Five practices to have meaningful discussions about mathematical ideas in the classroom.

These practices can be used to make connections in class and structure mathematical discussion towards particular goals. 

1. Anticipate- by having a firm grasp on possible approaches to solutions you can prepare to structure discussion based on what students will try on a problem. This minimizes the amount of improvisation you must do on the spot.
2. Monitor- keeping a close eye on student solutions and understanding during work time will allow you to make strategic selections for students to present solutions.
3. Selecting- through anticipating a flow of ideas from most accessible to most sophisticated, and monitoring which students have used the ideas you anticipated, you can select students to present who can progress the mathematical sophistication of the conversation.
4. Sequencing- student responses presented in a specific sequence can connect ideas based on level of sophistication and validate students understanding by clearly showing how superficial ideas connect to more sophisticated approaches.
5. Connecting- the student responses to show how each approach highlighted has valid connections to the underlying goals, and gives students a well rounded vision of a particular concept.

(Schwan & Stein, 2011)