WASHINGTON — Should money for federal student grants for college be cut back?

Should parents be able to spend local tax dollars to pay for private schooling if they don’t like their public schools?

Mitt Romney and President Barack Obama agree that a good education for all Americans is essential for democracy, individual success and the national economy.

The areas where they disagree – such as on school choice and federal spending – make education another of the stark public policy choices in this presidential campaign. Their divide was evident Tuesday at NBC’s Education Nation Summit in New York.

In an interview for the summit, the president said that the big difference between them on education reform was paying for it.

Romney and his supporters “talk a good game about reform,” Obama said, “but when you actually look at their budgets, they’re talking about slashing our investment in education by 20 to 25 percent.”

Romney, speaking at the summit, said he would not support more federal spending for education but would leave that to the states.

“I think we all know what it takes to improve schools – invest in great teachers,” he said.

Romney has said during the campaign that a “world-class education” for American students was paramount to boosting the economy. His top reform would be a dramatic expansion of school choice.

Obama has called education a “gateway” to the middle class, saying the United States must be able to “out-educate and out-compete” every other nation.

He wants Congress to approve more spending for his key reform, Race to the Top, a competitive grant program that rewards schools that improve.

The nation’s needs for education improvement are plain.

Federal data show that a quarter of all high school students fail to graduate in four years, low-income students lag academically, and many students are struggling in reading and math.

Pell grants

Romney wants to restrict Pell grants, the main source of federal financial aid for college, to just the poorest students. “Flooding colleges with federal dollars only serves to drive tuition higher,” a Romney campaign education policy paper says.

But campaign spokeswoman Amanda Henneberg declined to provide details about where Romney would set the limits.

Under Obama, Pell grants have more than doubled, from $16 billion in 2008 to $36 billion last year. The size of the grants increased, as did the number of recipients, from about 6 million to 9 million.

In addition, Congress passed an Obama-backed effort to remove commercial banks from the federal student loan business. The savings, in the form of subsidies that had been paid to the banks, paid for the increase in Pell grants, Obama has said.

Romney, however, has said he’d let commercial banks back into the student lending market.

“America is fast becoming a society where education is unaffordable, a government loan is an entitlement, default is the norm, and loan forgiveness is the expectation,” a campaign policy paper stated.