It is important that students understand that the focus is not on who is right or wrong but rather on whether an answer makes sense and can be justified. Students need to learn that mathematical arguments are logical and connected to mathematical relationships. When making a concept or strategy clear to a peer, the student-explainer is forced to reexamine and thus deepen his or her mathematical understanding. In settings where communication strategies are taught, modeled, and expected, students will eventually begin to adopt listening, paraphrasing, and questioning techniques in their own mathematical conversations. Teachers must help students acquire mathematical language to describe objects and relationships.
Specialized vocabulary is much more meaningful if it is introduced in an appropriate context.
In this way, words such as equation, variable, perpendicular, product, and factor should become part of students' normal vocabulary. Teachers also need to provide students with assistance in writing about mathematical concepts. They should expect students' writing to be correct, complete, coherent, and clear. Students will also need opportunities to check the clarity of their work with peers. Initially, when they have difficulty knowing what to write about in mathematics class, the teacher might ask them to use words, drawings, and symbols to explain a particular mathematical idea.