A Participation Quiz /Group Feedback is a strategy to help establish or reinforce norms for group work in a cooperative environment. While students work together in their group on a math task, the teacher takes public notes-on a document camera, white board, chart paper, or overhead projector-about the quality of their group work (social moves) and the quality of their mathematical discussions (math moves). The teacher can take notes on how students work together, their use of classroom norms, or the specific language they use to communicate their mathematical ideas.
You can promote discourse and stimulate student thinking through effective questioning. This, in turn, develops the habits of mind suggested by the Standards for Mathematical Practice. Here is a list of questions from the Professional Standards in Teaching Mathematics, grouped into categories that reflect the mathematical practices.