There are lot of wrong headed methods of piano instruction on the market. Looking back over my years in piano, it's a real garbage heap of useless published material out there that still sells today. One of the worst ideas of all is that used by, for instance, the Leila Fletcher method-- that of splitting a melody line between left and right hand. No real musician ever does such a thing since the left hand is mainly used for comping, bass lines and chords, while the right is used for the melody or improvisation combined with chords under the melody. It's a mistake to teach children this technique. It took me years to unwind the odd ball thinking that created. I would never mislead a student using a score like this...
The concept of alternating hands on one melody line does often occur in classical music but even there, not really all that much.... not enough to warrent the above disastrous page. Much more conceptually true in both classical and popular music is the following score. The melody is played by one hand, on a piano-- even though this is written for trumpet-- and the left hand would play the root note of the chord Eb-- which in this case would be the Eb to the left of Middle C. (Freres Jacques is the same melody as Are You Sleeping, by the way).
