Monday / August 15

Supporting New Teachers? Help Them Adopt Four Tried and True Math Routines That Center Student Thinking

Veteran teachers know that routines are set procedures and practices they use frequently to help organize their classroom. When new teachers come into the classroom for the first time, they may learn to use classroom-management routines for taking attendance or having students distribute materials. In math classes, routines can also add ease and efficiency to one’s pedagogical steps, such as having an opening question to start the class or a way to assign students groups randomly for problem solving activities. A new teacher may not leverage their routines every day, but the more they do, the more students become familiar with these consistent and predictable structures and the more they are able to focus on math content and feel safe sharing their thinking with their peers. Routines can also help students stay focused, and engaged, which minimizes disruptions and off-task behaviors. For example, a routine for group work sets up expectations and norms for students in how to share their thinking and work. It sets the expectation that each student must be an active part of any group they are working with. Not only do routines give structure to students, but they also benefit teachers because they can alleviate the need for answering innumerable questions about a classroom process, freeing the teacher’s time so they are able to focus on student work and the feedback they need to give.

If you’re in a position to mentor or coach new teachers in math classrooms, or would like to shore up your own practices, here are some quick-win routines to get you on the right path.

Routine #1: You do-We do-I do

In this routine, the teacher first gives students quiet alone time to wrestle with a problem or task. Next, students are placed randomly into small groups to share their thoughts and to collaborate on different ways to solve the problem. Finally, after sharing out and discussion, the teacher helps the students to make connections among the different approaches and to generalize what has been discovered and learned. This is a student-centered approach that is far more beneficial to students than the traditional I do-We do-You do model in which the teacher demonstrates a procedure or way to solve a set of problems, the students then work on a set of sample problems with the teacher, then the students work on their own. I do-We do-You do does not lead to student interaction or problem solving, and may lead to mimicking the teacher, which at best creates a short-term impression of learning.

Routine #2: Number Talks

Here, students discuss an image, a mathematical expression, something that may be done quickly by individual students. A number talk is meant to be brief, maybe only 5 to 10 minutes. After the teacher introduces a task, students have a few moments  to solve/simplify/and think about it. As students share their thinking, the teacher may act as scribe a recorder of student thinking.  Students listen and ask questions, but do not correct each other. By the end of the discussion, the hope is to have 3 or more different approaches recorded and have students reflect on what they have seen. Examples of number talks include having students solve proportion problems using different strategies (such as tape diagrams, scaling up or down, tables) or considering a prompt such as “What are different ways you can solve 32 x 4 =128 or 2(3x +1) – 4 = 22?”

Routine #3: Which One Doesn’t Belong

Which One Doesn’t Belong (WODB) is a set of four different answers or representations that are designed to be interpreted in different ways. Ideally, all answers are correct, so that students need to justify their mathematical thinking. The discussion for WODB sets forth a classroom culture where each student has a valid response and reason and where students listen to each other, justify their thinking, and make connections among different solution paths.

Figure 1. Example of Which One Doesn’t Belong

Created by Jay Sydow, Lead Teacher for Secondary Mathematics, Lexington County School District One, SC

Routine #4: Why did I choose this one?

Students receive a problem to solve on their individual white boards, devices, or a piece of paper. The teacher selects one answer to share with the class (from an anonymous student) and copies the answer for all to see. Students analyze the response and decide why the teacher chose that answer. The response may be correct and may be a typical solution, the response may be incorrect but contain a common error, or the response may be a non-typical solution path the teacher wants the students to discuss.

Help new teachers understand that it takes time and patience to get students to accustomed to using a routine. They don’t need to try to do more than one at a time, and they can take baby steps. Also help them see that routines are open to adaptation to align with the instructional goals for the day and that over time, they will build a repertoire of routines so they may vary which ones they use.

References and Resources

Routines for Reasoning: Fostering the Mathematical Practices in All Students,

Grace Kelemanik, Amy Lucenta, Susan Janssen Creighton,  Heinemann, 2016

Daily Routines to Jump-Start Math Class, High School: Engage Students, Improve Number Sense, and Practice Reasoning, Eric Milou, John J. SanGiovanni, Corwin 2018

Daily Routines to Jump-Start Math Class, Middle School: Engage Students, Improve Number Sense, and Practice Reasoning, John J. SanGiovanni, Eric Milou, Corwin  2018

Daily Routines to Jump-Start Math Class, Elementary School: Engage Students, Improve Number Sense, and Practice Reasoning, John J. SanGiovanni, Corwnin 2018 2019

Teaching Math at a Distance, Grades K-12: A Practical Guide to Rich Remote Instruction, Theresa Wills, Corwin, 2020

Answers to Your Biggest Questions About Teaching Secondary Math, Frederick L. Dillon, Ayanna D. Perry, Andrea Cheng, Jennifer Outz, Corwin 2022

Answers to Your Biggest Questions About Teaching Elementary Math, John J. SanGiovanni, Susie Katt, Latendra D. Knighten, Georgina Rivera, Corwin, 2021

Written by

Frederick L. Dillon is an author and national mathematics curriculum and professional learning consultant based near Cleveland, Ohio. He is a retired teacher with 35 years of classroom experience, having taught grades 7 through college. Fred is a frequent speaker at national, state, and local conferences and institutes. Fred’s most recent book is Answers to Your Biggest Questions About Teaching Secondary Math, co-authored with Ayanna D. Perry, Andrea Cheng, and Jennifer Outz, which is part of Corwin’s new Five to Thrive Series of books geared toward new classroom teachers or those looking to hone a more student-centered practice in elementary and secondary mathematics, reading, writing, and classroom management.

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