The first session I attended at OAME 2018 was “How do you
Visual Pattern? Exploring HOW we do what we do” with presenters Jimmy Pai
(@PaiMath), Alex Overwijk (@AlexOverwijk) & Nat Banting (@NatBanting). I
had signed up for this session because I was intrigued by the idea of exploring
the “HOW” with this team and fellow participants.

We were quickly divided into visibly random groups (Alex
handed out playing cards and we grouped by number at the whiteboard that had
that number) and worked on vertical non-permanent surfaces (whiteboards).

The problem posed was the following:

My group of three included an elementary math coach with
most recent classroom experience in kindergarten, an elementary school
principal and I am a high school math teacher. The diversity in our group led
to very rich discussion. One question we wrestled with in our group was: when is the first
term labeled “term 1” (

*t*_{1}or*n*= 1) and when is*x*= 0 (*t*_{0})? How does this affect the equation? When do we have this conversation in grades 7-11 math?
As we were working, Jimmy came around and listened in on our
conversation. After we had explored the linear and exponential cases, he asked
us what might happen if these weren’t

*t*_{1}and*t*_{2}. Our group chatted about cases where the picture above showed*t*_{1}and*t*_{2}, and terms*t*_{3}and*t*_{7}. We went down a rabbit hole of thinking about how to represent negative numbers.
It was interesting to "play" with this problem, but the real value in this session was when Jimmy, Alex and Nat
took a “time out” from the problem to make their teacher moves intentional
after we had played with the problem for a while.

Some of their intentional
moves were:

- To display the question on a slide because they way they would have drawn squares in front of us may have influenced what we viewed as “unit” (either each small square as a unit, or taking the group of four small squares as the unit. In this way, they left the thinking about what was “part” and what was “whole” to the groups.

- To display the slide for a few minutes then remove it. They wanted us to see the pictures, but once we had processed what the first two terms looked like, they wanted to remove the “tether” to the projected image in order to have groups focused on their own work rather than looking at the slide.

- I noticed all groups had one black marker. When Jimmy came around to our group, he made two notations on our work using a green marker. I believe this was to distinguish his “teacher” notations from our “student” notations to inform his future decisions in consolidating the learning.

After this discussion, we were asked to think about WHY we might visual pattern and HOW we might visual pattern. What is the purpose of this activity? What might our own intention be with this prompt? There’s lots to think about: intentions might be to focus on math processes, classroom norms, connecting different representations, specific content outcomes or other things.

We were given time to think about possible introductions to
the task. Would we reveal the pattern (pre-drawn) or draw it on the board?
Label the term numbers or leave them unlabelled? Use an increasing pattern or a
decreasing pattern? Use manipulatives or do this activity without
manipulatives?

In addition, we were given time to discuss what students
might do or ask with this prompt, and how we (as teachers) might respond:

And how we might consolidate the learning:

__intentional__about the choices we make with everything we do as teachers from choosing a question (focus on classroom norms? math processes? specific content?), how we respond to students' questions, and how we help students consolidate their learning. And the importance of coherence in the many, many, many decisions we make before and during each class period.