I found "math circle" information here:

http://www.mathcircles.org/

Math circles are a kind of math club. We found one near us that we'll be trying out this year. They put the kids into groups (4:1 student:teacher ratio) based on ability rather than age. The one by us says they do logic and reasoning games, puzzles, and word problems. It's all activity and group based; not a lot of worksheets. DS is excited.

Thought I'd pass the link on in case it helps anyone else looking for a math "club". There's information for starting your own on the website, too.