It sounds like your daughter's being taught with the Suzuki Method, which is fine to get started with, but you will want to switch her to a better teacher soon. Suzuki will train her ears, which is important, but that's about all it's good for. It's designed so that kids reaquit shortly after they enter high school, and it leaves them mostly unable to sight-read.

Background: I am a violinist, playing professionally at weddings and such about once a month (full-time student), and I started on Suzuki.

btw, my father (who also had very little musical training) forced me to improvise (make up music as I went) for five minutes every day, even if it didn't sound good. Today I am quite good at musical improvisation, a skill that is no longer really taught in the classical school of music. I don't know if my dad's method would work for everyone, but I'd recommend it.