Teaching Math: The Importance of Instructional Routines

Instructional routines are gaining popularity in mathematics classrooms. They’re effective best practices that help teachers engage students in the Mathematical Practices and increase students’ mathematical understanding. According to a 2009 article by Magdalene Lampert and Filippo Graziani, “Instructional Activities as a Tool for Teachers’ and Teacher Educators’ Learning,” instructional routines are designs for interaction that organize classroom activities. They are meant to be repeated, and this repetition makes them very effective vehicles for developing mathematical practices (see Routines for Reasoning: Fostering Mathematical Practices in All Students). Their predictable design provides a number of benefits to students and teachers, including:

• Making interactions between students, between students and teacher, and between students and the mathematics purposeful, consistently executed, and easier to manage
• Freeing up students’ brain space so they can focus on the mathematical tasks at hand, rather than classroom instructions and processes
• Freeing up teachers’ brain space so they can focus on eliciting and using evidence of student thinking
• Supporting educators in developing their mathematical teaching practices—especially when those teaching practices are intentionally woven into the design of the routine

NCTM’s Effective Teaching Practices give educators instructional routines that contain high-leverage teaching moves. For example, the Try–Discuss–Connect routine promotes the facilitation of meaningful mathematical discourse as described by NCTM by including Individual Think Time, Turn and Talks, and the Four Rs (repeat, rephrase, reword, record) to ensure all students are reasoning and communicating mathematically.

Teacher Moves That Engage Students in Discourse and Mathematical Thinking

Mathematical discourse is a powerful sense-making tool, but it doesn’t just happen. Students must develop both the inclination and habit of attending to each other’s mathematical ideas, and they must have the time and space to make sense of, critique, and develop the ideas. Teacher talk moves are crucial supports for developing students’ capacity to engage in productive mathematical discussions. Let’s unpack the three talk moves in the Try–Discuss–Connect routine that work in concert to ensure all students are taking up and talking productively about one another’s mathematical ideas.

Individual Think Time

Individual Think Time provides students a short time—typically 10 seconds to two minutes—to think about a question or problem before discussing with a partner, a small group, or the whole class. This private processing time significantly increases both the quantity and quality of student talk because it gives students time to make sense of the question or problem and begin to gather their thoughts and questions.

Turn and Talk

A Turn and Talk gives students an opportunity to share their thinking or ideas with a partner. Teachers often use this teacher move to prepare students for a full group conversation or when students go silent during a whole class discussion. It provides a safe space for students to work through ideas, questions, and language, and it ensures all students—not just the fraction of students who speak in a whole class conversation—have opportunities to “talk math.”

The Four Rs

The Four Rs—repeat, rephrase, reword, and record—is a strategy that strings together discrete talk moves in order to support students in processing information shared in classroom conversations and help them develop mathematical understanding and the language to communicate it. In Routines for Reasoning, the Four Rs are called “an essential strategy for helping students make sense of classroom discussions.”

The goal of these three teacher moves is to engage each and every student in productive mathematical discourse. As such, the focus of each is sense making, rather than merely answer getting or answer telling. They provide the time, structure, and support to engage students in the co-construction of mathematical ideas and understanding.

This post was adapted from Integrating Effective Teaching Practices: Teacher Moves That Engage Students in Discourse and Mathematical Thinking. To learn more on how to implement mathematical discourse in your school or district, click below to download the whitepaper.

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About Grace Kelemanik

Grace Kelemanik, M.S.T., has worked in education for over three decades. She is a cofounder of Fostering Math Practices, an organization that provides mathematics educational resources, training, and collaboration opportunities. She frequently presents at national conferences once worked as a high school math teacher. Grace is a coauthor of Curriculum Associates’ i-Ready Classroom Mathematics and Routines for Reasoning: Fostering the Mathematical Practices in All Students. You can find her on Twitter @GraceKelemanik.

About Amy Lucenta

Amy Lucenta, M.Ed., has extensive K–12 mathematics education experience, which includes a focus on special populations. She is a coauthor of Curriculum Associates’ i-Ready Classroom Mathematics and Routines for Reasoning: Fostering the Mathematical Practices in All Students. She is also a cofounder of Fostering Math Practices, an organization that provides resources, training, and collaboration opportunities for anyone interested in helping all students learn to "think like mathematicians." You can follow Amy on Twitter @AmyLucenta.