Class room Discussions And Talk moves
The National Council of Teachers of Mathematics has a long history of encouraging teachers to engage their students, at all levels, in rich mathematical discourse. For nearly 20 years, NCTM has promoted and encouraged Math Talk because it supports both students' ability to REASON MATHEMATICALLY and the ability to COMMUNICATE THEIR REASONING, especially when combined and focused on big ideas and power standards.
The Common Core State Standards For Mathematical Practice also advocate for discourse and discussion. Math Practice 3 asks students to construct viable arguments and critique others reasoning. A community of discourse, communication, and collaboration can make this happen. Math Practice 6 asks students to attend to precision, including precision of language.
Conversations need to be going on in the math classroom as much as possible, but consider your grade level standards, your curriculum, and your students. Mindfully choose the big ideas and concepts that students need to build upon and spend time discussing these concepts.
The Common Core State Standards For Mathematical Practice also advocate for discourse and discussion. Math Practice 3 asks students to construct viable arguments and critique others reasoning. A community of discourse, communication, and collaboration can make this happen. Math Practice 6 asks students to attend to precision, including precision of language.
Conversations need to be going on in the math classroom as much as possible, but consider your grade level standards, your curriculum, and your students. Mindfully choose the big ideas and concepts that students need to build upon and spend time discussing these concepts.
great classroom discourse: A Puzzle
In NCTM's "Five Practices for Orchestrating Productive Classroom Discussions," Smith and Stein have identified 5 practices for classroom discussions. With these 5 practices, teachers can mindfully cultivate discussions and substantive conversations in their classroom in order to increase student understanding and reasoning.
As teachers develop meaningful tasks and projects, these five practices will build on each other and fit together like a puzzle to support discussion and greater understanding of the mathematics. 
Anticipating 

Selecting 
While you monitor the students working, you can begin to select the students to present their finding in the whole class discussion, which ultimately will contribute and build towards the mathematical goal of the lesson.
Some ideas for managing the selections:

sequencing 
After mindfully monitoring students and selecting which students/groups to ask to present, you can purposefully sequence the order of the presentations to guide the discussion towards the mathematical goal. If you have already thought about what possible strategies and solutions your students might use, you can have a rough plan
for the order of the discussion already laid out. There is not a right or wrong way to organize a discussion, as long as you are mindful and purposefully working to build to your mathematical goal. Ideas for Sequencing:

Connecting 
As the classroom teacher and facilitator of the discussion, it is your role to help students make connections between their solutions, other students solutions, and the key mathematical concepts of lesson. Remember, the goal of productive mathematical discussion in a classroom is more than simply giving students time to share their ideas. It is to facilitate a discussion through the students presentations that will build deeper and more meaningful mathematical understanding.

Remember, all five practices fit together like a puzzle. They do not stand alone. Monitoring student work is not quite as daunting if you have anticipated and listed out several possible strategies that students might use. If you have anticipated and monitored students, selecting and sequencing will be more natural and flow out of what the students are doing. When you have identified your learning objective and the mathematical understanding you want you students to gain.
Talk moves
Below are several "talk moves" and videos of what they look like in the classroom. Talk moves are stratigies and classroom practices that encourage and facilite discussion as well as a culture of community and communication in your classroom.
As you are watching the videos, keep these questions in mind:
How do talk moves encourage students to make connections with each other?
How can talk moves be used within small groups? How do that compare to discussions with an entire class?
Which talk moves do you use in your classroom? Which could you add?
At the bottom of this page is a feedback form. I would love to hear your feedback and your own ideas about talk moves and conversation in the classroom.
As you are watching the videos, keep these questions in mind:
How do talk moves encourage students to make connections with each other?
How can talk moves be used within small groups? How do that compare to discussions with an entire class?
Which talk moves do you use in your classroom? Which could you add?
At the bottom of this page is a feedback form. I would love to hear your feedback and your own ideas about talk moves and conversation in the classroom.
Repeating, RevoicEing, Adding On
Asking students to repeat their peers thinking increasing listening skills as well as developing a student's own thinking. A student must speak clearly and precisely so that another student can repeat their thinking. Their classmate must be actively listening and tracking the speaker in order to repeat.
After students repeat another's thinking, then they can take it one step further and either revoice in their own words and addon to their classmates thinking.
After students repeat another's thinking, then they can take it one step further and either revoice in their own words and addon to their classmates thinking.
Turn and Talk (Think, Pair, Share)
"Turn and Talk" or "Think, Pair, Share" are just a few of the stratigies that can be used before and during whole group discussions. These types of stratigies allow students the chance to think and process independently, then share and verbalize with a partner (or small group) before sharing with the class as a whole.
Silent Signals
Silent signals are explicitly taught signals used consistently in a classroom for a variety of reasons. Silent Signals can be used to show agreement or disagreements with peers or encourage peers to continue. They can be helpful within whole class discussions and will also help develop community in the classroom. They can also provide informal formative assessment.
Wait time
Wait time is a research based strategy for classroom discussions. There is not a hard and fast rule that a teacher has to wait x amount of time, but teachers have to be mindful of allowing time for students to process. It is also important to be mindful of how to call on volunteers and extending wait time to get more students ready to answer. By combining other talk strategies that allow kids time to prepare and organize their thoughts as well as silent signals for informal formative assessment, wait time will be more effective and seamless.
Group Strategies and Classroom Community
The Five Practices for Classroom Discussions are like a puzzle and the talk moves and other strategies also fit into making the big picture come together for students. Another vital component of classroom discussion is community and classroom structure. This is also the area that is the most dependent on your students and their personalities as well as your comfort level and personality as a teacher. Below are a few snapshots of classrooms. As you watch them, decide what pieces of the videos could be applicable in your classroom.
Putting it all together
Video1: Reasoning with Division
Video 2: Third Grade Math: A Complete Lesson
Video 3: Skip Counting with Counting Collections
Video 4: Conjecturing about Functions
Video 5: What's Fun About Surface Area
How do you see the Five Practices for Productive Mathematics Discussions in these lesson videos? What practices are not explicitly seen but can be assumed to have been done by the teacher?
What are the strategies or talk moves that are being used? What are the positive or negative aspects of the video. How can you apply them in your classroom?
Why is it important to discuss and understand multiple strategies?
Video 2: Third Grade Math: A Complete Lesson
Video 3: Skip Counting with Counting Collections
Video 4: Conjecturing about Functions
Video 5: What's Fun About Surface Area
How do you see the Five Practices for Productive Mathematics Discussions in these lesson videos? What practices are not explicitly seen but can be assumed to have been done by the teacher?
What are the strategies or talk moves that are being used? What are the positive or negative aspects of the video. How can you apply them in your classroom?
Why is it important to discuss and understand multiple strategies?
Let me know what you think!
Additional Resources and References
National Council of Teachers of Mathematics (NCTM). 1991. Professional Standards for Teaching Mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). 2000. Principles and Standards for School Mathematics. Reston, VA: NCTM.
Chapin, S., O'Conner, C., and Anderson, N. 2013. Classroom Discussions in Math: A Teacher's Guide for using talk moves to support common core and more, 3rd Edition. Sausalito, CA: Scholastic
www.teachingchannel.org
National Council of Teachers of Mathematics (NCTM). 1991. Professional Standards for Teaching Mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). 2000. Principles and Standards for School Mathematics. Reston, VA: NCTM.
Chapin, S., O'Conner, C., and Anderson, N. 2013. Classroom Discussions in Math: A Teacher's Guide for using talk moves to support common core and more, 3rd Edition. Sausalito, CA: Scholastic
www.teachingchannel.org