BattingOdin13 said:
Well, Where to begin.
Extra Credits: Gamification [http://penny-arcade.com/patv/episode/gamification]
Extra Credits: Gamification in Education [http://penny-arcade.com/patv/episode/gamifying-education]
Extra Credits: ARG Part I; Alternate Reality Games [http://penny-arcade.com/patv/episode/args-part-1]
Those should help a little if you haven't seen them.
On to the topic at hand, from what I have heard from my mother (she was a special education teacher), one of the common things she and other special education teachers used to keep her class behaved was to offer rewards for good work (My mom used my old Yu-Gi-Oh cards after I stopped playing because they looked cool and were relatively inexpensive/easy to get, but anything they would value will work). One idea might be to introduce a reward system like this, let it sit for a few days (to become part of the natural environment for the class) then have the rewards "disappear", with a note being left behind that will lead them to the rewards. This note could be anything; a history question, a math question, etc... so long as you also create a condition to return the rewards (e.g. "Find the answer and write it on the board"). When they solve the question, you return some of the rewards (enough for everyone involved) and drop the next question. Rinse & repeat.
It's basically a real world version of "Where in the world is Carmen Sandiego?" but with much less valuable missing stuff. The goal is to create a mystery and get them involved and invested in solving it. Anything you can do to enhance the mystery (such as dropping clues as to who the "thief" is (usually the teacher or an administrator if you can convince one), upping the reward system from a lower reward (candy) to higher rewards (dollar-store toys), to having specific events that require "field trips" to the library) are useful and should be done, so long as it never detracts from the teaching element or compromises the question difficulty.
The advantages of this ARG are that it allows for large varieties of topics of any difficulty, creates a built-in, real-world reward-system, and creates a mystery that will engage the class and keep them invested in the "story" of the game.
The disadvantages I know of are that it doesn't have a teamwork mechanic to encourage cooperative efforts and it requires the higher-ups in the teaching staff/administration to be aware of the ARG (so as to not draw any excess parental ire when the kids go home talking of stolen stuff). The final downside is that the missing rewards will no longer be able to be used for behavior control, so you will need to find another way to maintain this control.
Hope this helps.