Hello! Thanks for your question. I am a piano teacher so I can help you with this question.
Here is what happens quite often. Primary books tend to teach the "number" system, regarding notes, meaning that each finger has a number that corresponds with each note. Many books incorporate this approach while introducing various new notes, such as D, E, F and so on. The problem with this, is that students can fall into that trap of a certain key position (for instance the "c" position) and then want to have the numbers of the fingers on each corresponding note. Not good, because the student does not learn to read the notes. In time, there is no such thing as a "position." The student will ultimately have to learn how to read. The teacher should be teaching theory and introducing how to read the line and space notes on the staff.
It is also easy for students to fall into the bad habit of not looking at their music. As a result, they end up memorizing the piece. Typically, they hear the teacher playing the song back and they get the rhythm through that (often instead of counting properly). With this, and also the typical "finger" positions, students end up memorizing the song. Move on to a new one, and they often have trouble because they aren't learning how to count properly, or to read notes. It's a common situation if the teacher does not stay on top of it.
Have you spoken to the teacher about this? That is the first thing I would do. I'm not sure of the level of your child. I'm assuming he or she is just starting out.
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