How do I encourage mathematical thinking and communicating in my students?

"...children, in learning to mathematize their world, will come to see mathematics as the living discipline it is, with themselves a part of the creative, constructive mathematical community, hard at work." (Fosnot & Dolk, 2001, p.13)


  • develop a community of mathematicians
  • create a safe environment where risk-taking is encouraged, mistakes are seen as learning opportunities and everyone’s contributions are valued
  • focus on thinking and reasoning, rather than only finding answer
  • value diverse approaches and encouraging flexibility
  • encourage various approaches to communicate and develop mathematical thinking (math talks, think/pair/share, number routines, math journaling, representing with materials)
  • foster multiple learning modalities to “show what you know”
  • responsive teaching-active listening, noticing, observing, guiding, asking prompting questions, providing mathematical language so that student ideas and contributions are central


Develop a community of mathematicians

Innovating the Secondary Math Classroom - OAME 2018 Panel

How are Ontario educators rethinking their secondary math classrooms?

Innovating the Secondary Math Classroom, OAME 2018 Panel

Check out this video showcasing a grade 6 class in the Comox Valley.

Click below for more information:

Laura Wheeler is a mathematics educator in Ottawa, Ontario. She has blogged about thinking classroom, and has created several sketch notes outlining specific aspects of setting up a thinking classroom.


This article was created by the Ministry of Ontario "to spark dialogue and debate on how to develop a mathematical habit of mind, not just for students but for educators as well, to move the math beyond the walls of the mathematics program to teaching and learning across the curriculum and across the day."

"Participating in math class feels socially risky to students. Staying silent often feels safer. In Motivated, Ilana Horn shows why certain teaching strategies create classroom climates where students want to join in.

Five factors of motivational math classrooms

She introduces six different math teachers, in a range of school settings, who found that motivation requires more than an interesting problem. Their experiences highlight five factors that lower the risks and raise the benefits of participation:

  • Belongingness comes from students’ frequent, pleasant interactions with their peers and teachers.
  • Meaningfulness answers the question, “When are we going to use this?”
  • Competence helps all students discover their mathematical strengths.
  • Accountability inspires students to participate in classroom life.
  • Autonomy produces learners with tools for making sense of their work and seeing it through.

These features of motivational math classrooms are explored in-depth. You’ll find suggestions for identifying what impedes each factor, along with strategies for weaving them into your instruction. You’ll also be introduced to an online community who support each other’s efforts to teach this way.

Create a safe environment where risk-taking is encouraged, mistakes are seen as learning opportunities and everyone’s contributions are valued


Tracy Zager's book, Becoming the Math Teacher You Wish You'd Had, offers numerous strategies to encourage mathematical thinking and communicating in classrooms. Along with the book, there is a study guide and a companion website to guide discussion and conversations between educators.

"BC educators will find Zager’s book profoundly helpful in making sense of the pedagogical shift in our mathematics curriculum, particularly in the shift from context as the main focus, to giving the big ideas and curricular competencies equal weight with content. Through Zager’s easy-to-read text, educators will learn practical ways to bring to life the habits of mathematicians."

Jen Barker, Vector magazine, Spring 2018,