Mike, I want to work with it - I like the metaphor of depth a lot.
I just did a teacher workshop on games in for the Bermuda math teacher community. A lot of people there liked, for example, Tarsia - a "content-neutral" jigsaw wrapper for matching expressions, or any question/response really. Many teachers said they make custom puzzles for their individual classes and even individual students.
So maybe we can talk about deep game-content ties, as in game mechanics intrinsic within particular topic. And contrast this with shallow game-content ties, which work for multiple topics. There can be multiple depths, too. For example, "Set" is just for sets, "Math Scrabble" works on equations - any equations, but only equations - and "Jeopardy" works on pretty much everything.
Cheers,
Maria Droujkova
919-388-1721Make math your own, to make your own math