Compared to many of the other famous artists we have studied, there aren't a whole lot of Kandinsky resources available for kids. If this subject has captured your child's interest here is where I would start:
Read:Kandinsky 1866-1944 A Revolution in Painting by Hajo Duchting
Color Your Own Abstract Art Masterpieces a Dover Art coloring book
What's the Big Idea?: Activities and Adventures in Abstract Art by Joyce Raimondo
Explore the Web:Making Art Fun has a few fun Kandinsky resources including a word-search and coloring page. (Parents, there are advertisements on this page, and one in particular looked like a game when I last was there. I would preview it before allowing the kids on this site.)
Watch:Want to see Kandinsky in action? Check out this old silent movie from 1926.
Create:Ready to make some more art? Try using your oil pastels to write your name in an abstract style. K-6 has some fun instructions. Remember, pastels are not crayons. Peel off the paper and use them sideways sometimes, and don't forget to blend the colors together!
You can also take a look at some of the other oil pastel ideas we have used over the years.