In order to use representation as a communication and thinking tool, students must be encouraged to go beyond basic work with representation. It is not enough, for instance, for students to be able to follow the prescribed steps for creating a diagram. Students must be actively engaged in developing, interpreting, and critiquing a variety of representations. This type of work will lead to better understanding and effective, appropriate use of representation as a mathematical tool.

We will begin with two examples of student work for you to consider. As you observe these problems, notice the different methods of representing data. Think about the opportunities the students have to learn about graphs and to connect graphic representations to other forms of representing data.

  Observe students working on representing and interpreting data