Dear TmT, sorry for being a little late with my response to you. We have Sonya and Phillip as our guests in Houston and I enjoy their company very much, teaching Phillip to play Hanon and 'French Song'
Yes, your teacher as well as most of piano teachers have different view on the fingers issue. Without Soft Mozart teaching goes on 'blind mode', when children look at keys and notes without seeing them, because they look similar and there are many of them. How do blind people learn? With the power of touch or muscle memory. They have to count, how many steps between sofa and a bedroom door to get there. This is why using correct fingers is extremely important.
All the music schools using muscle memory as a primer source of successful learning. 'Method books' is a way to keep children on artificial piano pieces that fasten each finger for a key - therefore they will learn something and parents will keep paying.
With Soft Mozart children see, what they play and they don't depend on muscle memory. Vision involvement help them to correct fingering on the way of reading music. No bad habits ever was developed - so we shouldn't worry about what fingers Lily uses at the beginning of learning a song.
I watched the videos and this is what I think:
1. In future, if she plays on grand piano, please, place step stool under her feet. Bouncing legs are not good idea for playing piano (TV journalists love to show that because it is cute, but posture should be stable)
2. Sitting at the piano. Lily is a small child. We have to create a sit for her, when her elbows are above the piano keys - not below them.
Lily. She has excellent mind, ear and her fingers independent, strong and she plays in good speed. She has a great foundation for progressing to play piano and read music. This is what I suggest for her to learn:
1. Exercises. She has to start with them every day:
softmozart.com/forum/55-teaching-videos/...the-first-level.html
Here is the stages of learning:
a. Play with 1 hand at a time
b. Play with both hands
c. Play with metronome
d. Increase the speed of metronome gradually
2. Piano pieces for technique development:
Boogie 1 - Robot Rock, Cat Boogie
Favorite Classics 1 - Radetsky March, Barcarolla
Nursery Songs 1 - Hickory Dickory Dock, Old Mac Donald, Old Woman in a Shoe.
My first piano pieces - any
3. Genuine Piano pieces that are not within 'method books' scope: any song from Simona's library 1 and 2
4. Album for reading: Nursery Primer. Ask her to play all the pieces on 2, 4, 5 and 6 (with no pictures). I suggest do not rush into playing on 4,5 and 6, because 2 is helping to build strong visual connection between lines and spaces and piano keys.
Set a goal for her to make no more then 5, 4, 3, 2, 1 mistakes.
Let me know, how it goes!
I am going to be available on Skype free consultations soon.