First graders need to be told what to do and how to do it. They are all easily distracted... To give a kid a pile of papers and tell them to do them, is not going to work at this age. Time management is not a skill they have mastered... it takes some kids well into college to learn that little skill.
It sounds to me like the classroom is distracting.
If the kids are talking and giggling, then little work is getting done.
If the teacher gives her a goal and she reaches it, is the whole class getting the goal?? Is the class quiet at that point? Is everyone working??
It could also be that she is bored...
I'd ask if I could sit in the class one day - ask if you can help cut out stuff or correct papers or whatever so you can see what is actually happening. You might have to sit a few times to get a real sense of what is going on in there.