Over the past year I have held this image in my head as a reminder and a motivation. It comes from Tracy Zager‘s 2015 NCTM ShadowCon talk ‘Breaking the Cycle‘, which is mandatory viewing. (If you have limited time, stop reading this post and go watch Tracy’s talk instead.)

At the same time that Tracy was giving her talk in Boston in April 2015, I was doing some last-minute preparation for my own talk (that same day!) for maths teachers in Adelaide, ~17,000 km away. But I was procrastinating by looking at Twitter. Fawn Nguyen, the live-tweeter for Tracy’s talk, tweeted out an image of these word clouds that stopped me in my tracks. Tracy had articulated so well what I *felt *but hadn’t been able to put into words. I grabbed a copy of the image, worked it into my presentation, and was talking about it that afternoon. I had no idea at that stage who Tracy was; I hadn’t yet heard her

*say*a single word, but her message was resonating with me loud and clear through the flurry of ShadowCon tweets.

In July 2015, I was honoured to give the Hanna Neumann keynote at the Australian Association of Mathematics Teachers (AAMT) biennial conference (the Australian equivalent of NCTM but with *far* fewer people). In my talk ‘More than mathematics: developing effective problem solvers’, I set out a case for incorporating into our classrooms the creative, active and collaborative ways in which professional mathematicians work, with examples from my own experience. In the middle of my talk, I said something like the following:

*This brings me back to the cat in the dark room. Andrew Wiles, the British mathematician famed for resolving Fermat’s Last Theorem, describes mathematical research like exploring a completely dark enormous mansion. You stumble around bumping into the furniture but gradually you learn where the furniture is. After a while — perhaps six months or so — you find the lightswitch, you turn it on, and it’s all illuminated. Then you move into the next room and spend another six months in the dark.*

*Mathematicians are chronically lost and confused, and that is how it is supposed to be. It would be ridiculous to think of mathematicians spending their days solving problems that they already know how to solve. Instead, we spend a lot of time uncertain about whether something will work, or uncertain about what to do next.*

*Mathematicians grow to feel quite comfortable with this kind of uncertainty, but I suspect that most of our students do not. So, let’s shift to thinking about our students. Put yourself in the mind of your typical student. What words would they use to describe maths?*

Cue, from Tracy’s talk, the word cloud about school maths (on the left of the above image), the word cloud from mathematicians (on the right), and the slide that defines my questions: ‘How do we, in our classrooms, shift from here to here? To help our students experience mathematics as a curiosity-driven, joyful, beautiful, endeavour?’ I spent perhaps five minutes in the middle of a 50-minute talk on this slide, but to me, it is one of the cornerstones.

For some reason my talk struck a chord. I’ve since been delighted by invitations to share the message — and Tracy’s slide — with hundreds of teachers at conferences around Australia. And I was amazed earlier this year to have a senior mathematics professor stop me in the corridor to say something about ‘that word cloud’. Turns out that one photo of my AAMT talk was shared at the Australian Council of Heads of Mathematical Sciences — and it was me standing in front of Tracy’s word clouds. I am beyond ecstatic that, even for the briefest moment, this question was in the minds of the leaders of Australia’s university mathematics departments and the Australian mathematics community.

These word clouds remind me what my purpose is. It is to orient my own students towards the creative, active and collaborative ways in which professional mathematics work, and to help them experience mathematics as a curiosity-driven, joyful, beautiful, endeavour. And, it is to help others position their own thinking and teaching towards this goal.

These word clouds prompted a ‘fourth-grade teacher at heart’ maths coach from Maine and a university mathematician from Australia to become friends and collaborators. Being able to meet Tracy at NCTM 2016 is one of the reasons that I finally decided to make the trip, and it opened up an abundance of other friendships, cemented mainly at #MTBoSGameNight. (That’s Tracy’s work again; she is the master of weaving together and strengthening the threads of this community.)

It doesn’t feel right to finish this post without mentioning Tracy’s new book, due out in December 2016. I’ve been fortunate enough to have a sneak peak at a couple of chapters, and it is *good*. Put it on your Christmas wish list. (The Australian distributor of Stenhouse Publishers is Hawker Brownlow Education.) If you can’t wait for December, you can read her blog now.

Friendships like this are why I advocate Twitter and the #MTBoS to every teacher I meet. We have so much to learn from one another. All it takes sometimes is one tweet to get it started.

This is so incredible, Amie. I am overwhelmed. Thank you for this post, your friendship, your feedback, your openness, everything.

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