A few years ago I had my ideal teaching position. My official assignment was Grade 7 and 8 Math but I also had the semi-official title of Math Leader in our biggish Grade 6-8 middle school. In that role, I could share, guide, and wonder out loud from amongst the group – a slight but powerful difference from my current role as a Math Coach. As a fellow classroom teacher, I know the challenges and stress of a typical day. I might have a warmer reception when offering ideas in lesson planning than someone who “doesn’t get what happens in a real classroom”. In that role, I would occasionally go to professional development sessions at the central office and bring back news, ideas, initiatives and the like to the teachers of math at home base. I was the contact at the school to receive math mailings and resources, and would always be called on to host an informal professional development session or facilitate discussion in-house when school-based PD days happened several times a year. It was in the planning and execution of one of these sessions for teachers that I discovered a new teaching move to add to my tool kit…

I was swamped with work. (Aren’t we always!?!) The school-based PD session was next week and it was on my mind. My principal hadn’t asked yet if I would lead a conversation with the math group – but I knew it was coming. If I was exhausted and overwhelmed and I only had two different classes to prepare for – how were the other teachers feeling right now? Some taught Grade 6 – a level of preparation that is impossible for me to wrap my head around – all core subjects with the same group of children for the whole day…I get tired thinking about that work load. Others in our group taught math, science, healthy living, physical education, core french, or any combination of these. If I was taking some of their valuable time and hoping to make an impact, this session had to be relevant, had to be something they could and would want to use in their classrooms immediately, and had to help unite us as a group of learners on equal footing. I wanted us all to work on a question – but not in an ‘*I’m the teacher – look at what you can learn from me’ * way. Something interesting but not intimidating, satisfying but not stressful. Do some math together to have that shared experience but an idea applicable to every or any math topic. And I wanted to show and talk about some actual student work too…Hmmmmmmm.

Luckily a problem I was working on with my students that week gave me an idea. Check it out:

We could work out this problem, discuss and share our work and reasoning, then have a look at some carefully selected student work that would generate some great conversation. Not groundbreaking I know but I wanted to model the way we discuss, revise, and edit in my class. Students often review each others’ solutions, offering feedback for clearer communication, then we incorporate some of those ideas, rework, and share. My students and I saw so many cool ideas this way: different methods to solve and different methods to organize. It was a newer practice for me as well and was so successful in my classroom that I wanted to share it – but not in a show-and-tell way. I wanted the session to mirror what happened in class. And by using a cool problem from the University of Waterloo’s Problem of the Week archives, I could show teachers a spot to look for more awesome problems they could use in the future. While there was only one correct answer for this problem – there were lots of ways to go about arriving at the solution and showing and organizing your work. Teachers might then see that offering just their own solution at the board in a this-is-how-you-do-it kids! kinda way might be lacking. There. Decided. A quick prep for me – just select some sufficiently diverse student solutions to decipher and copy problem sheets for the teachers to use first. I was excited. They were going to love this!

The morning of the session, the teachers filed into the library. I decided to host our session there instead of my classroom. Comfy chairs, softer lighting, we could all sit together around a big table. I had some coffee and muffins, my fun sharp pencils, and my fun sharp problem. I laid out my plan with enthusiasm: let’s all try this great problem first and compare our solutions. Then we can have a look at what some students did with the problem and see where that discussion takes us. I passed out the question, my new pencils, and paused. The vibe just wasn’t right. We were too quiet. Was there nervous tension? I remembered that I wanted us to be conversational, on equal footing. While I taught math all day and had for years, some of these teachers would describe themselves as language experts or science guys. In a split second decision I found a way to equalize and maybe remove some stress. “I think the answer we found in class was 74 square meters – but we can see if that matches what you find and compare how we found it and how we organized our work.” Almost immediately the atmosphere changed. Some teachers started in on their own, others grouped up casually and talked it through together. When people were finished they grabbed a coffee or snack sending the message they were ready for whatever came next. The rest of the session went great. Feedback from teachers revealed that doing the problem themselves first was really helpful. Seeing the different ways teachers and students handled their communication highlighted that there may not be one best way to record your work. Different teachers shared different ideas of what they liked or how they might incorporate what we did that morning. But the best takeaway for me was the power of giving the answer. Could I use this idea with my students?

This really got me thinking. How many times have I lamented that students just wrote down an answer – they didn’t show their work? How many times did my students see a problem and stress about being the last to figure it out or worry that the answer they shared was incorrect? How many times did I SAY we were focused on showing our work but ended up just solving and moving on? Through this reflection one of my favourite number routines was born: **Prove it!** I give any word problem or computation and supply the answer. Then the task was clear. The solution was secondary to the process. Stress removed. Creativity flowed. Variety was expected. Conversations, comparing, and revising were necessary in order to be concise and clear. I don’t do this all the time – but when I am focusing our energy on communication – I do.

I made another realization as well. I was so careful with my colleagues in thinking through the session. What did they need? What was relevant to them? Would this activity have an access point for everyone? Could everyone find something here to move their practice forward? Did we have supplies? Snacks? Could we all sit together? I realized that I needed to be this intentional when planning for my students as well. What did each of my lovely kids need each day to be successful? What could I give them to do so everyone, regardless of their starting point, came out of the lesson with some growth?

While I have had some classes where the lessons were just stellar I have also had classes where the best I could do that day was give 10 problems to try from a worksheet printed from the internet, found and copied minutes before students arrived. I’m human like everyone else. I remember one such occasion passing out a boring worksheet and realizing when students had it in their hands that I copied the sheet with the solutions given instead of the front side. One student said (a little too triumphantly), “Uh Mrs Sandford – you made a mistake! The answers are all here!”

“Nope kids”, I countered, “I meant to do that”.