Thanks for the comments. I used to think that the math had to be hidden. After working on doing that for almost five years on a commercial project (which did not see the light of day), I am no longer sure that is the required. Here’s why. I agree that symbolic expressions (formulas, equations, etc.) have no place in a video games unless their appearance makes total sense in the context of the game, and hence does not interfere with the game-flow. But (for middle-school math) symbolic expressions are required only if you want to capture the mathematics on a static flat surface, like a clay tablet, parchment, paper, slate, blackboard, whiteboard, etc. Mathematics can be represented up-front, in a natural fashion in an interactive, dynamic medium like a video game. In fact, I would say, in a video game we can be even more explicit about representing math than we can with a textbook. In a textbook, the math is actually hidden behind the symbols. With video game technology, we can provide a direct link to the math, the same way a piano or a guitar provides a direct link to music.

Maybe this is what you are saying. If by “hide the math” you mean keep symbols out, i agree with you 95%. But the symbols are not the math. We may just be using the same words to mean different things here!

Personally, I believe that making such a mainstream game cannot have the conventional computation skills unless they are a well thought out mechanic in the game. A good example of this is Math Blasters. I played this a ton when I was a kid, mainly because I knew I was good at math. But it never taught me anything I didn’t already know or could learn from a teacher. If I am to design a game, I want the math to be hidden behind the mechanics. A game that I see that has done this well is a recently released indie game called Waveform. I don’t know how much you follow the indie gaming scene, but essentially this game is about manipulating a sine wave’s amplitude and period to gather gems with various devices in game to change how the pathing works (black holes, mirrors to reflect the player, etc). Now a player that has never taken a high school algebra class or has just forgot it will never know this is a sine wave and all the game is doing is manipulating its properties. From this simple concept, the game has received fairly positive feedback from Metacritic ( http://www.metacritic.com/game/pc/waveform ), which is an achievement in itself.

If we really want to teach people complex math and get away from computational work, we need to start looking at hard concepts and hiding them behind the scenes. Can we teach elementary school children concepts in Abstract Algebra or Linear Algebra? Sure we can, but we need to be able to find a way to hide the fact that it is actually Algebra in the first place. I recently saw a speaker at a math conference at Lewis and Clark College where the keynote talked about how Linear Systems were embedded into puzzle games such as Myst and other point and click adventures. A player would click levers or buttons to move a certain interface, but coming up with the correct combination on your own proved to be very tedious. When you could write it on paper, the solutions took less time than just fidgeting with it, which was really cool. The only problem is, a person would never have the slightest knowledge that this was a linear system if they never made it into college mathematics… But, if these two examples say anything, it can be done, but it needs to be done right!

What I fear, though, is that the conceptual games will not gain purchase unless they also generate computational benefits.

But the conceptual thinking really is the generalization of concrete experience. So are these two game types really as distinct as you say? Maybe it’s more of a level up. Now that you’ve mastered multiplication, what’s true in general? How does it interact with other operations? How does it extend to other types of numbers?