Wondering about Wondering with Math Coaches

Once a month, Polly Wagner and Marta Garcia host a Virtual Math Coaching PLC (Professional Learning Community). (reference 1) Polly is a math coach and consultant in Massachusetts, and Marta is a math coach and consultant in North Carolina. Both are also instructors with the Math Leadership Program at Mt. Holyoke. This year, with a focus on access and equity, Carly Albee (one of my colleagues in the Math Leadership Program at Mt. Holyoke) and I were invited to co-host and share our fall action research with attendees.

We began with inviting coaches to engage with this image (reference 2):

We invited them to observe and think about what they noticed. Take time to do this yourself before reading on! Please share an observation in the comments section.

Here are some of the types of observations shared:

• squares, triangles, and shapes composed

• overlapping squares

• patterns of squares

• shapes appearing to move in and out

• lines of symmetry

• the illusion of 3D shapes

Then we invited the coaches to wonder. Paul Lockhart writes that mathematics is about “asking simple and elegant questions. . .crafting beautiful explanations.” I love his phrase “amusing yourself with your imagination.” (reference 3) What a dream fulfilled it would be for me if one day a student came up to me and said, “I am amusing myself with my imagination!”

The coaches then shared one burning question. We then invited them to choose one question (their own or another’s) to investigate in a small group, and we grouped them by type of question. Some people discussed area questions, some shape questions, and so forth.

I was able to pop into a few different breakout groups and was blown away at the interesting and varied discussions taking place. So many fascinating questions and ponderings were being shared. It was exhilarating hearing things that I had not noticed or considered myself. One group was considering whether symmetry was bound by color. Another was trying to determine how many squares there were. Yet another wondered about what would happen if you built the pattern out to be larger. This experience caused increased curiosity for me, which I find as essential to a good life as laughter.

The whole idea here was to offer a shared experience, gather the coaches reactions, and then share what we do regularly with our students. People used words like “freeing,” “exhilarating” and “eye-opening” to describe their experience. This is what we had hoped for!

The notice/wonder routine is not new, however Carly and I offered different and deeper ways to support children in broadening their sense of what mathematics is, and deeply engage as mathematicians in observing, asking questions, and pursuing those questions. (I will write more about this in future posts as I share some work done with my students.) Note: Carly is working on creating an online resource for doing this type of work with children. I will share this on my blog when it is ready!

In my experience teaching Kindergarten, children have a more full sense of what a reader or writer is. However, they often lack a complete or full sense of what it feels, looks and sounds like to be a mathematician. The words mathematicians use to talk about the discipline of mathematics are often quite different from those used by children (and parents). Even as young as 5 years old, at the beginning of Kindergarten, I hear children say things like, “math is well doing math,” or “we do equals,” or “we do 3 plus 2 equals 5.” This deeply saddens me. They seem to know a very tiny slice of the pie of mathematics. My “wondering workshops” are designed to help them experience and enjoy more of the pie. To feel freedoms and joy not often associated with math by children.

Children after all, are actually born with curious minds, they ask a billion questions, wonder about their ever-growing world, and they like to play. Interestingly, these are many ideas often used by mathematicians to describe doing mathematics. I mean stop and really think about this for a moment. What in the world do we do to children, to mathematics, that many end up talking about math as boring? Or they think it’s about getting answers quickly and following rules and procedures the all mighty teacher with the red pen told them to follow….in a neat little box.

As we wrapped up our virtual PLC, the attendees shared written feedback. Many people wrote about how this type of work often receives comments like, “these would be great but not enough time.” Many coaches wrote about how this type of work is essential and really disrupts the idea of who can do math, what it means to be “good” at math, and broadens students’ ideas about what math is. Thus, broadening who “gets” to participate in math. This type of work, I would argue, expands access to all students to be mathematicians and see themselves as good mathematicians. This work creates equitable opportunities for students with varied experiences, backgrounds and development to fully participate.

As I continue this blog, I will post more about what is happening in my classroom. Some very interesting things are happening right now that I would contend is the product in part of my wondering workshops. And...it’s happening with ALL of my students. I feel I must also note here that the math curriculum I use in my classroom is child-centered and offers children genuine opportunities to mathematize. Everything is integrated and connected. (reference 4)

Teaser...my Kindergarten students exploring a purple cabbage (for the second time), noticing the expanding spiral, shapes, and patterns occurring.

Stay tuned.

Please share your observations and wonderings or questions in the comments; either about the beautiful math image above, or my post.

References:

1: Virtual Math Coaching PLC through the Math Leadership Program at Mount Holyoke College: http://mathleadership.org/virtual-math-coaching-plc/

2: Florinne Meijer: https://wisknutsels.wordpress.com/2016/02/26/sio-mosaic/

https://www.101qs.com/3144-tiles

3: Lockhart, Paul. A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form. Bellevue Literary Press, 2009.

4. Contexts for Learning Mathematics: www.newperspectivesonlearning.com