My daughter went to parochial school through Junior High, and would have continued in that system but for the lack of a Catholic High School where we lived at the time. She excelled, and when she switched to the public high school, was far ahead of her peers. Now in college, she continues to achieve high marks.
Part of it is parenting, yes. Parents need to be involved and encouraging, but also motivated by the fact that they are paying real money for their child's education. Too many parents view public education as 'free', when it is most certainly not. You pay for public education through property taxes. More importantly, you also pay for the kid down the street in the apartment who's parents think that public education is 'free'. Because of the perceived cost, IMHO, some parents don't pay nearly enough attention to their child's education. You don't have to be the model PTA mom or dad, but you do have to be informed about what is going on in your kids classrooms, their school and the school district. This seems to be more the case at private and parochial schools, perhaps, again IMHO, because we lay out real money every month to ensure our kids get a better education. And we still pay property taxes so the kid down the street in the apartment gets their 'free' public education.
If the funding system were turned inside out, and people were required to pay for public education, you bet your ass parents would be sitting up and taking notice. The voucher system is one piece of it, as are scholarships for economically disadvantaged students, but the whole system needs to be privatized, getting rid of the bloated administration overhead, the special education/secondary language mandates that suck up an inordinate amount of a school district budget, and tenure.
It's also not enough to send your kids off to school, and attend a parent-teacher day once a year. You have to engage your kids in the home, with something other than XBOX and PS3. Look at your friends' homes and see the correlation with how their kids behave and the presence of actual books in the home. Encouraging reading, even if it's just Harry Potter, makes a huge impact on behavior and intellectual curiosity.