewall Jackson High School Principal Michael Campbell, who presides over a $5.4 million budget and 1,650 students. "And there are more items on the agenda."

But Campbell said he's enjoyed the challenge of finding new ways to run the school.

"We've marshaled the troops a little differently," he said.

This year Stonewall will have a Learning Lab on the school's third floor where two extra part-time teachers will help students with math, reading and study skills. They will be augmented by regular teachers, who are being relieved of parking lot and hall patrol duty to help in the lab as "a better use of their time and expertise."

Kelly said he hopes Prince William County will develop a "system where no child fails."

That should be the county's goal, he said. "It doen't mean necessarily that there are no F's given," he said. "It means they learn to the degree they're capable, and they're taught skills they can build on."