That kind of game is relatively easy, because the problems are trivial ("2 + 6 = ?"); the task is only to present them in an interesting way. You could do a World of Warcraft clone where you travel across a 3D map and people give you quests in form of "2 + 6 = ?" and then you have to fight a dragon with "8" written on his belly (there are also other dragons available, but those will kill you). There is no relation between a dragon and a number 8, therefore you have complete freedom in designing such games.
The only drawback is that without care, this could degenerate into "guessing the teacher's password", because the underlying model is just question/answer without a mechanism explaining why the given answer is correct. You could replace texts "2 + 6 = ?" and "8" with texts "Which religion is the true one?" and "Christianity", and maybe you wouldn't even need to recompile the binaries. -- OK, this is exaggerated, because with math the game can generate many new question/answer pairs instead of having a fixed database of them, so it is easier to learn some algorithm to determine the correct answer instead of memorizing them, which is exactly what we want to do. But the point is that this game does not show you why for a question "2 + 6 = ?" the answer "8" is more correct than "9". It just rewards the former and punishes the latter. (Could be fixed by adding an animation that displays 2 red and 6 yellow spheres on one side, 9 green spheres on other side, then moves them to pairs and shows that on one side there is more.)
Last month, mobile gaming superstar Angry Birds was out-sold in some countries by DragonBox, a kids game in which players solve alegbra equations.
How does the game work? Jonathan Liu explains:
The key to DragonBox's success is not that it's the best algebra tutorial available, but rather that it's actually fun for its target audience to play.
Others have noticed the potential of "computer-assisted education" before. Aubrey Daniels writes:
Remember what works in reinforcement: Small reinforcements are fine, but the reinforcer should immediately follow the target behavior, and it should be conditional on the specific behavior you want to strengthen.
Video games are perfect for that! Little hits of reinforcement can be given many times a minute, conditional on exactly the kind of behavior your want to reinforce, and conditional on exactly the behavior you want to reinforce.
DragonBox is just a particularly successful implementation of this insight.
One of the goals for the Center for Applied Rationality is to develop rationality games and apps. But it's tricky to think of how to make addictive games that actually teach rationality skills. So I'd like to provide a place for people to brainstorm ideas about what would make an addictive and instructive rationality game.
See also: Rationality and Video Games, Gamification and Rationality Training, Raytheon to Develop Rationality-Training Games.