The NCTM Standards emphasize the importance of developing mathematical language and communication in order to understand concepts rather than merely following a sequence of procedures. Our problem solving curriculum and teaching strategies seek to build a community of learners who have frequent opportunities to explain their mathematical thinking through Math Talk and thereby develop and support one another's understanding. The dialogue that takes place helps everyone understand math concepts more deeply, and it helps children to increase their competence in using mathematical and everyday language. Students' ability to use mathematical expressions to model real-world situation will be central to their progress in math and science. While children engage in dialogue, the teacher acts as a guide to maintain the focus of the discussion and to clarify when necessary. Children use discussion to support the mathematical learning of everyone in the class. In a respectful community of this type, children:
- develop and share their own mathematical thinking
- Listen carefully to others ideas
- Wait time provides more thinking space and can help all students track what is going on mathematically, and think about their responces to the discussion.
- revoice ( restate in their own words what they hear others say)
- Ask questions, elaborate, agree and disagree, providing insight into the mathematical ideas of others.
The mathematical thinking of many students is aided by hearing what their peers are thinking. Putting their thoughts into words pushes students to clarify their thinking.
At the beginning of this process, teachers model "Math Talk" for children and elicit responses. Teachers wait patiently and refrain from intervening immediately to correct children’s errors in order to create space and support for children’s voices to emerge. Teachers eventually guide children from the side or the back of the classroom so that children can sense that their questions, ideas, and discoveries are the focal point of instruction.
I have witnessed a noticeable shift in responsibility from teacher directed learning to a more classroom community directed learning. Our second grade students are thinking, evaluating, and demonstrating a higher level of understanding in the problem solving process. They are discussing math concepts, strategies, and justifying their solutions. This more advanced thinking has made our math discussions more fun and there are times I sit back and just say WOW!
