It seems to me every mother's dream is to put her daughter in Music School to learn to play the piano or any other musical instrument. This does not necessarily mean that the child has to pursue a career in Music. It simply is a status symbol when a member of the family, usually the girls, can play Classical compositions and have a Piano Recital.
I had been teaching piano to very young children, having had advance units leading to an Associate degree in Music along with my Bachelor's degree in Arts and Education. But being a graduate at the age of 18, I could hardly find a job as prospective employers think I was too young to be employed. So I went into tutoring piano for 2 years and the experience I had with children learning piano is something that might be valuable to mothers.
As early as 5 years old, some parents would prod these kids to enroll in Music schools. Unless a child is really gifted, this does not cause any problems. However, if the child is merely forced to-- to keep her busy in the summer months, learning becomes a horrifying experience for the child who would play a "tug of war" with either the parents or the piano teachers.
In my case, I accepted kids only from age nine (9) for piano beginners. The attention span of those younger is very short and usually, it takes 10 minutes to get them concentrated on the piano before the actual lessons start like reading notes, simple exercises for finger dexterity and hands-on on the keyboard. After 20 minutes, the child sighs (sign of getting bored and tired) and as the teacher patiently pursues the lessons for the day, the kid's eyes wander off. or may even complain (just about anything) or ask you instead to tell stories. As a teacher, you have to do justice to what you are being paid for an hour's tutoring. So your tendency is to try as much as possible to keep the child at the piano with her struggling little fingers on the keys. I think of this not as piano tutoring but piano torturing with the eager parents as accomplices. It is for this reason that I gracefully turn down any child below 9 years old presented to me for piano lessons. And even if the child qualifies my age requirements, I would still assess if the child really wants to take up piano or have the lessons postponed in his later years. Sometimes, it takes some degree of a teacher's creativity to get the child to appreciate piano. I would ask her what songs she likes and play them on the piano. Or play some light simplified classical music to get her acquainted with the Great Masters. I became popular in the community for making a child play the piano in just one year of tutoring and soon enough my young students grew in number. As soon as they have learned the Basics and moved on to Kohler or Czerny, I would advise them to enroll in the Music School, so they could join a Student's Piano Recital which is every parent's dream. Many pursued piano studies til high school while others dropped off after I stopped piano tutoring. But to all of them, I would say---never give up what is most dear to your heart. And many of them (now professionals) would remember me for that and say---though they have gone to various fields and ended in good careers, they still play the pieces I taught them and could play them by memory.