DragonBox algebra is a cool iPad game that teaches the mechanics of algebra in a very clever manner. The player is presented with a field divided into two halves. There is a magic box card (marked with a star) on one side (though on later levels you can suddenly see several of these boxes. These higher levels and the surprises they give are part of the fun). Your objective is to free the magic box by removing any other cards that might surround it on the side it is on.
It took me a moment to figure out that the magic box is “x” and by removing any cards surrounding it you are solving for “x”. The target audience of course cares nothing for “x” but is very eager to free the magic box to see what is inside it.
The first lesson introduces the concept of the “night card” which is the opposite of a regular “day” card and can be used to eliminate it. This also introduces the concept of balancing operations on either side of the field by holding up play until you make the required balanced moves. So if you add a card to one side, you have to add the same card to the other side otherwise the game will not proceed. I helped my child remember this by saying “We have to be fair”.
At the next level we are introduced to multiplication by one, and later elimination of common variables by dividing or multiplying. Of course these are introduced as abstract game mechanisms which my child was very quick to pick up.
I was astounded by how quickly she was basically solving linear equations without actually knowing basic arithmetic. I was reminded that algebraic is basically like a game, and you can “play” it abstractly – computers can be programmed to perform these algebraic operations to solve equations without “knowing” math.
At some point some of the cards, which usually feature pictures (like fish, or dragons or monsters) started instead to show “x” and “b” and importantly “-b”. It was a seamless transition for her, and she quickly adjusted to the idea that “-b” was the night card for “b”. It was quite amazing, but I did get the feeling the cards with pictures on them were more attractive than the boring “x” and “a” and “b”. Or perhaps that was just me projecting.
Now it’s likely that the game is not really teaching the child mathematics. It’s easy enough to make the leap with addition – adding a card on one side, requires you to add the card on the other side to keep things balanced or fair. The “night card” is a little strange: why not just take away the card? Because then it’s hard to explain how to take away the same card from both sides and so on. Things completely breakdown with multiplication and division: these operations aren’t easily explained to the target age group so what the kids are learning is some kind of strange ritual. Yes they learn that the fish on top is turned into a “1” on a dice by a fish on the bottom, and then this “1” can be merged with whatever is stuck to it by a “dot” but they are doing this mechanically, a bit like Searle in his Chinese room experiment.
I agree that my child is likely learning these game rules very abstractly, without making a link to numbers and counting and mathematical operations. But I’m hoping this is setting up a framework. While my child internalizes these, so far, arbitrary game mechanics, one day, when algebra is actually introduced to her, she’ll remember this game and it’s arcane rules and start to make connections with division and multiplication. I’m hoping that even if it doesn’t teach mathematics, it makes math less of a shock through familiarity.
DragonBox algebra gets two thumbs up from me!