I teach piano to people ages 7 to 80. As a professional pianist, formerly at Daytons and Nordstrom amongst many other places in the US and overseas, I use "Fake Books". These are wonderful music books, but a person needs to know how to play using chords. This is what I teach.
A person can start lessons in the September, and by Christmas can play Christmas songs with 2 hands, using chords.
I also teach using classical teaching methods, with notes, timing, technique, even a bit of composing.