According to Amy Lucenta, Grace Kelemark, Claire Nuchtern in their NCTM 2017 presentation, "Students do well with this routine because it's predictable, combats learned helplessness by inviting multiple sensing modalities and habitualizing "ask yourself" questions, articulates features of structure so that they are not "magic" or disconnected, places a premium on processing time and modalities, and provides opportunities to develop and practice language.

The primary goal of the Connecting Representations Instructional Routine is to expand students' repertoire of structural noticings, SMP #7. This routine positions students to think structurally as they connect two representations by articulating the underlying mathematics.

There are five key steps to this instructional routine: Think, Make Connections, Share and Study Connections Create Representations, and Reflect on Learning. Each section provides a space for students to either think individually, with a partner or with the whole class about the mathematics, and how they and others are communicating their reasoning.

the first step in the routine is to have students ask themselves if there is another way to think about the number, expression, or visual.

The next step creates a space for students to think language and incorporate their thoughts and mathematical representations (such as the use of visuals, numerical, tabular, written, graphical) with other equivalent representations.

Collaborating is crucial in constructing meaning and understanding of multiple representations. In this phase, students are now asked to share their reasoning with their partner and/or table mates.

As you approach the end of this routine, the fourth section is segmented into time for solo reflection, partner discussion, and whole-class debrief.

After students have formulated their own connections between expressions and visual representations, they are asked to share with a partner.

Before students enter the fifth step of meta-reflection, they should have an opportunity to speak to and/or hear from their classmates about what they noticed and learned.

the Meta-Reflection is critical in creating a space for review of conversations, revisit ideas, and affirm the new connections between visuals and expressions made during the routine.

Remember, "Students do well with this routine because it's predictable, combats learned helplessness by inviting multiple sensing modalities and habitualizing "ask yourself" questions, articulates features of structure so that they are not "magic" or disconnected , places a premium on processing time and modalities, and provides opportunities to develop and practice language."

This info-graphic shows the flow of the Connecting Representations Instructional Routine. Take a minute to review it.