Am I Doing This Right?

So far, my school year has been GREAT... or that's what I thought. Today, I went into the first grade classroom down the hall during my prep time out of curiosity.  This classroom didn't look like mine at all. The students were sitting in straight rows and quietly working on their assignments. When the teacher would ask them questions, they would silently raise their hand and wait to be called on. I feel that my students are respectful and still listen to me, but they are NOT quiet. They are constantly talking to one another and to me. I have my students in groups so that they are able to talk to one another and help eachother out. Am I doing this all wrong?  Should my students silently be working all day?

HELP!