Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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RepresentationSession 05 Overviewtab atab btab ctab dtab eReference



Representations are useful in all areas of mathematics because they help us develop, share, and preserve our mathematical thoughts. "[They] help to portray, clarify, or extend a mathematical idea by focusing on its essential features" (NCTM, 2000, p. 206).

"Mathematical representation" refers to the wide variety of ways to capture an abstract mathematical concept or relationship. A mathematical representation may be visible, such as a number sentence, a display of manipulative materials, or a graph, but it may also be an internal way of seeing and thinking about a mathematical idea. Regardless of their form, representations can enhance students' communication, reasoning, and problem-solving abilities; help them make connections among ideas; and aid them in learning new concepts and procedures.

Learning Objectives

This session shows you how to help students do the following:

  • Create representations from given data
  • Use representations to develop and deepen concepts
  • Use representations to model operations and solution methods
  • Translate among representations
  • Use representations to communicate mathematical knowledge

NCTM Representation Standard

Instructional programs . . . should enable all students to --

  • Create and use representations to organize, record, and communicate mathematical ideas
  • Select, apply, and translate among mathematical representations to solve problems
  • Use representations to model and interpret physical, social, and mathematical phenomena

Principles and Standards of School Mathematics (NCTM, 2000). For more information on this Process Standard, see the NCTM Web site


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