Math was created by humans and is social in nature. Learning is social. We need to work together, and show care for others in the room.
Be respectful when talking with one another. Active listening is a whole body commitment. Let everyone in your group speak once, before one person speaks twice.
Use mathematical language. Be clear, convincing and precise with your communication.
*based on the work of Dr. Peter Liljedahl (http://www.peterliljedahl.com/)
There is research that shows that when students are working on vertical nonpermanent surfaces, they are quicker to get started, stay on task longer, spend less time being distracted, and take more risks. Having the work easily seen by everyone in the room, makes it easier for the teacher to see where she is most needed, easier for students' ideas to be shared with the group as a whole, and easier to identify questions with the task.
Every student has something to add to the conversation, and so grouping will be random. Students will have an opportunity to work with a variety of people, and will be exposed to different ways of thinking. If your group doesn't work one day, chances are you will be in a different group the next day. Along the way, we will learn that random doesn't always feel very random.