There is some debate between supporters of sight reading and supporters of learning by ear. I support sight reading because, just like learning to read English, it allows for students to analyze and understand what they are playing.
Reading music is not easy. It requires focus, repetition, and support from parents. This hard work does not cater to immediate results the way memorization would. Many children may want to start learning by ear or reject reading the music, but this does not do them any favors in the long run.
What is sight reading? It is playing the music at first sight. There are many levels of sight reading, from beginner to advanced. When the student plays “one hand first, then the other hand, and finally both hands together,” that is not sight reading, although many teachers may allow their students to learn pieces that way. Sight reading is playing the music as it is written, even if it is at a very slow pace.
If a student learns to play by ear, he will find it easy to continue doing so. If he leaves the learning to read music until after he is well acquainted with playing by ear, he will not want to learn, for it is tedious. If he is taught to read musical notation when he is young, he will not remember NOT knowing to read.
Playing by ear and improvising is gained with experience. Students train their ears and develop musical principles through their years of reading music. As a young student, I was taught to sight read and learned music theory in my middle school years. When I was required to improvise or compose, the scales and chord progressions that were taught to me came in handy. Today, I introduce improvisation very carefully, depending on what the student already knows.
