PHOENIX — Campaign signs are clustered on street corners and highway ramps across this low-slung, sun-baked city, proclaiming “#YesforEd” and “Protect Public Education.” In TV commercials, the Republican governor promises to “put more money in the classroom, not bureaucracy.” “Our schools are falling apart,” his Democratic challenger counters.

Six months after tens of thousands of red-clad teachers swarmed the Arizona Capitol in a weeklong walkout, demanding higher pay and more funding for schools, education is a dominant issue in the state’s elections next month.

The teachers’ protest movement, which calls itself #RedforEd, has transformed the political battleground. The movement remains so popular in Arizona that candidates and causes across the ideological spectrum are competing to identify with it — including conservatives who, in years past, might have been more likely to criticize teachers or unions than associate with activist educators.

That has left some Democrats — teachers’ traditional allies — scrambling to differentiate themselves.

It is a pattern that has played out in several states where teachers have walked off the job this year, including Oklahoma, West Virginia and Kentucky. The teachers’ movement has energized Democrats in red states, with record numbers of educators running for office. But it may have had an even greater impact on Republican politics. In primaries, it has picked off Republican legislators who opposed funding for teachers and schools. And it has convinced conservative leaders that voters, particularly suburban parents, are looking for full-throated support, and open pocketbooks, for public education.

In Arizona, which has some of the lowest school funding in the nation, nowhere are these issues more prominent than in the governor’s race. Both candidates have claimed the mantle of education champion.

“I’m the one who’s been on the side of the teacher,” Gov. Doug Ducey, the Republican incumbent, said in an interview at his campaign headquarters last week.

Before his state’s teachers threatened to walk out, Mr. Ducey had offered them a 1 percent raise. But under pressure from the #RedforEd movement, he eventually proposed and signed a bill promising a 20 percent pay hike by 2020.

Teachers have already seen some of that money in their paychecks. And even before the walkout, Mr. Ducey had signed several other bills that provided new money for schools. Still, overall education funding, adjusted for inflation, remains significantly below the pre-recession levels of a decade ago. Parents and teachers say they can see the difference through aging textbooks, staff shortages and fewer electives and field trips.

The governor, the former chief executive of the ice cream franchise Cold Stone Creamery, argues that a growing economy will ensure that schools funding and teacher pay will continue to rise. He also says that if re-elected, he will seek to cut taxes — a pledge that leaves some educators skeptical they will see all the funding they have been promised.

Mr. Ducey’s challenger, David Garcia, a professor of education at Arizona State University, has a radically different vision.

Mr. Garcia strongly supported the walkout and a ballot initiative effort that grew out of it, called InvestinEd, which would have funded schools by raising income taxes on individuals and households earning more than $250,000. The State Supreme Court struck InvestinEd from the ballot in August, citing technical questions about the proposal’s wording.

Mr. Garcia says that if he is elected, he will push to close corporate tax loopholes, end tax credits for private school tuition and revisit the effort to raise taxes on the wealthy, perhaps through a new ballot initiative.

Those are fighting words in a state where libertarianism runs deep, and where a decades-long tradition of cutting taxes has maintained some of the lowest corporate and personal income taxes in the nation. (Arizona relies in part on sales taxes for funding schools.)

But Mr. Garcia is betting that concern about public education among women, younger voters and Latinos — including many who are newly registered, or do not typically turn out for midterm elections — can carry him. He says those voters are not being reached by pollsters, who have him trailing Mr. Ducey.

Mr. Garcia is an unusual candidate in Arizona. He is an Army veteran with a Ph.D. from the University of Chicago and an expert on the huge troves of data that have transformed education research over the past two decades.

He used some of that data to create the state’s first school rating and accountability systems when he worked for the state Education Department in the late 1990s and early 2000s. In that role, he sometimes butted heads with teachers’ union leaders, who at the time were skeptical of using student data to judge schools, he said.

Nevertheless, the state’s largest teachers’ union, the Arizona Education Association, has enthusiastically endorsed him this year.

Mr. Garcia sometimes sounds more like Senator Bernie Sanders of Vermont than the centrist Democrats more typical in Arizona, like Kyrsten Sinema, the Senate candidate, who has not endorsed him.

In addressing the other big issue roiling the state — immigration — Mr. Garcia has called to “replace ICE” with an immigration enforcement system “consistent with our American values.” The Ducey campaign and its surrogates quickly reframed Mr. Garcia’s position as “abolish ICE.”

Mr. Ducey believes his opponent has misjudged an electorate that remains fundamentally conservative.

“For a fourth-generation Arizonan, he doesn’t seem to know the state of Arizona very well,” the governor said.

Swing voters are paying close attention. Katy O’Connor, an art teacher wearing her #RedforEd T-shirt, went door to door in an upper-middle class neighborhood in Phoenix last week, campaigning for the Democratic ticket. She spoke with Curtis Miller, 57, who described himself as an undecided “liberal Republican.”

 Mr. Miller said he was sympathetic to teachers and willing to pay higher taxes if the money was spent efficiently on education. But he was concerned, he said, about illegal immigration, and leaning toward voting for Mr. Ducey.

“We don’t have the money to support everybody,” Mr. Miller said.

Ms. O’Connor said that even if Mr. Miller would not support Mr. Garcia, she hoped he would vote for other education priorities down the ballot. Democrats have a shot at flipping control of the State Senate, and there is a fierce contest for state schools superintendent.

Then there is Proposition 305, a ballot initiative that, if passed, would expand access to educational savings accounts, a voucherlike system that provides tax dollars for private school tuition.

The campaign to approve it has produced red posters and a slogan, #YesForEd, seemingly intended to ride the popularity of #RedforEd while standing at odds with most of its activists.

Even campaigns that have little to do with schools are trying to align with the teachers’ movement. The electricity industry opposes a ballot initiative that would require utilities to draw some of their energy from renewable sources. Their yard signs declare: “Higher Electric Bills Hurts AZ Schools.”

Despite the diversity of causes and candidates elbowing for the education platform, the differences between the Republican and Democratic visions remain stark. Mr. Ducey sees education in Arizona as a competitive marketplace. He supports sending more tax dollars to private and religious schools and increasing the number of public charter schools. “Parents are good consumers,” he said. “They know what’s best for their child.”

Mr. Garcia wrote his dissertation on Arizona charter schools, and has continued to research them. When asked about the subject, he grabbed a notebook and pen out of a reporter’s hands and drew a graph in the shape of a “U.” Most charter schools in Arizona, he said, are either excellent, like the one his older daughter attends, or low-performing. Few are average.

Arizona’s school-choice sector is already the largest in the nation, and has struggled with problems like astronomical executive pay and self-dealinglegislators involved in the industry.

Mr. Garcia said he supported school choice, but only within the public system. He opposes spending taxpayer dollars on private school tuition, which he says leeches funding from public education. When he was growing up in Mesa, outside Phoenix, his own parents, a factory worker and commercial painter, chose to send him to an elementary school outside his neighborhood that was better than the local school.

“The Legislature and the governor believe that only those who have left traditional public schools are making a choice,” Mr. Garcia said. “And that’s not true. Hundreds of thousands of parents are making a choice to be in a traditional public school. And we need to honor that choice.”

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