Please see my answer to question five.
It's not all about the schools (see below), but I think that schools could do much more to bring parents in. We spent an interesting evening at an elementary school in New Orleans at the beginning of the year - a potluck supper with entertainment provided by the Louisiana Endowment for the Humanities. A great storyteller entertained kids and their parents. Later all the kids received a book or two, along the model of Reading Is Fundamental.
In my experience, too many administrators complain about apathetic parents or develop grand strategies for "parental involvement" that involve councils and evening meetings and "campaigns." I think most of that is a waste of time.
The best approach, in my view, would be to have the kids do the work. How? Have the second graders' writing assignments be about some aspect of their parents' lives. "Write a paragraph about your mother's favorite movie when she was little." "Write two paragraphs about your parent or guardian's favorite food." "Ask your parent or guardian about (fill in the blank) and write two paragraphs about it." And so on. You can be sure that parents will be "involved" and they will be eager readers of their kids' writing.
Years ago I tried (and failed) to persuade Burger King, whose president I happened to sit next to at a luncheon, to have his restaurants hand out cards with 10 boxes to check off, each box to be checked when the parent read a story to his/her child. Then the parent could bring back the card with all ten boxes checked and get a free order of French fries (small).
The president was skeptical because he suspected that parents would cheat. I'm sure a few would, but most would not because they wouldn't want to teach that lesson to their children. And I guaranteed that almost no one (even the cheaters) would just get the free French fries and leave - most people would spend real money. That card would send the message that reading matters, and it would take the school out of the equation (which I happen to believe is crucial).