I'm also not anti-summer math. I'm not anti learning in summer at all. My kids take all kinds of summer courses and intensive camps in summer. And they did AoPS. But it's because they want to.
If they don't want to, I would think hard about whether there is really a need, before I force them to. In our case, usually I will realize that they don't need to, and I will drop my idea.
I don't quite understand why the kids need to take a prep course in the summer, so that they can handle more advanced courses in the fall. In my opinion, this simply means that they should be taking a less advanced course in the fall. Unless, of course, they want to.
