* This summer, I spent three weeks in Park City, Utah as part of the Park City Math Institute (PCMI) Teacher Leader Program. PCMI is a teacher math camp of sorts, and is sort of like if PROMYS for Teachers and Twitter Math Camp had a baby. PCMI captures the intense but thrilling mathematical experience of PROMYS with the pedagogical reflectiveness and social bonding of TMC. This post focuses on the pedagogy and socializing. *

**Reflecting on Practice**

Every day, we had 90 minutes of class devoted to thinking about classroom practice. While the facilitators shared many interesting strategies and problems, what stuck with me were questions.

Do my students see themselves as mathematicians? **Do my students see themselves as competent?** How do they define “mathematician” and “competent”? **How do my students know what I value?** Part of how they see what I value is through what I assess and how I grade. **Do I assess what I value?** What do I value? If I value conceptual understanding and application as much as procedural fluency, how do I assess those in kind? Why do I give notes if students don’t look at them? **How do I make notes useful and meaningful?** The only thing that matters about feedback is what kids do with it. **How do I give feedback that students will use?**

### Thinking Classroom

One day, Peter Liljedahl led us in a session on thinking classrooms. I had seen these materials before, but experiencing them and getting a chance to ask questions pushed my thinking forward. I realized that I have been going halfway in my exploration of Vertical Non-Permanent Surfaces (VNPS). I always provide lots of markers to try and get kids writing, but after experiencing it, I see how limiting groups to **one marker focuses the group on one thought**. I have struggled with getting students to stand and work on whiteboards after they sit through my directions, and it was fascinating that **we stood the whole time**! We stood during directions and during the discussion afterward.

I’m left with some questions to ponder:

- If students are supposed to start at their whiteboards, then what is the role of a “warm up”? I asked Liljedahl, and he said that the warm up should just be the first problem, but I’m only sort-of convinced.
- If directions should be given orally, then what about language instruction? I asked Liljedahl, and he said that while it is counter-intuitive, in his research, ELL students did better when presented oral instructions. I am still left to wonder where/when/how to teach language.
- I am intrigued by what Liljedahl calls “meaningful notes” and how they happen toward the end of the class. But taking meaningful notes is a skill. How do I teach it? What can I do at the beginning of the year to show students what this could look like?
- I was surprised how few teachers were compelled to go all-in with the thinking classroom model. For many, the concerns were related to administrative pressure and the practical realities of state testing and class size. I wonder how many teachers would embrace this system if given more pedagogical freedom?

### Working Group

Every day, we had two hours to work on a small group project. My group’s project was called, “Collaborative Planning Protocol for High Cognitive Demand Tasks,” and it included three parts:

- Research summarizing the value of co-planning and high cognitive demand tasks and some of the decisions we made,
- An overview of the protocol, and
- A worksheet to take notes while implementing the protocol.

This project helped me reflect on my experiences co-planning the last two years. We talked about how co-planning the facilitation of a task is far more productive than co-writing curricular materials. We decided to prioritize understanding the math, making the lesson engaging/relevant, and differentiating the lesson.

### Structured Social Time

I was impressed by how many events there were beyond the structured part of the day, and it was awesome how much the teachers bonded during just three weeks. Below is just a few examples.

Just a few days after we arrived, we had a float and walked in the Park City 4th of July parade. It was probably the most intense expression of mathematical pride and nerdiness I have ever been a part of.

There were two building parties, where we made ghost cubes, modular origami, straws thingy, hyperboloids, and much more. It was a blast.

There was a competitive estimation event called the “Estimathon.” I’ve never seen people so excited to watch someone update a spreadsheet.

### My Talks

I enjoyed and learned a lot by giving two short talks at PCMI. The first was an ignite talk that I called, “More than high quality math instruction.” The talk was about how I have used restorative circles to get to know my students better as people and why I think that is important. (I apologize if I embarrassed or misrepresented any of the students I talked about.)

About an hour later, I presented a ten minute “teacher share” about Play With Your Math. After about 5 minutes, I stopped talking and challenged the group with 2. Pentagram. A couple people solved it eventually, and many people kept trying throughout the week.

### Utah

It wasn’t quite all math all the time. We got to explore Park City and Utah, and I learned that Utah is way prettier than I had realized.

And we saw a rattlesnake and a moose!