Well, I can't speak for others, but my personal experience with math tends to be that I only start properly learning why something works once I have the rules pretty well memorized. Before that, my working memory is so occupied with trying to just remember how to apply the rules that I don't have the space to remember why they work. Or alternatively, I can learn why the rules work - but in that case I don't have the memory capacity left for remembering how to apply them.
Of course, this is complicated by the fact that during the process of trying to memorize the rules, I often stop to think about why they work in an attempt to rederive them and make sure I'm not misremembering them. So it's not pure rote memorization, like the way it seems to be with DragonBox. But I would still expect that if somebody first learned them as meaningless rules in the game, and was then later taught math and the reasons for the rules, they'd have a good chance of being delighted at discovering where the rules came from, and could spend all of their cognitive capacity on developing an actual understanding.
Fair enough; it's possible that you and I simply think in different ways. I personally find it very difficult to memorize (seemingly) arbitrary rules, and I found it very difficult to un-teach the "guess the teacher's password" mentality to people. But it's quite likely that I'm making an unjustified generalization from a very small number of examples.
I wonder if there's any layman-accessible literature on this topic...
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.