Use Illustrations

The Implementing the Mathematical Practice Standards (IMPS) project has developed a professional development curriculum to support learning about the Common Core’s Standards for Mathematical Practice (SMP) for grades 5–10 mathematics teachers. This professional development experience centers on the use of the Illustrations found on this website, along with student work analysis and instructional planning activities. We anticipate publication of this program by the National Council of Teachers of Mathematics in 2017.

In the meantime, below is a suggested protocol for using the Illustrations from this website for professional learning. The protocol is written for groups of educators working together (e.g., during common planning time) but individuals can also engage in these steps by replacing discussions with reflective thinking and writing time.

Step 1: Choosing an Illustration

As a group, discuss the Standard for Mathematical Practice you are interested in further exploring and choose an Illustration that targets that standard. Alternatively you can browse the Illustrations and choose one based upon mathematical content or task of interest.

Step 2: Explore the Mathematics Task

Take some time to individually work on the mathematics task. Afterwards come back as a group and share your responses. Finally discuss the different ways people approached the problem and the types of reasoning used.

Step 3: Read the Student Dialogue

Either read the student dialogue individually or act out the dialogue using three teachers. While reading the dialogue, you should think about the reasoning used by the students.

Step 4: Group Discussion

As a group, begin by discussing what you see in the dialogue. What types of reasoning did the students use? What behaviors did the students in the dialogue exhibit that you would like your own students to adopt? Next, review the Common Core Standards for Mathematical Practice. Afterwards discuss which of the SMP you see illustrated in the dialogue and why. Finally, discuss the Teacher Reflection Questions in order to 1) further explore the mathematical ideas in the dialogue and 2) engage in mathematics problems that support the mathematical practices.

Step 5: Read and Discuss the Mathematical Overview

Individually read the Mathematical Overview and then discuss as a group your reactions. Some questions to consider include:

  • What mathematical practices were discussed in the Mathematical Overview that you had not initially considered?
  • How did the Mathematical Overview change your thinking about what it means to engage in the Standards for Mathematical Practice?
  • What new ideas, insights or questions did the Mathematical Overview provide you about the mathematical content?

Step 6: Application to the Classroom

As a group discuss how you can apply what you have learned about the mathematical practices to your classroom. Reflect on how you can support student engagement in the SMP when teaching both mathematical content that is similar and different to that in the dialogue. Also think about ways the Student Dialogue and Student Materials (Discussion Questions and Related Mathematics Problems) may be used with your own students.