“Voucher” is a fighting word in education, so it may be understandable that when Mitt Romney speaks about improving the nation’s schools, he never uses that term.

Nonetheless, as president, Mr. Romney would seek to overhaul the federal government’s largest programs for kindergarten through 12th grade into a voucherlike system. Students would be free to use $25 billion in federal money to attend any school they choose — public, charter, online or private — a system, he said, that would introduce marketplace dynamics into education to drive academic gains.

His plans, presented in a recent speech at the U.S. Chamber of Commerce, represent a broad overhaul of current policy, one that reverses a quarter-century trend, under Republican and Democratic presidents, of concentrating responsibility for school quality at the federal level.

“I will expand parental choice in an unprecedented way,” Mr. Romney said, adding that families’ freedom to vote with their feet “will hold schools responsible for results.”