Gingrich has correctly noted one of the biggest problems facing the States today: the fact that a large portion of our educational system is failing the kids it's supposed to serve. It's sort of hard to argue with that when many schools don't have enough cash to even buy their students books and supplies; the shortcomings of the system seem to be something that politicians all over the spectrum can agree on. But when it comes to strategies for solving the problem, we see a much wider variety of opinion.
Most conservatives will argue that doing away with unions will improve America's schools. Some will go so far as to state that all schools ought to be privatized so that competition drives up quality. But Newt's got a new one for us. He's declared that child labor laws are what's keeping this country's schools behind.
The solution, then, would be to do away with--or at least greatly reduce--the laws that keep children and young teens from being employed. Instead of having unionized janitors work to clean schools after hours, students should do so. Putting the kids to work will help instill pride in schools, allow poor students to make money, and improve morale across the board.
Maybe there's a theoretical world where this strategy could work. After all, there are private boarding schools where student labor is required or encouraged to a degree. But Gingrich speaks from a few misguided assumptions here. He seems to think that the failure of America's schools stems from the failure of their students--that the schools are working fine and it's those darn poor kids who just aren't proud enough of them to do well. Any teacher in a poor neighborhood can tell you that's not the case. The poorest schools are (often physically) falling apart, and putting kids to work cleaning them up isn't going to change that on its own.
Gingrich speaks from a vantage point of incredible privilege, imagining a world where all poor people are poor because they're too lazy not to be and where everyone with money has earned 100% of it. It's a nice thought, the objectivist ideal, but until we actually make sure that our schools serve every socioeconomic bracket equally, we can't assume that it's the kids who are failing themselves. Build good schools first, and then maybe you'll be in a position to ask students to clean them.