Iowa Core Curriculum - ....Ability to Construct and Apply Multiple Connected Representations

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Mathematics

Essential Skills

Ability to Construct & Apply Multiple Connected Representations

All students should be able 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

"The ways in which mathematical ideas are represented is fundamental to how people can understand and use those ideas. When students gain access to mathematical representations and the ideas they represent, they have a set of tools that significantly expand their capacity to think mathematically" (NCTM, 2000, p. 67). Students should be able to choose appropriate representations in order to gain particular insights or achieve particular ends. Students should understand that different representations represent different ways of thinking about and manipulating mathematical objects. An object can be better understood when viewed through multiple lenses. As students encounter new representations for mathematical concepts, they need to be able to convert flexibly among those representations. (Adapted from NCTM, 2000)

Implications for Curriculum, Instruction, and Assessment
Teachers should introduce students to multiple connected mathematical representations and help them use those representations effectively. They should highlight ways in which different representations can convey different information and emphasize the importance of selecting representations suited to the particular mathematical tasks at hand. Assessments should allow for students to have choices when representing problems and solutions. Students should be encouraged to evaluate which representation is best to use when solving a problem or investigating a mathematical idea. (Adapted from NCTM, 2000)

"Representations should be treated as essential elements in supporting students' understanding of mathematical concepts and relationships; in communicating mathematical approaches, arguments, and understandings to one's self and to others; in recognizing connections among related mathematical concepts; and in applying mathematics to realistic problem situations through modeling. New forms of representation associated with electronic technology create a need for even greater instructional attention to representation." (NCTM, 2000, p. 67)