We have two teaching methods at KMS. But for children under twelve we generally start by teaching them to read notes. If they also learn to playing by ear later, then all the better. If a person learns to play by ear first, it becomes harder to learn note reading. It's hard to resist ignoring the notes and playing by ear once they become familiar with the song. But keep in mind that God has the last word on everything.

And if He designs a person to play by ear, forcing them to play by notes can be very frustrating to the student. If a young child is already finding songs on the piano on his own, chances are he'll only be happy playing by ear. 

We use the ALFRED lesson book series. They are simply the best in our opinion. (Far better than the JOHN THOMPSON books that bored me to tears as a kid). The ALFRED method introduces duets  as early as the third song (the kids are delighted) and easy classical as early as the second book. FANTASTIC!