Why is communication during Math important?

After reading only a few chapters in Classroom Discussions, I have already read a number of interesting things. Key points so far:

• Research has been urging teachers to emphasize communication during Math for over 2 decades.
• Learning skills, such as communication, collaboration, and cooperation, fit nicely with this style of teaching.
• Asking different and open ended questions allow students to gain a deeper understanding of concepts.
• Students often understand when teachers explain but do not have a deep enough understanding to put their learning in their own words. "Math talk" does two things: 1. It allows the teacher and student to know how much they really do understand; 2. It forces students to explain what they do understand, thus further deepening their understanding.