Pianimals was developed using the concept that "children who know their finger numbers and learn where to place them on the keys can almost immediately play familiar songs". This method puts strong emphasis on finger numbers and learning one concept at a time. Once children know their finger numbers and where to place their hands on the piano, they can easily play familiar songs. I've also found that after using "Pianimals", it is easy to transition to Piano Adventures (which is normally my method of choice) and soon after teach notes on the staff.
To give you an example, I have a 4 year old that I started in My First Piano Adventures. While she knew all the notes on the keyboard, knew her terminology and was doing fantastic with rhythm, she was resistant to work on songs at the piano. So, I switched her over to Pianimals. What a difference it made!
She loves to play now! She is so much more successful using this approach and she doesn't need nearly as much help. She just came to her first group lesson and played for the other kids WITHOUT a problem! I was so proud of her! It was a huge step! Her mom told me that it has made a huge difference in her practicing at home.
I've been very impressed with the success rate this method has with younger, pre-reading children! If you haven't tried this method, I highly recommend it!