It depends on the subject. The best strategy where reading is concerned is for parents to read more and encourage reading by visiting the library and selecting books from the school's list. Good luck. This may sound like a radical concept, but the more parents stay out of the whole process the better. You know as well as I do that most parents are ignorant yokels who only impede the foundation of knowledge children receive from public education. I have three kids and our school is always getting parents involved in homework and in their child's education. It's a disaster. Parents are not professional educators. Most parents lack the time and education that the average teacher possesses. Half the time, the parent scoffs at the assignments and says, "this is stupid! you'll never need this. Your teacher's an idiot" Exactly how is that parent qualified to say what a child should or should not know? I guess to answer your question, a parent can try to take a personal interest in reading. But we're so far from being a literary culture at this point that parents don't even know what qualifies as literature anymore. You've got 2/3 of parents undermining the teaching of the formation of proteins, genetic similarities and mutations and fossil records that prove the evolutionary theory. Teachers have crazy parents threatening them.
To qualify my remarks, how about I mention the most-involved parents in any school: The young ladies who run my kids' school's PTA can only be described as lunatics. They don't even understand the purpose of school. After raising a significant amount of money (good job there) for the school, they then took a wrong term by asserting that because the PTA raised the money, the PTA should decide how the money is spent. Lab equipment? more books? better maps? computers? anything educational?--nope. They decided the school needed 2 dozen park benches that clutter up the front of the school--but at least they all have a place to sit their fat asses while they wait to pick up their children. That's what's important.