What it teaches
How each piece moves, which is the only thing standing between a child and a real game of chess. A rook draws a cross, a bishop draws an X and never leaves the colour it started on, and a knight does neither.
The board is empty on purpose. The first thing to learn about a rook is the shape it draws, and other pieces in the way only hide that shape.
How it works
A piece appears somewhere on a real eight by eight board. The child taps every square it could move to, and each right one turns green with a dot on it. The question is not finished until all of them are found.
A wrong square shakes and carries a cross. Three levels add pieces rather than replacing them: the rook and the bishop first, then the queen and the pawn, and the knight last.
What to look for
The knight is the one that takes time, and the reason is worth saying out loud: it is the only piece whose move cannot be seen along a line. "Two along and one across, in any direction" is the sentence that usually does it.
The bishop has a fact worth pointing at too. It can never reach half the board, ever, because it never changes the colour of its square.