Teaching by Example

This week I saw the power of teaching by example. In previous classes I had seen the reality of the huge variety of responses that can be generated within a diverse classroom.  I fully agree with the authors of the article, Orchestrating Discussions, who concluded that one of the primary challenges in this situation is "to build on and honor student thinking while ensuring that mathematical ideas at the heart of the lesson remain prominent."   (Smith, Hughes, Engle and Stein, 2009).  Our math instructor this week modeled for us the implementation of the "Five Practices Model" of orchestrating whole-class discussions.  In following this model, she:

1. Anticipated our responses
2. Monitored our work, and engagement with the tasks
3. Selected particular students to present their mathematical work
4. Sequenced the responses to be displayed in a particular order
5. Connected our responses to one another's and to key mathematical ideas.

Through watching her accomplish each step I realized how important this process is in order to hold meaningful class discussions.  It was an eye-opening class, and one in which I believe that the goal of furthering our mathematical thinking, as well as our pedagogical thinking, was accomplished.

My only question is what would a teacher do if no one in the class had come up with a "correct" solution?  Also, how do the students whose work is not chosen feel?