In a brochure for his Montgomery County Council campaign, Ryan Spiegel says he will fight to increase school construction, close the achievement gap, and attract and retain the best teachers.

Another council candidate, Del. Tom Hucker (D-Montgomery), wants to redraw attendance boundaries to improve school choice for low-income families.

Council member Marc Elrich (D-At Large), running for a third term, calls the achievement gap “the defining issue” of the next four years.

Night after night, in libraries, town halls and community centers, candidates for council and county executive talk to voters about public schools, the issue that polls consistently identify as voters’ greatest concern.

What candidates seldom remind audiences is that Montgomery has an eight-member elected Board of Education and a schools superintendent, hired and overseen by the school board. They rarely acknowledge that with state funding mandates, the council has limited leverage over annual education spending — a proposed $2.3 billion this year, nearly half of the county’s operating budget. Land use, transportation, and delivery of police, fire and other basic services —not schools — are the core of the council’s responsibilities.

Given that questions facing K-12 education are complex, and inextricably linked to poverty and other broad social conditions, what can the council do?

“It’s a fair question,” said Spiegel, a Democratic Gaithersburg City Council member running for the District 3 county council seat (Rockville-Gaithersburg) being vacated by Phil Andrews, who is running for county executive.

The real power of a council seat, Spiegel said, is as a bully pulpit “to build coalitions and advocate to colleagues in other bodies” such as the school board and the state legislature. His opponents in the District 3 race are also focused on school issues: Gaithersburg Mayor Sidney Katz and Derwood business consultant Guled Kassim call for expanded early childhood education, after-school programs and career and technical training, while Rockville City Council member Tom Moore cites the need to begin with “broken families” before addressing broken schools.

“Some of the mail pieces I get from candidates, I think, ‘Huh, are they running for school board?’ ” said Board of Education Vice President Patricia O’Neill, the panel’s longest-serving member. “I think, if you’re so interested in that, you’re in the wrong race.”

County school officials say they’ve been working for years on the issues highlighted by candidates — issues that have challenged educators across the country. Superintendent Joshua Starr’s proposed 2015 budget calls for additional funds to reduce class sizes, add counselors and psychologists, and encourage top teachers to work in needy schools.

School officials and the county council have clashed recently over a study by the council’s Office of Legislative Oversight, which concluded that Montgomery has failed to close the gap in academic achievement that separates poor and wealthy student populations.

Students in schools where poverty is high are 9 percent less likely to graduate on time than their economically advantaged peers at other schools, and 45 percent less likely to earn at least one passing score on an Advanced Placement exam, according to council researchers.

Some disparities have grown over time, stirring frustration and tension among politicians — feeling the heat from constituents on matters over which they have little direct control — and professional educators, convinced that they know best.

Hucker, a state delegate running for the District 5 county council seat that represents Silver Spring and eastern Montgomery, calls the council report “a devastating indictment of public schools.” It challenges the stellar reputation of a school district that County Executive Isiah Leggett (D) calls “the crown jewel” of the county.

Doug Duncan, Leggett’s other challenger in the June 24 Democratic primary, said the report “should have been a wake-up call” to Starr and the school board. “I’m not sure they’re seeing it that way. What we’re doing isn’t working,” he said.

Starr said in an interview that he appreciates the broad discussion of the achievement gap. But his resentment was obvious at an April school board meeting, when he said the council report, a follow-up to a study released last year, allowed politicians and pundits to simplify issues that are dauntingly complex.

“For the second year in a row, we have a report that reiterates what we know and talk about all the time: We have an achievement gap,” Starr said. “For the second year in a row, we find ourselves in a situation where, right as budget is being decided, it is convenient for people to write headlines and discuss the fact that we have an achievement gap.”

Council member George Leventhal (D-At Large) said Starr and other school officials can be maddeningly opaque when council members attempt to better understand what they are trying to do. “They slide and elide,” he said.

Starr rejects the idea that he’s been evasive. But he concedes that he has struggled to crystallize a vision that parents, elected officials and other stakeholders can easily rally around. Part of the difficulty, he said, is the state of flux in the K-12 world. As the Obama administration shifts away from absolute annual measures of progress measured under No Child Left Behind to a new curriculum and testing under the Common Core standards, improvement will be more difficult to gauge, at least in the short term.

“What we are striving for is more elusive in many ways,” he said. “It’s not straightforward and won’t be for a couple of years.”

But Starr also said he would resist what he called “the panacea syndrome,” in which officials seize on one reform as the game-changer.

Council members said the school system would engender more goodwill with the council if it showed a willingness to clearly assess the value of programs it has already launched.

In 2008, officials started the Kennedy Cluster Project, a joint effort by the county and the school system to lift the performance of African American students by improving access to social services and other supports. It was targeted to Silver Spring’s John F. Kennedy High School and its middle and elementary feeder schools.

While there is encouraging anecdotal evidence that the approach is working, officials acknowledge that the program has not been rigorously evaluated. When the school system and other county agencies recently proposed that the effort be expanded to the Watkins Mill High School cluster, some council members pushed back.

“We’ve got to have some discipline,” said Leventhal. “We have to hear from the school system what is working and not working.” He said the school board is “part and parcel of the institutional culture” in a system that asks for increasing amounts of funding each year but resists feedback and oversight.

Starr said the county has never provided the money for an evaluation, and argued that the expansion is justified.

“I am satisfied that the model itself is a good model,” he said.

The expansion eventually was approved, by a divided vote, in a joint meeting of the council’s education and health and human services committees.

O’Neill, the school board’s vice president, said many council complaints grow out of the complexity of the issues the school system must address.

“It’s easier to criticize than to really take the time to understand what’s going on,” she said. “We live with it day in and day out.”