Effective teachers are able to facilitate classroom dialogue that is focused on mathematical argumentation.
Creating an environment where students are taught how and encouraged to explain and justify their solutions expands students’ mathematical language and ideas and pushes them to consider other methods. Such mathematical communication and argumentations focuses the students less on the answers and more on the processes that peers have used to reach those solutions.
Students need to be guided to listen attentively to each other, to take intellectual risks and encouraged to debate issues to arrive at common understandings. Students need to be shown how to actively engage with other students’ ideas and protocols for these discussions need to be collaboratively established. It takes a very skillful teacher to mediate in such interactions.
The stories here present examples of effective mathematical communication, however recent data indicate that more work needs to be done in classrooms on developing peer learning communities in which classroom dialogue is focused on mathematical argumentation.
Opportunity was also provided for children to work independently on their goals and next learning steps, as well as in pairs or small group sessions to practice, clarify or debate thinking. In providing a learning environment inclusive of small group debates I felt that children were able to collaboratively make sense of ideas and engage in mathematical arguments in order to make meaning of new learning. It is important to note that any pair or small group debates occurred more successfully when the children were familiar with the task at hand and each member understood their roles, such as taking turns, no put downs when sharing back and allowing time for people to think before they were to respond.