Are you supposed to learn rhythm first? Or the melody? Or are you supposed to use correct fingers and keep good posture? What is the priority?
In twelve years of teaching, I have had students approach a new piece of music in the way that they feel most comfortable. A student with a developed sense of rhythm will like to play a piece directly and quickly, the way he hears it (if he has heard it before). This causes some problems because most young musicians do not sight read quickly, and the piece becomes frustrating.
I prefer to have students play the correct notes only, even if it very slowly. I correct their fingers, make sure that they keep good wrist position, backs straight, and both feet on the floor. Rhythm is not yet a priority. Young children, about age ten and younger, do not really understand rhythm, but they do understand to hold a whole note for four beats, a half note for two, &c.
Because I am not with the student during the week for practice, I have to make sure that, before the lesson is over, he is able to play the piece and correct mistakes on his own. Again, I look at fingering and other muscle control.
The priority is muscle memory if the question is “What are you supposed to learn first?” The written music is to be a guide, an instructional manual. If the student has practiced correctly, he will be ready to correct the overlooked mistakes and pick up the tempo. Remember that correct practice does not only mean playing the correct notes but also keeping down those whole notes, resting when required, keeping the wrists off of the piano, and the shoulders back for good posture. All this aids in learning the rhythm correctly.
Rhythm is the backbone of music, which is definitely a priority.
