Besides not having enough double consonants to appear with these two, I really didn't feel worthy, to be blunt, to keynote with them. At first it was just to present together, great!, but Edmund knew from the start that this could be a keynote. But there's never been a group keynote at Twitter Math Camp (or any conference I've been to, now that I think about it) so how much did I have to worry? But then it was approved. Still not too worrisome, but when the keynotes were announced, there was an explosion of interest. (Listen to Edmund if he has ideas for topics.) And, whoosh, there again were the feelings of 'what do I have to add to these two?' (Then Julie's keynote the day before was on this exact point.)

But I love to collaborate. And I've had the chance to do great things with people for TMC. GeoGebra with Audrey and Jed, James Cleveland, Joe Schwartz, and the whole Tessellation Nation experience at TMC16 (Joe's coverage). This time, preparation was spread out over almost a year. We met in Google hangouts, and exchanged posts and articles, ideas and tweets. These conversations were invaluable to me. As I think I said in the keynote, though maybe it sounded like a joke, when Edmund proposed the talk 'Mathematics isn't everywhere' my first reaction was that I say the exact opposite. A lot.

As we conversed, two themes emerged. The first revolved around what teachers are addressing when they say math is everywhere. We're justifying our courses. When am I going to use this? Why am I learning this? For me, teaching preservice teachers, the answer is the mathematical processes, the practices. It's doing mathematics. Dave Coffey and I gave a presentation once upon a time about verbing math. To math should be a verb, like to read. This has been a theme for me for decades. But still in discussing and preparing for this I realized the extent to which I still objectify the content.

At one point I told a story about one of my favorite pastors. (

*Aside*: He never had printed sermons. Turns out when he was in seminary, he discovered he always froze if he had notes, fully written or even outlined. He was stiff and unnatural. Instead, he developed a routine of just reading, rereading and praying over the texts, and then just letting it go when it was time for the sermon. I think my teaching is a lot like that, actually. I really ruminate on what I'm teaching, how I think about it, why it matters and have the start of a lesson, but will follow it wherever it goes.) Jim gets up one sermon, and says, you may have heard, holding his hands up clasped, "here is the church, here is the steeple, open the doors and here's all the people!" Your grandmother probably taught you that. IT IS HERESY!

(Image source)

I felt like that is what we were doing. "Math is everywhere" is accepted doctrine, and we wanted to tell a room full of our friends that No, It Is Not. Fr. Jim's point was that the people were the church, not the building. And our point was it's your doing that is the mathematics.

Well, part of our point. One of my takeaways from this was thinking about mathematics as a way of knowing. At the moment I'm thinking about this as a kind of particle-wave duality. The wave is the doing of mathematics, and the particle is the field itself. One of the benefits of being in mathematics is how long a history we have of making progress and understanding. This side of our discussions became the Levels of Abstraction.

- Seeing mathematics in the world.
- Seeing the world through mathematics.
- Finding aspects of the world through mathematics and mathematics through the world.
- Finding aspects of mathematics through mathematics
- Finding the limits of thought itself!

I love the verbing here - even when we're looking at the particle, we see the wave.

But at this point, the idea of the talk felt disjointed. We thought about a unifying theme of lines. But as we discussed, we found that there was a unifying theme. We wanted people to know we weren't adding to their burdens, this was something already present in what they were doing. Play is the element that connects the elements of great teaching.

Finally it was time for TMC18. We had slides, just. But had had no chance to practice. And TMC is busy. We talked it through twice more and planned out the timing. All while Marian delivered a quiet, intense, thoguhtful, heart felt challenge. Blew me away. Julie went full cheerleader/Oprah and encouraged everyone. How could we follow them? But the people were so generous and supportive, it all worked out.

So, I think you should present. Find people with whom to present, commit to it even if you're not ready, and give it a go. Regardless of the end, the work is worth it, and talking with other teachers or mathematicians is the way to get better. In your school, a local conference, NCTM regional or national. Ask someone you want to talk to, or say yes when someone asks you. I promise: you'll love it.