# Mathematically Productive Instructional Routines

When we embed routines into our classrooms, we free up space in our minds and schedule to focus on learning while encouraging growth in the routines themselves. Through purposeful use, routines can support all students in their mathematical development.

Mathematically Productive Instructional Routines (MPIRs) are research-based instructional practices that position student ideas as central, make student thinking visible, and provide opportunities for mathematical discourse, thereby allowing space for students to make sense of mathematics. Engaging in these routines can inform teachers’ instructional practice, mathematical content knowledge, as well as beliefs about what mathematics is and who can do mathematics. Additionally, these routines engage students in the Fundamentals of Learning: making meaning, participating and contributing, and managing learning (Heritage, et. al, 2013).

Mathematically Productive Instructional Routines can be implemented with students in any grade from preschool to college. MPIRs often take place at the beginning or end of a math lesson as a launch or synthesis activity. Because the routine is often independent from the mathematics in the core lesson, in the elementary grades the routine can take place any time within the day. It is appropriate to use routines daily, and recommended that they occur often.

# What are they?

Mathematically productive instructional routines are short (5–15 minutes) learning activities that teachers and students engage in together on a consistent basis so that the activity becomes routine. They have a regular structure for interaction among teachers and students, and can be used across content and grade levels for a variety of instructional objectives (Lampert, 2010).

# Why are they important?

A number of researchers have recently begun to identify certain instructional routines, aligned with the rigor of the State Standards and the NCTM Mathematics Teaching Practices, that “can significantly affect the quality of teaching and subsequent learning of students” (Heibert & Morris, 2012). Mathematically productive instructional routines make students’ mathematical thinking visible and require teachers to pay attention to, build on, and respond to student thinking. Using such routines frequently can support the development of a classroom culture in which sense-making is at the heart of all activity, and mistakes are “expected, respected, and inspected.”

# What makes a routine an MPIR?

While there are several different formats for these routines, all Mathematically Productive Instructional Routines share these common attributes:

**They are routine**. MPIRs are brief and used frequently. Students and teachers engage in these activities often enough that the routine itself is learned and can be engaged in quickly and meaningfully. The predictable structure creates a safe time and space for students to take risks and explore and share their ideas.**They are instructional**. While classrooms also rely on routines designed to manage student behavior, transitions, and supplies, MPIRs are routines that focus on student learning. MPIRs provide an opportunity for students to share their mathematical ideas and make connections and deepen understanding as they listen and respond to other students. These routines also provide an opportunity for the teacher to assess and stimulate student learning.**They are mathematically productive**. Prompts for each MPIR are carefully chosen to engage students in making sense of important mathematics content and allow opportunities for students to enact the Standards for Mathematical Practice. Student discussions highlight central mathematical ideas. Students gain important insights and develop positive dispositions about engaging in mathematics through their participation in MPIRs.

While implementing these routines in the classroom, teachers can learn, practice and reflect on key components of effective instruction. Strategies for supporting productive mathematical student discourse are embedded in these routines through talk moves and questioning strategies. The routines are structured to invite and enable more students to participate in and contribute to the mathematics learning in their classrooms.

As teachers and students engage in Mathematically Productive Instructional Routines on a regular basis, the process will become routine for both. As a result, teachers will be able to focus attention on students’ thinking, as well as notice instructional moves that make that thinking central and draw it out. Students will then make meaning, participate & contribute, and manage their learning. They will develop conceptual understanding of rich, relevant, and meaningful mathematics, see themselves and others as capable and competent in mathematics, and expand their view of mathematics and what doing mathematics means.

# Examples of Mathematically Productive Instructional Routines:

| Clothesline Number Talks |

Notice and Wonder | |

My Favorite kNOw | |

Ten Minute Talks | |

Which One Doesn’t Belong |

# Attribution and License

Attribution

- Clothesline: Image by Aktim from Pixabay
- Doesn't Belong
**:**Photo by**Karolina Grabowska**from**Pexels** - Ten minute talks, favorite kNOw, notice and wonder, and number talk: Photos by Allison Shelley for American Education: Images of Teachers and Students in Action.

All MPIR examples are linked to The Learning Space, a professional learning portal created and jointly sponsored by OSPI/AESD Statewide Network.

License

Except where otherwise noted, this work by the Washington Office of Superintendent of Public Instruction and the Washington Association of Educational Service Districts is available under a Creative Commons Attribution License. All logos and trademarks are property of their respective owners.