The character of Fairfax County’s next school board will depend in large part on the outcome of this fall’s race for three at-large seats, a wide-open contest that could help sweep a change-minded, Republican-backed majority into office.

Members endorsed by the Democratic Party currently dominate the board, with nine of the 12 seats, but half of the incumbents are retiring and others are in tough races against challengers, guaranteeing substantial turnover.

Among the key issues dividing candidates is how to pay for popular initiatives — such as reducing class sizes and boosting teacher pay — in an era of tight budgets.

Republican-backed candidates have proposed finding that money in the $2.2 billion budget through cost-cutting, particularly in the system’s central office.

“I would like to remind everyone that our funds come from the taxpayers,” said Lin-Dai Kendall, a self-described tea party member who said she was motivated to run by the board’s decision to close Clifton Elementary. “We need to make do with what we have.”

Democratic-endorsed candidates, meanwhile, have questioned whether significant savings can be found in a budget that has remained flat since 2008, even as enrollment has grown about 7 percent.

“Everyone wants to hear about trimming costs, and I’m in favor of that, too,” said Ryan McElveen, who graduated from Marshall High School in 2004 and now works in Boeing’s international policy office. “But we have an increasing population, and we need more money to pay for those needs.”

Central office costs have indeed grown over the past 10 years, prodded in part — according to the schools’ budget director — by rising salaries and health-care costs. But since 2008, the school system has cut 147 central-office positions, according to budget documents — an 8 percent reduction.

Meanwhile, since 2008, the proportion of Fairfax school employees who work in schools — such as teachers, principals and guidance counselors — has risen slightly to about 93 percent, akin to the proportion in Montgomery County.

Republican-endorsed candidate Lolita Mancheno-Smoak is a business consultant who has made a career out of finding cost efficiencies for businesses and federal government agencies.

She said she would support asking for more local and state funds only after squeezing the current budget. She said a proper audit would find savings of about 15 percent — or about $330 million.

That is approximately the cost of all central-office operations, except the county’s bus fleet, according to an analysis by budget watchdog group FairfaxCAPS.

“We have to go systemically and surgically through things,” said Mancheno-Smoak. “It gets a little painful because folks don’t want to hear that some of their programs need to be shut down, but if that’s what it takes, that’s what we need to do.”

The down-ticket race has drawn more interest than usual this year as parents and teachers have expressed increasing frustration with the school system’s handling of high-profile, hot-button issues such as boundary changes, budget cuts, and overhauls of grading and discipline policies.

But besides cutting further into the central-office staff, there is much in common between the two slates of candidates.

In the at-large board race, six of the seven candidates have supported the current staffing formula, which sends more teachers to schools with higher proportions of poor children and non-native English speakers. Kendall said she would like to reconsider many school policies, including the staffing formula.

All the candidates have proposed establishing an independent team of auditors and program evaluators who would help find potential savings and would report directly to the school board, rather than to the superintendent and his staff.

“We need to be sure that those funds are going directly to the classroom, where they can most benefit parents and teachers,” said Sheree Brown-Kaplan, a Republican-backed candidate who has been a special-education activist in the school system for several years.

Candidates from both parties also have said that the next board should help schools push beyond standardized-test preparation to provide students with the skills they need to compete in the 21st century.

“Every school board has got to deal with the issues that are current,” said Democratic-backed Ted Velkoff, a software engineer and former PTA officer in the Chantilly area of Fairfax. “I think we’re going to do a disservice if we don’t always have this long-term vision in mind.”

Dissatisfaction with current school leadership has been bipartisan, and the board itself is officially nonpartisan. But political parties have historically played a role in board races, and political observers say no candidate has won a school board seat without a party endorsement.

The at-large candidates have split down party lines, however, in their support for current school leadership, with the sharpest criticism coming from the three Republican-backed candidates and from Steve Stuban, who is running without partisan support.

“They might smile at you and look at you as if they’re listening, but the school board has demonstrated that they don’t care about what you believe or think should be changed,” said Stuban, who is known for his efforts to reform the county’s discipline policy. Stuban’s son, Nick, committed suicide in January in the aftermath of what Stuban says were overly harsh disciplinary proceedings.

Stuban and Republican-endorsed candidates have promised to beef up oversight of Superintendent Jack D. Dale, to listen to parents and teachers, and to find alternatives to seeking additional tax dollars from the Board of Supervisors.

Democratic-endorsed candidates Velkoff, McElveen and Ilryong Moon — the sole incumbent seeking reelection — have defended the school system against attacks, citing its students’ high achievement and arguing that its next set of leaders should not veer too abruptly from the current path.

“I’ve been saying throughout the course of this campaign that we’re not a perfect system,” said Moon, a lawyer who has served on the board for 12 years. “There are areas we need to improve on, but we don’t need to make a drastic change.”