NEW YORK -- When it comes to the nuts and bolts of education policy, a topic that ranks high among the concerns of female and Latino voters, Mitt Romney and Barack Obama are remarkably similar: both think standardized tests are important, that teachers need to be evaluated rigorously, and that charter schools are an important component of America's educational landscape.

So at a Monday night debate at Columbia University's Teachers College, the education advisers of both presidential candidates tried to spotlight differences. What it boils down to, both said, is the federal government's role in education.

"The view of budget policy that the governor has and the … belief that the federal government should be consolidated or shrunk a lot, that these are various issues that are not for federal involvement, … represents a significant contrast between the two," said Jon Schnur, who has been advising President Barack Obama on education since 2008.

An example of these differences, said Phil Handy, co-chair of Mitt Romney's advisory panel on higher education, is that Romney thinks the teacher evaluations should not be mandated by the federal government -- echoing the National Education Association position during the recent unsuccessful reauthorization of No Child Left Behind. Handy said a Romney administration would use the federal government for two purposes in education: transparency on school performance and promoting school choice. (Romney has previously said he would use the U.S. Education Department to fight unions). And while Handy stressed that early childhood education is important, he said it should be the province of states. He chided Head Start, the federal pre-school program, saying it has "been allowed to go on for decades ... much more as a social experience, not preparing children for school."

Schnur argued that shifting these issues to the states was tantamount to the federal government giving up on its responsibility to serve poor and minority students. But Handy said the Obama administration's policies -- particularly the waivers the White House is offering states that want to get out of the No Child Left Behind law -- are simply too prescriptive. "If anyone has seen a waiver, it's not about flexibility," Handy said, adding that they have led states to set different performance standards for minority groups -- "a very unfortunate result."

Handy said the effects of Romney's budget on shrinking education have been overstated. Vice presidential nominee Rep. Paul Ryan's (R-Wis.) budget calls for significant cuts to domestic spending, and the Obama campaign has applied those overall cuts to education programs to make its case. But at the first presidential debate, Romney promised not to cut education. "You can easily hold public education harmless without impacting the creation of more deficits," Handy said.

Now that Romney has pledged to leave education spending alone -- despite his recent remarks that expanding the teaching force does little economic good -- the Obama campaign has been forced to shift its rhetoric. So instead of painting Romney's education vision as one that takes a hatchet to education, Schnur compared Obama's investments in education with Romney's lack of willingness to spend more on education. Schnur also said cuts to areas outside of schools could have profound effects on education.

"The choice that the country has between Barack Obama and Mitt Romney includes that Barack Obama at the end of the day, year after year is making a major focus on supporting kids ... and doesn't regard that as just a set of these programs," Schnur said. "You see a legitimate difference in philosophy about whether you prioritize education as president."

Handy argued that Massachusetts success in education and Romney's involvement in schools as governor shows Romney "believes in education."

Schnur agreed -- somewhat. "I might vote for Mitt Romney for governor, but i don't think that's the basis for being president on education," Schnur said. He said many of the education policies Romney implemented in Massachusetts would be relegated to the states in a Romney presidency.

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