Gwen Dewar has  nice collection of examples of research that supports the idea that children learn best by playing: http://www.parentingscience.com/benefits-of-play.html

Here’s my favorite section:

“1. Most play involves exploration, and exploration is, by definition, an act of investigation. It’s easy to see how this applies to a budding scientist who is playing with magnets, but it also applies to far less intellectual pursuits, like the rough-and-tumble play in puppies. The animals are testing social bonds and learning how to control their impulses, so that friendly wrestling doesn’t turn into anti-social aggression. Play is learning.

2. Play is self-motivated and fun. Thus, anything learned during play is knowledge gained without the perception of hard work. This is in contrast with activities that we perform as duties… Play is an obvious gateway to the state of flow.

3. … kids treat play as a tutorial for coping with real life challenges. All around the world, children engage in pretend play that simulates the sorts of activities they will need to master as adults (Lancy 2008), suggesting such play is a form of practice. And when kids are fed information during pretend play–from more knowledgeable peers or adults–they take it in….