Descriptive Statement

Communication of mathematical ideas will help students clarify and solidify their understanding of mathematics. By sharing their mathematical understandings in written and oral form with their classmates, teachers, and parents, students develop confidence in themselves as mathematics learners and enable teachers to better monitor their progress.

Meaning and Importance

Mathematics can be thought of as a language that must be meaningful if students are to communicate mathematically and apply mathematics productively. Communication plays an important role in making mathematics meaningful; it enables students to construct links between their informal, intuitive notions and the abstract language and symbolism of mathematics. It also plays a key role in helping students make critical connections among physical, pictorial, graphic, symbolic, verbal, and mental representations of mathematical ideas. When students see that one representation, such as an equation, can describe many situations, they begin to understand the power of mathematics. When they realize that some ways of representing a problem are more helpful than others, they begin to understand the flexibility and usefulness of mathematics.

K-12 Development and Emphases

Communication involves a variety of modes: speaking, listening, writing, reading, and representing visually (with pictures, graphs, diagrams, videos, or other visual means). Each of these can help students understand mathematics and use it effectively. Students should also use communication to generate and share ideas. Communicating with each other, with peers, with parents, with other adults, and with the teacher, orally and in writing, helps students learn mathematics as they clarify their own ideas and listen to those of others. The language of mathematics itself is a thinking tool that facilitates mathematical understanding and connects to natural language and everyday thinking.

Students need to have many experiences in communicating about mathematics in a variety of settings. Some experiences will involve working in pairs; for example, kindergartners can sit back-to-back with one giving the other directions about how to make a tower of Unifix cubes. Other experiences will involve working in small groups, such as when tenth-graders combine information from several separate clues to find the distance around a park. Some experiences will involve explaining something to the whole class,while others may involve drawing a picture, making a model, or writing in a journal.

Students need to learn the appropriate use of mathematical language and symbols. Most experiences relating to mathematical communication will involve the use of natural language, but some will also involve the use of tables, charts, graphs, manipulatives, equations, computers, and calculators. Students should not only be able to use each of these different media to describe mathematical ideas and solutions to problems, but they should also be able to interrelate the descriptions obtained using different media.

In summary, communicating mathematics - orally, in writing, and using symbols and visual representations - is vitally important to learning and using mathematics. Students should use a variety of forms of communication in a variety of settings to generate and share ideas.