I've been reading a lot about square foot gardening lately. I think that this really makes sense and would be a great way to start a garden in a child care setting where you may not be able to "give up" much of your playground space.
I would advise that you make the boxes 4x2 however, to allow the small arms of children to reach their own squares.
If you buy the book, be sure and get the newer version. They're both about the same price, so that's not an issue... but the author has made some advances in the technique that are particularly welcome. For instance, in the past, he recommended that you dig down into your existing soil where the box is going to be. In the new version, this step is not necessary.
There's a Yahoo! Group for this that I've been following, and almost nobody does anything with their existing soil. In fact, most folks lay down a weed blocking fabric or old newspapers and cardboard boxes (cheaper than the fabric!) and put the boxes right on top.
Also, the book isn't really necessary, although there is a ton of reference material in there with charts and such... very handy. But the author has a Web site and shares his knowledge and experience very generously. He's quite an advocate of this system and is even spreading it to poverty-stricken areas of the world and to Habitat for Humanity homes.
If you join the Yahoo! Group, you'll be able to see member pictures -- there are many albums that have stunning examples of gardens in all stages of growth, arbors and fences covered with tomato vines and such... just really great stuff to inspire you and your students.
Also see pictures of square foot gardens and their bounties at Flickr.