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March 3, 2021

6 Routines to Support Mathematical Thinking

Whenever I take a new teacher to observe a veteran teacher, I’m surprised at what they notice. We could have observed the most impressive lesson ever, but without fail the new teachers notice the little things in the classroom: the way the chairs are set up, the routine the teacher has established for collecting work, the posters on the wall. They inherently know that seemingly small details can make or break teachers.

Back in July, Teaching Channel released a video series produced with the American Federation of Teachers showing how the Common Core math practice standards progress across the grades. This series is one of my favorites; in each classroom we watch students collaborating, explaining their reasoning, testing their ideas, and enjoying the problem-solving process.

If you’re like me, as you watch these videos, you will find yourself wondering how the teachers got their students to this point. What had happened to help students become independent problem solvers who could apply math to real life? Of course there must have been tons of rich math instruction, practice, guidance, and modeling. But there is something else going on in these classrooms — each teacher established routines and norms that support students to develop critical thinking skills.

The videos below are all under 3 minutes and highlight some of the strategies that form the foundation for inspiring math learning:

Organization, Organization, Organization

Seating Arrangements

1. Think about seating. When I was a beginning teacher, I quickly found out that having an entire class get out of their seats to simultaneously get scissors was not efficient. Fourth and fifth grade teacher Amy Spies developed a great system for keeping students and materials organized: creating seating arrangements with workstations. By keeping materials close at hand, students are set up for success before they even start working.

2. Take notes. As we all know, organizational tools aren’t just for students. Middle school math coach Audra McPhillips shares how she uses clipboards as a tool for informal assessment. So often I’ve walked around and conferenced with students without taking helpful notes. The clipboard system Ms. McPhillips uses would have enabled me to effectively record and respond to student learning needs.

Use Color

Problem-Solving Tools

3. Use color. Ms. McPhillips is full of useful tools. In this video, she shows us how she encourages her students to use color to organize and show their mathematical thinking. By helping students see color as a thinking tool, Ms. McPhillips helps students learn to communicate their thinking in multiple ways.

4. Take a moment. Fourth grade teacher Becky Pittard shares an interesting strategy for setting students up for successful collaboration. Ms. Pittard developed a routine where all students get “think time,” a chance to work independently before working in groups. This practice allows students a chance to practice learning both on their own and with a group. It’s interesting to see how incorporating independent learning time enriches group collaboration.

Math Passion

Creating a Joyful Math Culture

5. Believe that math is fun. Becky Pittard is one of the most enthusiastic teachers I have seen; her ability to inspire students to engage in complex mathematics is remarkable. I believe that the perseverance and problem-solving skills that her students exhibit are a direct result of Ms. Pittard’s commitment to helping her students become passionate about mathematics. Watch how she does it!

6. Make it real. Another part of the engagement puzzle is connecting learning to life outside of the classroom. First grade teacher Jeanne Wright explains how she encourages students to see math in everyday life. We get to see how this strategy takes shape in high school as Peggy Brookins and Raymond James help students apply their knowledge of trigonometry to real-life scenarios. It’s great to get a glimpse into how to develop a culture that supports passionate and engaged mathematicians.

Thinking about the infinite layers of teaching makes my head spin. Teachers need to constantly think about differentiation, assessment, transitions, and about four hundred other things. Establishing a solid foundation of routines makes it possible for teachers to do complex teaching. And with the addition of one essential ingredient (JOY!) students are prepared to engage in complex learning.


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