But the debate mostly concerns the enormous mix of federal aid programs for students, which will disburse about $175 billion this year in the form of grants and loans.

Q. What’s Obama’s record on student aid?

A. Obama can rightly claim he’s transformed the federal financial aid system. Partly that means more money — Washington is on track to disburse almost $50 billion more this year than in 2008-2009. Spending on Pell Grants for low-income students has nearly doubled to about $35 billion, supporting about 10 million students, up from 6 million when he took office, and he successfully pushed Congress to postpone a scheduled doubling of the interest rate on subsidized Stafford loans.

But he’s also made structural changes. Obama stopped subsidizing banks to make student loans, and now almost all student loans come directly from the government. Much of the estimated $60 billion in savings over 10 years is channeled back into other student aid programs. A new income-based repayment program caps loan repayments for 1.1 million recent borrowers at 15 percent of discretionary income and forgives their debts after 25 years. The program will soon become a 10 percent cap and forgiveness after 20 years.

Romney says the increased aid from Washington is driving up prices, arguing in a campaign position paper the president “returns over and over again to the old liberal playbook that has driven up tuition rates for decades.”

Q. What did Romney do about college costs as governor of Massachusetts?

A. Romney has touted the John and Abigail Adams scholarship that started when he was governor, offering top Massachusetts public high school students free tuition at state universities. A recent Harvard study argues the program steered students to colleges where they were less likely to graduate, and may have confused recipients by promising “free tuition” but not covering mandatory fees, which are much higher than tuition at Massachusetts colleges. The report found the award is much less than similar state scholarships in places like Georgia and California.

Q. What would Romney do as president?

A. He’s pledged to reverse Obama’s “nationalization” of the federal student loan market and return private lenders to the process. He wants to consolidate what he calls “duplicative” student aid programs but hasn’t specified which ones.

Romney education adviser Phil Handy, in a recent debate with an Obama counterpart, called the income-based repayment program a “creeping entitlement” but the campaign has not said publicly whether or how he would reform it. (A recent New America Foundation calls for reforms to the program so its benefits will be less weighted to higher earners).

Q. What about tax credits?

A. Obama wants to extend the American Opportunity Tax Credit, which provides about 10 million families a tax refund of up to $2,500 for tuition, fees and course materials. Romney’s tax plan would allow that credit to expire and revert to the old HOPE tax credit, which is less generous to students and less expensive for the government. Unlike HOPE, the AOTC is partly refundable, meaning low-income students can benefit even if they don’t owe taxes.

Some education finance experts have criticized the AOTC, arguing other programs channel benefits more effectively to the neediest students. Obama campaign policy director James Kvaal counters it’s important to help middle-class families afford college as well as the low-income students who use Pell Grants.

Q. What is the problem with Pell Grant funding and what will the candidates do about it?

A. Pell is the main college aid program for low-income students. The awards are given on a sliding scale, and only about one-third of recipients receive the maximum (currently $5,550). Typically those who get the maximum are the very poorest students (more than 90 percent come from families earning under $30,000).

Congress has essentially laid out a schedule of Pell awards where the maximum rises to $6,030 in coming years, but hasn’t provided full funding for that commitment. There’s a shortfall averaging roughly $8 billion annually starting in 2014. Obama’s latest budget proposal calls for filling the immediate shortfall, partly through redirected savings, and working with Congress on a long-term fix. But he doesn’t propose tightening eligibility requirements.

Romney said during the second debate he wants to keep Pell “growing.” But a Romney campaign paper calls for “refocusing” Pell on the neediest to preserve its financial viability. Handy, the Romney education adviser, said Pell Grants need to be “radically fixed.”

In short, Romney’s campaign has made it increasingly clear he’s talking about keeping the maximum Pell on track for its scheduled increase, but limiting eligibility or lowering awards for the those who get less than the maximum — currently about 6.5 million students who typically come from families earning $30,000-$50,000 annually. If Romney ever signed into law the House budget of his running mate, Rep. Paul Ryan of Wisconsin, more than 1 million students could be on track to lose their Pell Grant eligibility over the next decade, according to an analysis by The Education Trust, a non-partisan Washington, D.C.-based policy and advocacy group.

Q. How do the candidates differ on student loans?

A. When Obama took office, two federal loan systems existed side-by-side — one offering direct loans from the government, the other subsidizing a kind of federal loan provided by private lenders. Obama ended the second system and moved entirely to direct lending.

Romney’s campaign says the decision “moved a trillion-dollar obligation” to the federal balance sheet and is proving more expensive than expected, citing a Barclays research report that estimates costs of direct lending have been underestimated by $225 billion between now and 2020. Even accounting for the $60 billion in lender subsidies Obama has eliminated, Romney contends returning to a system that incorporates private lenders would offer taxpayers more efficiency and students better service.

Obama argues the $60 billion previously allocated to paying private lenders was wasted. Kvaal says it’s actually Obama’s direct-lending approach that makes better use of market forces — instead of getting subsidy checks, the student loan companies now compete for government contracts to service the direct loans, replacing bureaucrats. Jason DeLisle, a former member of Senate Budget Committee’s Republican staff who now directs the Federal Education Budget Project at the New America Foundation, agrees, calling the changes Obama made “something Bain Capital would come up with” rather than the government takeover Romney describes.

Q. Is Romney right that Obama’s direct lending changes are costing the government and that taxpayers are “on the hook?”

A. The short answers are “not really” and “possibly” — but those are complicated questions.

Romney’s campaign points to figures that the Department of Education borrowed billions more from the Treasury than expected to meet student loan demand, and that those loans are performing worse than expected.

But experts such as Mark Kantrowitz, creator of the website finaid.org and a leading student aid expert, and others say looking at a given year’s cash flow the way Romney’s campaign does isn’t how you tell whether any lender — whether a bank or the government — will eventually make or lose money on the loans it’s making.

In fact, it’s impossible to know whether taxpayers will make or lose money over time on the student loans Washington’s now disbursing; that will depend on unpredictable variables like future interest rates, and how many borrowers default or choose the income-based repayment option.

Still, there are accounting methods to estimate the present value of the payments the government will collect on those loans over the coming years. The method the Congressional Budget Office is required by law to use values the $113 billion in direct loans Washington will disburse to students this year at $150 billion — in other words, an asset worth $37 billion to taxpayers, not a liability. A different valuation method favored by some in Congress and many economists shows direct lending as less profitable, but still in the black and far more profitable than subsidized lending.

True, like any lender, the federal government could be “on the hook” for big losses if current projections are off and defaults jump. But that would also be true in the old system of government-guaranteed loans. Under current projections, direct lending will make money for taxpayers (though the point of the federal student loan program wasn’t originally to make money; it was to help students attend college).

DeLisle, the former Republican staffer, is more blunt. He calls the Romney campaign’s argument about costs in direct lending “a totally phony concept meant to bamboozle people into thinking we’re borrowing from China to make these loans and it’s going to take the federal government down.”

Q. Any other differences?

A. The Obama administration has aggressively pushed to regulate for-profit colleges, which receive billions in taxpayer-funded student aid dollars but have higher default rates and lower completion rates than other types of schools. Romney says those regulations are misguided and will stamp out innovation and student choice.

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Follow Justin Pope at http://www.twitter.com/JustinPopeAP