Instructional Shift 3: Use multiple representations of mathematical entities.

Chapter 4: Picture It, Draw It

What should we see in an effective mathematics classroom?

-Frequent use of pictorial representations to help students visualize the mathematics they are learning

  • Discuss with your team the various ways teachers are using pictorial representation to support teaching and learning of mathematics. Ask team members to share ideas and artifacts that support the use of representation.
  • Facilitate a team discussion to identify effective strategies for moving students from concrete representations (manipulatives) to pictorial representations and finally to the abstract representations. Identify key characteristics of strategies that are most effective.

-Frequent use of the number line and bar models to represent numbers and word problems

  • Lead a brainstorming session designed to develop ideas for multiple strategies for using number lines to conceptually develop these topics; number density and between-ness, comparing numbers, whole number and integer operations, rational numbers, irrational numbers, square root and radicals, absolute value, solving equations, measures of variability, box-and-whisker plots, midpoint, distance between two points, and scale.

-Frequent opportunities for students to draw or show and then describe what is drawn or shown

  • Facilitate a team discussion focused on the nature of the tasks typically presented in mathematics classroom. In what ways do these tasks provide frequent opportunity to represent mathematics through drawing, sketches, or diagrams? How are students encouraged to explain or justify their work?