The biggest reason that there's a huge gap between the education of rich kids and poor kids is the summer. The first summer I lived on the farm, Time magazine published a cover article on the topic which I studied closely.
The second summer, it's clear to me that kids in our town do not go beyond our town of 2000 people for enrichment. This is remarkable given what the rich kids are doing. The New York TImes just published an article about the breathtaking variety and quality of summer programs that rich kids attend.
The problem with not leaving your home town for the summer is that you never get an outside perspective. You never know where you stand compared to the rest of the world. This doesn't matter if you never intend to exist in the rest of the world. But I want my kids to be able to choose from a wide range of lives that are not necessarily possible in Wisconsin. Which means I have to expose them to that outside world very early on.
The gap is not so much about achievement at the early satge. It's about exposure to achievement. And this summer both my boys went to camp in another state. I didn't realize it, but doing that is equally as subversive as homeschooling my kids. It's a rejection of my town's way of doing things.