Cultivating Mathematicians… of All Ages

Original published for @autismplusmath ‘s Guest Blogger Week at:

“I mean, you know… I’m not a math teacher,” said Jessica*, who teaches Kindergarten.

She didn’t whisper this confession in an empty classroom, or bury it in a long paragraph in an e-mail. She said it loudly. Plaintively. In the faculty room. Because she believes it’s true.

I wrote about some experiences collaborating with Jessica (and her kindergarten mathematicians) in the blog posts about kindergarten geometry (Same or DifferentShape Hunt, Mathematical Connections in a Kindergarten Science Unit). Look at the way that Jessica helped her students build understandings, and make their thinking visible. Jessica is decidedly a math teacher.

In preparation for the return to school in the new year, I reread the beginning of Kassia Wedekind’s Math Exchanges. (Kassia can be found on twitter at @kassiaowedekind.) One thing I love about Kassia’s book is that it is profoundly respectful of mathematical learners — of all ages.

In the first chapter, “Creating Space for Math Workshop,” Kassia writes about classroom culture that breeds opportunities for learning.

“In math workshop, learning occurs when children are actively engaged in their environment and create a system of meaning and deep understanding. Within this framework of learning and teaching, teachers are not the guardians of knowledge whose job it is to pass down information held sacred and untouchable under the rules that govern math. Quite the contrary.

Kassia Omohundro Wedekind, Math Exchanges, page 9

Kassia describes the role of the teachers and students in math workshop — no matter what format or definition of workshop is being used (page 7).

Kassia Omohundro Wedekind’s Math Exchanges, page 7

Look at those first two entries for teachers and students! I had to read it several times before moving on.

Teachers should identify themselves as mathematicians who are continually growing and learning.

Students should see teachers not as a source of mathematical knowledge, but as fellow mathematicians who are continuing to learn both inside and outside the workshop.

Teachers should believe that all students are powerful mathematicians and treat them as such.

Students should identify themselves as mathematicians who have valuable ideas to contribute to the field of mathematics.

What does that mean for a coach?

I work with plenty of teachers like Jessica: strong classroom leaders, who, for some reason or another, do not consider themselves to be a real “math teacher.” It’s my job to illuminate the work these teachers do that makes them math teachers.

“When I first began teaching math I fully believed that if I only explained a concept clearly enough and provided enough engaging experiences to reinforce the math skills I was teaching, all of my students would learn. It took me a while to realize that this approach simply wasn’t working for all of my learners and did not support the development of strong mathematicians.”

Kassia Omohundro Wedekind, Math Exchanges p. 9

I see all of these beautiful strengths in Jessica’s instruction. She listens to students. She makes sense of their thinking, and helps them make it visible, often for the whole class to digest. Jessica supports making connections across representations, and across mathematical ideas. 

Jessica might not know the same for a 12-sided polygon, but what qualities in a teacher are high leverage when it comes to student learning? It’s hard to learn how to listen. It’s easy to google “name of a 12-sided polygon.”

Kassia wrote about the use of “mathematician statements” in Math Exchanges. I wrote about the idea in a blog post, too, in the context of the presentation I gave with Heidi @heidifessenden at NCTM Hartford 2018. 

Mathematicians take notice of patterns and relationships between numbers.

Mathematicians make connections to problems they’ve seen before.

These are also true of math teachers. More additions:

Math teachers listen to student thinking.

Math teachers support students in making their thinking visible.

Math teachers pose purposeful questions.

Math teachers facilitate meaningful mathematics discourse.

The last two came directly from the 8 Effective Teaching Practices in NCTM’s Principles to Actions (2014). They are statements I wholeheartedly agree with, and also ones that may feel less accessible to teachers like Jessica. They’re more formal. What if we started with things like:

Math teachers ask questions that get students to pause.

Math teachers encourage students to talk about their ideas with one another.

…and then connected these back to the 8 Effective Teaching Practices.

I wonder how, as a coach, I could build these math teacher statements strategically, to support all teachers in developing a math teacher/learner identity, while also celebrating that there are ways to grow.

Because Jessica is definitely, unequivocally, without-a-shadow-of-a-doubt a math teacher.





  1. Some students also think they are “not good at Maths” and we, teachers, can help them “see” the Maths in their thinking


    1. Absolutely!

      I like to use the five equity-based mathematics teaching practices from The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices (Aguirre, Mayfield-Ingram, and Martin, 2013). They are:

      – Going deep with mathematics
      – Leveraging multiple mathematical competencies
      – Affirming mathematics learners’ identities
      – Challenging spaces of marginality
      – Drawing on multiple resources of knowledge

      I think these are true for educators, as well. In order for teachers to be able to develop a positive math identity, and to continue to grow in their practice, they need to feel affirmed.


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