WASHINGTON - On the campaign trail during the past week, US President Barack Obama talked a lot about education.

Making a bid for young voters and their parents, Obama accused Republican rival Mitt Romney of planning to slash aid to college students. Romney hit back by noting that Obama, a Democrat, has not been able to rein in the soaring cost of tuition.

But the differences between the two candidates on education policy extend far deeper than a war of sound bites over college costs. In an echo of their broader philosophical divide, Romney and Obama split sharply over what role the private sector should play in the US education system.

"There are very, very meaningful differences in philosophy," said Phillip Handy, a businessman who was chairman of the Florida Board of Education for six years and now advises Romney on the subject.

Romney seeks to encourage - with federal subsidies, when necessary - robust participation from the private sector in teaching American kids and training workers. He would use public dollars to enroll more children in private schools; keep federal aid flowing to private, for-profit colleges; and pay private banks to take over part of the federal student loan program.

Obama, by contrast, has sought to expand government's role in education.

He has directed billions of dollars in federal funds to states that adopted his vision of a revamped kindergarten through 12th grade curriculum, with more emphasis on standardized testing. He has secured billions more in public funding to help states avert teacher layoffs.

And in higher education, Obama has expanded federal student aid and cracked down on for-profit colleges that he says leave students with too much debt and too few job prospects.

Here is a look at a few key disputes over education policy:

Charters and vouchers

In K-12 education, Obama has gone much further than his allies in the teachers unions would like in embracing charter schools, which are publicly funded but privately managed, in some cases by for-profit companies.

Obama has pushed states to allow more charter schools to open and has directed federal funds to some of the most successful, including a five-year, $50 million grant to the KIPP network of charter schools.

But Romney, the presumptive Republican nominee, would go further.

He has called for redirecting up to $25 billion in federal aid to help schools serve disabled and impoverished children.

Under his plan, up to 12 million needy students nationwide could use the funds to pay tuition at private or religious schools or to enroll in charter schools that might not otherwise have the resources to serve them. Romney would press states to lift all caps restricting the number of charter and online schools. And he would expand federal funding for charter management companies, with the aim of helping the best grow rapidly.