# The Rationale

Upon seeing mention of “The Virtual Conference of Mathematical Flavors” on Twitter, I thought “that’s neat, but that’s not really anything I could contribute to”. And then I read the call for presenters.

You may be thinking… “But no monsieur! I am not worthy of presenting at such an auspicious conference such as this one!” or “I don’t even have a blog!” And to that, I say “Pssssshaw!” I firmly believe that all teacher voices have value, from first-year teachers to veteran teachers, and yours does too.

Well then. I do already have a blog (albeit with little in it1), and I could be seen as a first-year teacher as I teach for a full term before getting my teacher registration. But then I’m still left with the question of how could I possibly answer the prompt?

How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?

I’ve not taught in a school from the start of the year, and I still feel like I’m working on getting through each day or week rather than truly purposefully working towards lasting long-term change in student outlooks on mathematics. So I can’t talk from experience of how I make that happen, or what I intend on changing in my class to improve since last year.

What I can do, however, is reflect on what I would like to have happen in my classrooms in the future. The very exercise of doing that will likely help me to plan, and then implement those ideas once I am in a position to do so. By sharing these thoughts, maybe I’ll get the chance to discuss them with others to develop them further, and just maybe there might be something useful to anyone who chooses to read these thoughts.

So what then is my vision for transforming how my students see mathematics?

# The Vision

Maths2 , I feel, is thought of as a dry, dull subject, filled with numbers and formula, with no room for any creative thought. After all, you just learn things that some guy came up with a few thousand years ago, right? I know I’ve sat through my share of classes like that, not that I usually minded3. But that is not at all a maths classroom must look like. Creativity and play most certainly can be found in a maths classroom, and really, not just can be found but should be found in the maths classroom. And there’s more than one way that can be done.

A small thing is just having games, or really any sort of activity, in the classroom. This is something I experienced more during primary school (I believe) which mostly died out once I reached high school. By having an experience that is fun, you’ve broken away from that image of the dreary maths calls. Of course, it does mean you have to do this frequently enough to break that image entirely and selecting an activity can be hard. A danger, as discussed by @mrbartonmaths in his book “How I wish I’d Taught Maths”, is of lessons that are memorable, but not for the learning that occurred. The goal is for learning or some form of mathematical development, and joy to occur at the same time. I do think I managed to achieve this in one of my lessons on my final practicum – we just spent the lesson playing a modified version of bingo that required them to apply inverse arithmetic operations to mark of boxes on their bingo sheets. In this situation, as far as they were concerned, they were just having fun playing a game. And had fun they did – every single student was engaged in the activity for the entire lesson. But just by process of playing the game, they were practicing a skill that I knew that many of them needed practice on.

Another small thing is the making the time for open questions, where there are no wrong answers, that encourage students to think about and discuss mathematical concepts. This is the idea of Notice and Wonder. It is something, like everything else, that requires forethought and planning, but if you can get your students thinking and talking about maths, you’ve provided an opportunity for creative thinking to arise. Unlike the image of the lecturing teacher out the front who tells you what to think, license is instead given to think, and that very fact may just make the maths classroom just a bit more welcoming, and lessons more engaging. Once I finish merely surviving, this is what I want to try to focus on next in my teaching.

I think the ultimate goal in my classroom would be to firmly embed these two aspects across all of the content that I teach in any class, and aim towards the point where they intersect, and the creative thought of open questions becomes playful, as you begin exploring ideas at the edge of your understanding. Maybe I won’t be able to reach every student, every time, amidst the constraints of curriculum and policy, but I want to try, because that’s where I find my own mathematical joy.

Through high school, my peers had a passion for puzzles and puns4, and so many a lesson or lunch was spent musing over some idea, or another. I recall one of us posing the question of finding a curve that touched each of the derivatives of $sin(2x)$ exactly once when we learned about differentiating trigonometric functions. Amusingly5, when we came up with these sorts of questions in our year 12 specialist mathematics class, the teacher would spend 30-60 minutes of the class discussing and exploring the question with us. In one instance, and possibly it was for this question, they came back the next lesson, and restarted the conversation, having been thinking about it over the weekend. Possibly allowing that level of distraction was problematic – I don’t recall getting much work done in class – but as it was a small class (10 total, if I recall), and we did a pretty good job of getting work done at home and supporting each other, we got through the class, and I look back on my time in that class fondly.

This sort of play I continued through university once I stumbled across this:6

While I had seen @DavidKButlerUoA around the university previously, and maybe even had heard something about One Hundred Factorial7, walking through the university and seeing the construction of the Stage 7 Sierpinski Sponge would have been my first proper introduction to David and his love of cool8 maths stuff. I ended up skipping a physics lecture to help9 finish assembling the sponge, just because it was one of the coolest things I’d come across – after all, when was I going to get to help build something like that again?10 But more on this later – there is a point to be made about this, but it’s not the one I want to make right now. Right now, I want to talk about One Hundred Factorial.

One Hundred Factorial is a puzzle and games club run by David. The time and format have varied somewhat over the years, but at its core, it is about talking and exploring mathematical ideas with anyone and everyone. The regulars are made up of a spread of first year undergrad students to those with PhDs in mathematics and working at the uni, but anyone is invited to join in, whether or not they claim they are a maths person. And the puzzles themselves? Anyone is able to offer suggestions, or say “Hey, I don’t understand what you did there, can you explain it again?” And probably the best part is that the goal is not the goal. More often than not, a question is posed and then explored, but then someone will say “but what if changed/expanded the question like so?” and the exploration continues long outside the scope of the initial question or puzzle.

I may still be getting side-tracked, but the point of that ramble is that is the experience of mathematical play that I’ve been able to have, and it’s that experience that I want to be able to provide for my students. I think those aspects of having creativity and play in the classroom provide a framework that lets you build up to an experience somewhat like One Hundred Factorial. I don’t think you could achieve the charm of One Hundred Factorial in a classroom for every single lesson, because you have a fixed curriculum through which to get, but I believe it is something that can be incorporated into lessons purposefully, and that is something I wish to achieve in my future classrooms.11

# Closing Thoughts

So there you have it. That is my vision, my goal for how to run my mathematics classroom in the future (or during my final placement, if I can at all manage it). I’m sure there’ll be more to it than that, that there’ll be challenges to be able to achieve that in my classes, but it is something to strive for as I take my first steps as a teacher. And I’m sure that with the help of #MTBoS, I’ll be able to eventually arrive there.

1. Yet!
2. Shush, I’m Australian.
3. I’ve always loved numbers and trying to understand mathematical things for the sake of knowing. I was the sort of kid to ask my mum about the difference between the $+$ symbol and the $\times$ symbol when I was 5, before starting school, and I was very proud in grade two that I not only could I do two digit addition, but also three digit addition, which was what the year threes in my combined two/three class were learning.12
4. Here the allure of alliteration was all too much to avoid.
5. It has been amusing to me up to this point, but as I write this, I realise that now I would describe it rather as ‘admirable’ instead.
6. While the tweet is from 2016, the photo was taken in 2014.
7. It’s hard to think back 5 years – I may have actually attended some sessions in the second half of 2013, so before that date.
8. Just typing that out, I can hear him saying that in my head.
9. You can see the back of my head as we held the stage 6 sponge on top to stop it from collapsing.