Week 2 #MTBoSBlogsplosion: Building Our Mathematical Identities

“We teach who we are.”

My favorite part of my job is being in classrooms and working with teachers and students supporting mathematics teaching and learning. I’m inspired every day by students and teachers. One of my goals is to change how students, teachers, and parents experience mathematics, in essence, change the culture of how we see, think about, and engage around this subject.  I want mathematics to pique curiosity and make sense, and for our student- and teacher-mathematicians to reason and think critically and deeply. And, I want us all to see the mathematics around us; it’s everywhere! We all know friends, family, co-workers or acquaintances who don’t identify themselves as mathematicians. For some, mathematics was lorded over them, and they may have a phobia of mathematics due to what Jo Boaler (@joboaler) refers to as “math trauma” they suffered along the way. Knowing no other ways, we often teach how we were taught.

I encourage teachers in taking risks and I share bite-sized ways to “hack” math class. I know the term “hack” might offend some and I don’t mean to do that, or to underestimate the immense expertise involved in teaching. Teaching is complicated work. Most teachers don’t want to change everything but will try something. Hence, the use of “hack.” I leverage a few instructional activities, predictable routines (IAs) that have a high yield in terms of student learning and opening up mathematics. Giving teachers choice in where they’ll begin gives them control and ownership.

In some classes, those hacks start by changing one aspect of a lesson by using IAs such as Quick Images, Number Talks, Counting Collections, Mathematizing Read-Alouds, Numberless Word Problems, Noticing and Wondering, etc. to nurture number sense and problem solving, engages students in the Standards for Mathematical Practice, and build a community of mathematical thinkers and problem solvers. In my own practice, I started with Number Talks. What I learned was invaluable: how to listen to my students and to see and understand math how they saw and understood it. This changed everything, and I want other teachers to experience this. In other classes the hack might start with flipping the problem solving; engaging students in problem solving (using the strategies of Noticing and Wondering or Numberless Word Problems) first rather than after they “know the skills.”

Together we work through the emotional challenges of change and not knowing where that change might lead. While hopeful for what these changes may bring about, there are also concerns. Concerns worth addressing: “How will I respond?” or “What will I say, or ask, next?” Additionally, we tackle the content and pedagogical impacts of opening up the mathematics and shifting the ownership of the knowledge to the students. For example, when planning with teachers around addition and subtraction, I wonder aloud with them if it is always (or ever) necessary to subtract? Are there times they might want to add up/on instead? As teachers try these “hacks” the students respond: they want more! “This is math?” they say when engaging in a Number Talk! Yes, in fact, that is math! “When can we do that again?”

In The Heart of a Teacher: Identity and Integrity in Teaching the author, Parker Palmer (@parkerjpalmer), starts off with, “We teach who we are.” If this is true, then I want teachers to identify themselves as mathematicians. Only then can we hope to build our students’ identities as mathematicians allowing them to see the beauty and joy of mathematics. Coming alongside, and investigating mathematics and students’ thinking around mathematics, we are learning together and changing our identities. Sharing our successes and challenges with our peers continues to shift our mindsets.

I wonder what has worked for you in supporting others in building their identities as mathematicians, or in building your own? I’d love to hear from you.


Week 1 #MTBoSBlogsplosion: One of my favorite sites–WODB

“That one doesn’t work. There are only two that have flat surfaces that are circles.”

This is my first attempt at blogging. I have been thinking about it for a long time and realized I was spending too much time pondering the title of my blog, the topic for my first post, etc. All things that don’t really matter. Thanks to some advice on exploring the MTBoS,  and some encouragement from colleagues, I decided to stop pondering, dive in, and continue to build the site as I go. I joined Twitter in April 2015 just before arriving in Boston, MA for the Annual NCTM Conference. I’m still learning about Twitter but have found it, thanks to #MTBoS, to be welcoming and a vital source of professional growth. I so appreciate #MTBoS for all the support and encouragement in just getting started blogging. They have a great challenge to blog each week in January and even give you prompts to blog about. So, here goes …

I’m interested in creating more opportunities to engage students (and educators) in sense-making, reasoning, critical thinking and problem solving while also engaging their sense of curiosity and wonder about mathematics. With that in mind, I chose WODB as one of my favorite websites. (There are a LOT of great ones from which to choose!)

Every August, I have the opportunity to work with all K – 5 teachers new to my district. Typically, I include  a couple of what I think of as high-leverage instructional strategies. Things like: Quick Images, Number Talks/Mental Math, Noticing and Wondering. This past August, I decided to take a bit more time talking about how teachers can mathematize their classrooms. A colleague pointed out that we spend a lot of time at elementary, typically, creating a literacy-rich environment but not very much time making it a numeracy-rich one. So, I mathematized information about me and turned it into a poster as a way to show teachers how they might share about themselves with their students in a way that highlights mathematics. (Thanks, Pinterest.) I also shared children’s books about mathematics and mathematicians, and estimation 180 and WODB both sites that are highly engaging and get kids and adults talking about mathematics. We discussed ways to build our (students and adults) identities as mathematicians through these various instructional activities.


Fast forward to December. One of my colleagues, Hillary Chandler (@hillylilly) decided to try WODB with her first graders. She chose the image above. Hillary allowed students to digitally ink their ideas about which image didn’t belong. One student started by saying that, “the basketball didn’t belong because it is the only sphere”.

Then crickets. She waited. And waited. Then, Hillary prompted, “What if I said the brownie in the top right didn’t belong. Why might I think that one doesn’t belong?” After some thinking, a student said, “It’s the only one that has vertices.” Students then began making different claims:

  • “I pick the brownie because it doesn’t have two flat surfaces that are circles.” Others pointed out, “That one doesn’t work. There are only two that have flat surfaces that are circles.”
  • “The cookie doesn’t belong because it’s the only one that’s pink.”
  • “I think the cake doesn’t belong because it’s the only one that has writing on it.”

A bit more discussion ensued with ideas being tossed out and then retracted because they “didn’t work.” Students would choose an attribute that only worked for two of the images. One student said that the image he’d picked didn’t belong because it didn’t have a circle as two flat surfaces. Another student said, “That one doesn’t work. There are only two that have flat surfaces that are circles.” Loving this discussion and the students’ use of vocabulary.


What impressed me is their comfort level with sharing ideas with one another and that their peers could push back on thinking, and their discussion of attributes and definitions. Christopher Danielson (@trianglemancsd), in his blog, Talking Math with Your Kids, shares the importance of and ways we can talk math, or mathematically, with kids in order to instill a love of mathematics, reasoning and making and supporting conjectures.

I don’t know about you but my math classes growing up NEVER included anything quite so fun and interesting, which would have nurtured my logical reasoning.

So, I wonder, how do I support more teachers in growing this type of discussion and reasoning in their practice? How do I support Hillary and her students in their growth? I’m curious what you find has helped to engage students in meaningful mathematical discourse and building young mathematicians. I’d love to hear your ideas.

Math on!