Defining Representation
 The Representation Standard | Connections | Structure | Additional Points | Summary | Your Journal
"Mathematics is one of humankind's greatest cultural achievements. It is the "language of science," providing a means by which the world around us can be represented and understood. The mathematical representations that high school students learn afford them the opportunity to understand the power and beauty of mathematics and equip them to use representations in their personal lives, in the workplace, and in further study."

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Why does this standard matter? The effort to expand students' facility with representation pays off in many ways. Representations tend to help students identify the pertinent facts of a situation, organize their thinking, and remember effective strategies and important concepts. Students who can develop and interpret a variety of representations are likely to have greater success in present and future mathematics coursework. They are also better prepared as citizens and as future workers.

Representations, whether visual, symbolic, verbal, or in other forms, are an important tool when solving problems. They allow us to identify patterns and relationships, and to interpret and manipulate the given information to reach a solution. When using representations to solve a problem or make sense of a new concept, a student is likely to go back and forth, using the representation to help clarify the problem and using the problem to extend understanding of the representation. Through this process students become able to move among different representations, choosing forms as needed for the problem-solving task at hand. Fluency with representation also provides a means to self-monitor in problem solving. For instance, the reasonableness of a conjecture based on looking at a data table can be tested by looking at the same data in a graph.

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