Reasoning and Proof, and Representation
In middle school, the mathematics curriculum is more complex and abstract than at the elementary school level. Students at this age are making the transition from concrete representations to expressing mathematical ideas using symbols. Through communicating both orally and in writing, students can begin to clarify their thinking and learn how to express their ideas in more abstract ways, for example, by using symbols. Explanations should include the "why" and not just the "how" of the problem-solving process.
Problem Solving and Connections
As students work to solve problems through talking and writing about their thinking and listening to the ideas of others, they will begin to build a repertoire of strategies they can use to solve a variety of problems. They will begin to see and appreciate the connectedness of mathematical concepts as well as how mathematics is used outside the classroom in all aspects of everyday life.
A classroom that encourages communication