Teachers need to be concerned if a particular method help students to become musically and functionally literate and what teaching materials might be needed to overcome either a method's or student's potential weakness. For example, methods that begin with music in five-finger positions allow students to quickly transpose melodies in a number of keys and various ranges. Yet if a teacher is not careful, a student might not learn intervallic relationships and note name. Students need to understand that finger number two does not always play a note between the thumb and finger number three. The popular Alfred and Bastien methods emphasize position playing.
Some methods stresses intervallic reading of notes from the beginning.
Students still need to learn specific names of all the notes in both clefs. The Music Tree of Francis Clark and Louis Goss is an example of a method using intervallic reading. Ideally a teacher understands the various teaching approaches of various methods and can employ them whenever they increase students' understanding. For information on specific methods, check out the links below.