In Rick Hess's eyes, President Barack Obama has a big choice to make.

"The president campaigned with a different face of education reform than what he championed during the first term," Hess, an influential education scholar at the American Enterprise Institute, said in an interview. "I'm curious as to whether what he said on the campaign trail is more reflective of what a second term will be or whether the first term will be reflected in the second term."

In other words, Barack Obama was reelected Tuesday night with huge support from teachers' union members that have so publicly clashed with his policies. He got that vote, in part, by stressing the softer part of his education agenda on the campaign trail. In speeches and debates, he sparred with Mitt Romney over the federal government's role in hiring teachers -- since Obama spent billions on teacher hiring as part of the stimulus bill -- and the importance of class sizes.

But Obama's first term also saw the creation of the Race to the Top program, which angered unions by requiring participating states to evaluate teachers based on student test scores. His rhetoric toward teachers was tough during his first term, but softened as reelection approached. So which Obama will we see?

It's a question teachers are asking, with some hoping to see a course correction.

"With the election behind us, it is time for the Obama administration to step back from its education policy and access whether its foundation is sound and supported by evidence," Stevens Institute of Technology professor Arthur Camins wrote on aWashington Post blog. "It is a moment to summon the courage to change course." Camins continued to argue against a focus on standardized testing and firing underperforming teachers.

"My worst fear is it'll continue to be the same," said Diane Ravitch, a New York University historian and one of Obama's most vitriolic critics on education. "His education policy is indistinguishable from Mitt Romney's, aside from vouchers. It's based on test test test test."

While Randi Weingarten, president of the American Federation of Teachers, is one of the union presidents who helped reelect Obama, she has similar reservations. "We're going to be out there pushing to end the fixation on testing and displace that fixation with a fixation on teaching, to fight to fix and not close public schools, but to make public schools the centers of community," she said.

Maybe Obama has been having it both ways all along, said Alexander Russo, a blogger and former congressional education aide. "They've figured out how to give resources to education and on a separate track, push for reform, and doing those things separately but simultaneously wins them the reluctant allegiance of teachers and career educators who want schools to be better funded and reformers who want schools to have better outcomes," he said.

The policies, Ravitch says, have been confusing. "The president sends out mixed messages," she said. "He says he doesn't want teachers teaching to the test, and that he likes that his daughter's school doesn't focus to the test, but I wish someone can get across the idea to him that he should want that for other children."

Though some teachers took to Twitter to call for the ouster of Obama's education secretary Arne Duncan, that probably won't happen. Obama and Duncan arebasketball buddies -- with Duncan, a former pro Australian player, even playing against Obama on Election Day -- and Obama has expressed pride in Duncan's accomplishments. And Duncan once told HuffPost that he would stay for eight years if asked. On Thursday, Politico speculated that if Duncan does leave, he would be replaced by Michelle Rhee, a former Washington, D.C. schools chancellor. Choosing Rhee, a lightening rod in education policy, would signify a return to the harder-line Obama rhetoric on education -- but administration insiders say that is highly unlikely. Duncan was not available for comment Thursday.

Dennis Van Roekel, president of the National Education Association, said he expects the second term to focus on early and higher education -- topics that are less polarizing within the administration's own base. That focus also resonated with Education Week reporter Alyson Klein. Speaking on a Thursday American Enterprise Institute panel, Klein said she expects the administration to focus on higher education because it gave states waivers from the expired No Child Left Behind law -- and would prefer to see those waivers used, rather than encourage a congressional overhaul of the law.

Obama's education-related campaign promises were modest -- he pledged to create100,000 new math and science teachers, 2 million more community college slots, and to cut tuition in half over 10 years. Hess called most of these promises "vacuous campaign rhetoric." It will be hard for Obama to fund all these promises, Hess said, as the country dangles over a fiscal cliff. Hess said, "folks hoping for new outlays would be well advised to temper their expectations."