President Obama said last month that America can educate its way to prosperity if Congress sends money to states to prevent public school layoffs and “rehire even more teachers.” Mitt Romney was having none of it, invoking “the message of Wisconsin” and arguing that the solution to our economic woes is to cut the size of government and shift resources to the private sector. Mr. Romney later stated that he wasn’t calling for a reduction in the teacher force—but perhaps there would be some wisdom in doing just that.

Since 1970, the public school workforce has roughly doubled—to 6.4 million from 3.3 million—and two-thirds of those new hires are teachers or teachers’ aides. Over the same period, enrollment rose by a tepid 8.5%. Employment has thus grown 11 times faster than enrollment. If we returned to the student-to-staff ratio of 1970, American taxpayers would save about $210 billion annually in personnel costs.

Or would they? Stanford economist Eric Hanushek has shown that better-educated students contribute substantially to economic growth. If U.S. students could catch up to the mathematics performance of their Canadian counterparts, he has found, it would add roughly $70 trillion to the U.S. economy over the next 80 years. So if the additional three million public-school employees we’ve hired have helped students learn, the nation may be better off economically.

To find out if that’s true, we can look at the “long-term trends” of 17-year-olds on the federal National Assessment of Educational Progress. These tests, first administered four decades ago, show stagnation in reading and math and a decline in science. Scores for black and Hispanic students have improved somewhat, but the scores of white students (still the majority) are flat overall, and large demographic gaps persist. Graduation rates have also stagnated or fallen. So a doubling in staff size and more than a doubling in cost have done little to improve academic outcomes.

Nor can the explosive growth in public-school hiring be attributed to federal spending on special education. According to the latest Census Bureau data, special ed teachers make up barely 5% of the K‑12 work force.

The implication of these facts is clear: America’s public schools have warehoused three million people in jobs that do little to improve student achievement—people who would be working productively in the private sector if that extra $210 billion were not taxed out of the economy each year.

We have already tried President Obama’s education solution over a time period and on a scale that he could not hope to replicate today. And it has proven an expensive and tragic failure.

To avoid Greece’s fate we must create new, productive private-sector jobs to replace our unproductive government ones. Even as a tiny, mostly nonprofit niche, American private education is substantially more efficient than its public sector, producing higher graduation rates and similar or better student achievement at roughly a third lower cost than public schools (even after controlling for differences in student and family characteristics).

By making it easier for families to access independent schools, we can do what the president’s policies cannot: drive prosperity through educational improvement. More than 20 private-school choice programs already exist around the nation. Last month, New Hampshire legislators voted to override their governor’s veto and enact tax credits for businesses that donate to K‑12 scholarship organizations. Mr. Romney has supported such state programs. President Obama opposes them.

While America may have too many teachers, the greater problem is that our state schools have squandered their talents on a mass scale. The good news is that a solution is taking root in many states.