They’re in demand among parents who say traditional public schools have failed — but they’re not always successful. Their intense rate of growth has fueled an equally intense debate about the role they’ll play in the future of U.S. education. Advocates see their expansion as evidence that parents have a huge appetite for school choice. Critics see the beginning of the end of public education, with systems of neighborhood schools replaced by independent, privately run companies without the same obligation to teach the toughest students. A great deal of confusion surrounds charter schools.