I don't think this is a great idea, for several reasons:

Arithmetic is a very small part of mathematics, and perhaps the least important. But even as far as arithmetic goes, I don't see this game giving children a good "number sense". Why are different numbers the same size? If we don't relate the abstract concept of numbers to counts or sizes, then arithmetic is just meaningless manipulation of symbols.

Worse, the game doesn't seem open-ended. Children need not figure the answer out themselves, because they can just try an action and see what happens. I can see children just trying different actions over and over until they finally perform the winning combination. And I can also imagine the possibility of children thinking that they understand a subject when they really don't (for example, not being able to generalize beyond what they've seen in the game).

On a much smaller note, I hope the game has more to it than "when the result is zero, things disappear." For multiplication and division, doesn't it make more sense for that to be 1?

I don't see a video game like this helping kids to learn math and to learn to enjoy math. The children like the game because most video games (such as Mathbreakers, I'd say) are stimulating. What kid doesn't love video games?

So I've been quite a curmudgeon. What do I think kids should do to learn math in a fun way? I totally agree that games are a great idea. But I think a game such as the ruler/compass construction game [1] (featured on HN before) is a much better game. The ruler/compass construction game allows you to interact with the mathematics in a much more open-ended way than Mathbreakers. It emphasizes the importance of thinking logically, rather than simply manipulating symbols. Unlike Mathbreakers, which takes a complex system of base-10 arithmetic and adds to it even more complex game mechanics, the geometry game has extremely simple mechanics. You can let children simply play and come up with their own shapes, or they can try to make certain specific shapes (the link has several challenges). And the geometry game is deep! With these simple mechanics, we can encode some of the most interesting and challenging problems. For example, whether someone can construct a 17-gon [2] (and if so, how to do so) was only answered by Gauss (in the affirmative) in 1796. (Of course, that's not a puzzle we'd give to children! But how about a hexagon?)

So really, the geometry game is one that should be appropriate and challenging for people of all ages and math backgrounds! And it doesn't need to "dress up" the math with auxiliary puzzles and cartoon characters and 3D worlds. The math is already interesting as it is.

And finally, from Lockhart's Lament [3]:

Simplicio: Then what *should* we do with young children in math class?

Salviati: Play games! Teach them Chess and Go, Hex and
Backgammon, Sprouts and Nim, whatever. Make up a game. Do
puzzles. Expose them to situations where deductive reasoning
is necessary. Don’t worry about notation and technique, help
them to become active and creative mathematical thinkers.

[1] http://sciencevsmagic.net/geo/
[2] http://en.wikipedia.org/wiki/Heptadecagon
[3] http://www.maa.org/external_archive/devlin/LockhartsLament.p...