Educational apps for kids are supposed to be fun. The Holy Grail is getting your kid hooked on something that is basically their homework. Via BoingBoing, I found the Holy Grail: Dragonbox. (You can get it through iTunes and from other sources, I’m sure.)
It’s just algebra, rewritten as a genuinely addictive solitaire-ish card game. You have to isolate the ‘box’ (or card) so your dragon will grow. You have ‘powers’ to transform and move and eliminate boxes in various ways (analogs of algebra stuff); and, periodically, you gain new ‘powers’ as you clear levels and your dragons grow. The first thing to say is: gosh, my daughters now fight with each other about who gets to do algebra after breakfast, on the iPad, before school.
The second thing to say is that it raises kind of a funny issue in the philosophy of mathematics. Everything gets introduced in a cartoony, pictorial, non-mathematical way. The x you are solving for is the box with its shy, peeking dragon that won’t grow until it’s ‘alone’ (everything needs to be moved to the other half of the screen). Parentheses are bubbles that a few boxes may be suspended in. Negative numbers are ‘night cards’. A black-and-purple ‘night’ version of a picture card will cancel the regular version out, removing both from play. Numbers are dice pips. Gradually the cartoony stuff is pared back until kids are zipping through screens of stuff that looks a lot like plain old algebra (although, as far as we’ve gotten, the cartoon stuff has not fully disappeared). In the screencap above you see some ‘night cards’ but also something that looks like a negated c. It gets more like that. Belle was amazed to see our 9-year old ‘solve for x’, from a pretty snarly and complex starting point, in a dozen-or-so rapid and confident steps. Now: the philosophy. Algebra turned into a card game is a nice case-in-point for the debate about formalism in mathematics. Is my daughter actually doing algebra, even though she thinks she’s growing a dragon, or clearing a level, or playing a card game? She’s a bit like those tribespeople Wittgenstein writes about, whose stamps and shouts can be related, in a regular way, to moves in chess, but who have no conception that they are playing chess. Very ‘wax on, wax off’.