When Leslie started hosting a playgroup for preschool-age kids in our Brooklyn, N.Y., backyard, there was no major-league ideology attached. She was thinking she’d attract a group of like-minded moms and dads who were skipping official preschool for a wide range of personal reasons. As it turned out, those personal reasons dovetailed to a remarkable degree. Everybody who showed up to let their kids smash melons and chase bunnies in our yard was already opting out of the mainstream system, at least temporarily, which involved some sacrifice: time or money or both.

Almost all of them had either decided to home-school already (at least for a while) or were right on the cusp of that decision. Although the methods they chose as they moved forward with home schooling are all over the map, their reasons for doing it are roughly similar. They didn’t feel comfortable about sending their kids to “school” at the age of 2 or 3, and wanted them to have much more open-ended, free-form play than most preschools and pre-K programs allow.

So at least for a while, the bunny chasing and melon smashing, and the trips to the Bronx Zoo and the New York Hall of Science, were free of any explicit educational intentions, beyond the universal goals of all exhausted parents of small children: to get through the day without unacceptable acts of violence, while demonstrating that the world is full of cool and exciting stuff. But as the months rolled on and the 3-year-olds in Leslie’s group turned 4 — the age when most public-school kids head off to pre-K — their parents began to face the inevitable question: What do we do now?