Representation

Students should be able to choose specific 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 study new content, they will encounter new representations for mathematical concepts. Students need to be able to convert flexibly among these 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. Teachers should highlight ways in which different representations can convey different information and to emphasize the importance of selecting representations suited to the particular mathematical tasks at hand. Assessments should allow for students to have choices when representing solutions. Students should be encouraged to evaluate which representation is best to use when presenting a particular set of data. (Adapted from NCTM, 2000)

Essential Skills in Representation:

  1. Creates and uses representations to organize, record, and communicate mathematical ideas | Example
  2. Selects, applies, and translates among mathematical representations to solve problems | Example
  3. Uses representations to model and interpret physical, social, and mathematical phenomena | Example