The Obama campaign came out yesterday with a new ad attacking Mitt Romney's positions on education:

There are two basic claims here.

"Mitt Romney says class sizes don't matter." This is a fair representation of Romney's comments. Romney stated that as governor of Massachusetts, he had conducted a study comparing the class sizes of schools in the state with their performance on standardized tests, and found no relationship. He also cited a report (pdf) from McKinsey that compared the performance of education systems in different countries that also found no relationship between performance and class size.

This is a point of contention among education scholars. Much research has focused on Project STAR, a fully randomized experiment in which Tennessee kindergarteners were randomly placed in classrooms of different sizes with teachers of different quality. Raj Chetty of Harvard analyzed (pdf) that study and found that students in smaller classes did better on tests, were likelier to graduate from college, own homes, and save for retirement, among other metrics, though their incomes at age 27 were not noticeably higher. Eric Hanushek of Stanford, who is known for arguing that teacher quality is more important in determining student outcomes than student-teacher ratios or other factors, has disputed this interpretation of the STAR study.

"He supports Paul Ryan's budget, which would cut education by 20 percent." Romney did indeed endorse the Ryan budget, and the budget seriously cuts federal education spending, including aid to low-income districts, special education funding and Pell Grants. The Center for Budget and Policy Priorities notes (pdf) that the Ryan budget cuts non-defense discretionary spending across the board by about 22 percent, and education would comprise about a quarter of those cuts.

However, it's worth noting that Romney has his own education plan that differs in important respects from Ryan's budgets. Rather than cutting Title I spending on low-income students and spending on IDEA, a program that funds special education programs, the Romney plan would make that spending portable, letting students take it with them to private schools and charter schools if they choose to exit their existing publics schools. The research on whether these kind of voucher programs actually work is mixed. Caroline Hoxby of Stanford has found (pdf) that students in districts with greater school choice perform better, a finding which was seriously critiqued (pdf) by Jesse Rothstein of UC Berkeley, prompting a major academic row. By contrast, a Department of Education found that the District of Columbia's voucher program did not improve student learning outcomes.

In any case, the Romney campaign has yet to clarify whether the Title I and IDEA money being converted to vouchers would be at current funding levels, or whether those specified by the Ryan budget. In lieu of such a clarification, noting Romney's endorsement of the Ryan budget, and that budget's cuts to the programs, seems fair.