That kind of game is relatively easy, because the problems are trivial (“2 + 6 = ?”); the task is only to present them in an interesting way. You could do a World of Warcraft clone where you travel across a 3D map and people give you quests in form of “2 + 6 = ?” and then you have to fight a dragon with “8” written on his belly (there are also other dragons available, but those will kill you). There is no relation between a dragon and a number 8, therefore you have complete freedom in designing such games.
The only drawback is that without care, this could degenerate into “guessing the teacher’s password”, because the underlying model is just question/answer without a mechanism explaining why the given answer is correct. You could replace texts “2 + 6 = ?” and “8” with texts “Which religion is the true one?” and “Christianity”, and maybe you wouldn’t even need to recompile the binaries. -- OK, this is exaggerated, because with math the game can generate many new question/answer pairs instead of having a fixed database of them, so it is easier to learn some algorithm to determine the correct answer instead of memorizing them, which is exactly what we want to do. But the point is that this game does not show you why for a question “2 + 6 = ?” the answer “8” is more correct than “9″. It just rewards the former and punishes the latter. (Could be fixed by adding an animation that displays 2 red and 6 yellow spheres on one side, 9 green spheres on other side, then moves them to pairs and shows that on one side there is more.)
Another well-regarded educational app is Math Evolve.
That kind of game is relatively easy, because the problems are trivial (“2 + 6 = ?”); the task is only to present them in an interesting way. You could do a World of Warcraft clone where you travel across a 3D map and people give you quests in form of “2 + 6 = ?” and then you have to fight a dragon with “8” written on his belly (there are also other dragons available, but those will kill you). There is no relation between a dragon and a number 8, therefore you have complete freedom in designing such games.
The only drawback is that without care, this could degenerate into “guessing the teacher’s password”, because the underlying model is just question/answer without a mechanism explaining why the given answer is correct. You could replace texts “2 + 6 = ?” and “8” with texts “Which religion is the true one?” and “Christianity”, and maybe you wouldn’t even need to recompile the binaries. -- OK, this is exaggerated, because with math the game can generate many new question/answer pairs instead of having a fixed database of them, so it is easier to learn some algorithm to determine the correct answer instead of memorizing them, which is exactly what we want to do. But the point is that this game does not show you why for a question “2 + 6 = ?” the answer “8” is more correct than “9″. It just rewards the former and punishes the latter. (Could be fixed by adding an animation that displays 2 red and 6 yellow spheres on one side, 9 green spheres on other side, then moves them to pairs and shows that on one side there is more.)