Reflections on maths, learning and maths learning support, by David K Butler

Category: Conferences

Descriptions of my experiences at conferences and other professional development., including my own presentations.

  • My first Maths Teacher Circle

    Last week I participated in my first Maths Teacher Circle . I just want to do a quick blog post here to record for posterity that I did it and it was excellent. I choose to take the practical approach of just relating what happened.

    I had been interested in somehow going to one since I heard about them a while ago, and then the founder of the Aussie Maths Teacher Circles, Michaela Epstein , contacted me through Twitter back in November to ask if I might like to facilitate an activity at an online session in 2021, and of course I said yes. She invited me to a session about mathematical games, and I was so excited to share some of the games I have invented with some interested teachers.

    Of course, the closer it got, the more nervous I got. When I heard there would be 40 or so teachers ranging all through primary to secondary to post-school teachers, I was rather intimidated! But Michaela and Alex  assured me I would be ok and that what I had planned would work. And they also put up with my scatterbrained discussion of random maths stuff whenever I met with them too. So, feeling a little reassured, but still nervouscited (as Pinkie Pie would say), I dove right in feet first last Wednesday morning.

    To start off with, Michaela invited past Maths Teacher Circles participant Samantha  to  set the scene by sharing what she has gotten out of Maths Teacher Circles in the past. This was a nice way to begin by grounding it in a real teacher’s experience. Then Michaela shared the goals of Maths Teacher Circles, which were exploring maths, strengthening classroom practice, and bringing maths enthusiasts together. I was so glad I had come to a place that resonated with all the things I love. It really matched with the goals of One Hundred Factorial, which is probably why Michaela invited me to present in the first place. This was all a really smart way to begin, because it set the tone for the rest of the session. Even when the housekeeping notes about breakout rooms and whiteboards and chat windows came, it was clear that these were there to support the overall vibe.

    Then we had a very quick chat in breakout rooms with a couple of people. We were supposed to talk about Noughts and Crosses too, but we only just made it through the introductions! But honestly I was happy to just have met a couple of friendly faces to help reduce the nervous part of the nervouscieted.

    By this time, so much had happened already, yet it had only been a few minutes. And now it was my turn. Michaela introduced me and I was now responsible for the journey of these 45-ish hopeful people. I put up the rules for Which Number Where, and asked everyone to quietly have a read, then ask any questions they might have. People had some very useful questions in the chat and out loud, and I felt we were ready to try it live. I asked for volunteers and described how to play the game Mastermind-style, with one player being the Secret Keeper and the other players asking questions. After a couple more questions, we were ready to break into groups to play.

    Michaela put people into groups of fourish, and I popped into about half of them to have a chat. I asked people how they were going and played with them for a bit, seeding a different kind of question than the ones they had been asking so far. I found everyone to be gracious and thoughtful and engaged. Such a thrill to meet such wonderful people and play maths with them. These moments when I was in a small group with people were my favourite parts of the session.

    I brought everyone together into the big group to discuss how the game went. I started by asking people if they had a favourite question that was asked. And then people shared any thoughts they had at all about how to use this in a classroom.

    Suddenly it seemed my time had run out, so I quickly showed everyone my other two games Digit Disguises and Number Neighbourhoods, and encouraged them to go back to their breakout rooms to keep playing Which Number Where or to try a new game instead. I stayed out in the main room where Michaela made sure I was ready to do a wrap-up when people returned. I very much appreciated being able to think in advance about that part!

    One question Michaela asked was why I chose the game I did. I said I chose Which Number Where because it’s about logic, and not any particular maths topic per se. As someone said earlier, it’s about locations rather than numbers per se, which means it’s really about the yes-and-no questions, and about logical arguments and joining information together, and those are skills you use everywhere in maths, which is why I like it so much. Plus I just love to hear how people think and this game gives me a chance to do that.

    And then it was time for me to participate in someone else’s activity. Toby  and James  shared the Multiple Mysteries game and some problem-solving/proving prompts to go with it. I got to play the game with some lovely other people and join in with the play. It really was a lovely thing to just play around with something that someone else shared that they were excited about. I am very grateful to Toby and James for providing such a great game to play and think about, and to the members of my little breakout room who I had such fun with.

    After this, it turned out that Michaela had read the time wrong and had cut short my activity the first time! So I got to have a few more minutes! I decided to share Digit Disguises properly, and instead of using breakout rooms, to play a game as a whole room with me as the Secret Keeper. Some brave souls shouted out questions and I wrote the questions and responses on a Word document on the screen. After a few questions, I decided that I would stop people and ask them what they can figure out from the information we have so far. This part was just wonderful. People had multiple different ways of gleaning new information about the numbers and their letter disguises from what we already knew, and quite a few of the participants expressed a satisfying amount of delight at these fascinating new possibilities. It was extremely gratifying to have people so excited about something that I am excited about (and egotistically, satisfying that people liked something I had invented).

    At this point, my laptop ran out of battery power and I had to scramble to find the power cord. By the time I came back, things were starting to wrap up, with participants filling out a Padlet with their thoughts. And then it was over. It felt like almost no time at all had passed, which is a good sign that I’ve been deeply engaged.

    After all the other participants left, Michaela, Alex, Toby, James and I had a debrief, which was some lovely discussion about how it went and how cool it was to work mathematically with people rather than just present them with stuff, and just some nice discussion about teaching and learning maths with some lovely people. And after that, couldn’t help but keep working on  one of the investigations that Toby and James set me off on, because that’s how I roll and is the sign of a good maths problem.

    So that was my first experience of a Maths Teacher Circle. For me, the best part was the chance to think and play together with other teachers. The environment was so safe to just play and talk, and this was very carefully set up by Michaela in the first place, by discussing what was important and how to keep it safe. Being told explicitly that we were allowed to adjust the activities to match the level of the group made us free to play in our own way. And really, everyone was just so gracious and excited and, well, lovely. I am so grateful to have been a part of it.

  • Who is worthy to ask stupid and smart questions?

    This post was going to be part of the Virtual Conference of Mathematical Flavours, which you can see all the keynote speakers and presentations here: https://samjshah.com/mathematical-flavors-convention-center/ . The prompt for all the blog posts that are part of this conference is this: “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?” In the end, it didn’t end up being there, because my computer started dying painfully at the critical time, but I still want to highlight the Virtual Conference anyway because it was a great idea.

    There are many things I could have written about this, but I think I will choose one thing that is about my approach in the MLC to student questions. In the MLC everyone is worthy to ask both stupid and smart questions.

    My Maths Learning Centre is a place where any student doing coursework at the Uni of Adelaide can visit to talk about their maths learning with a tutor (often me). People come to talk about all aspects of their maths learning in all sorts of places where maths appears, from dividing whole numbers by hand to understanding proofs about continuity of functions between abstract metric spaces. My point here today is that people from both ends of that spectrum and everywhere in between are allowed to ask questions that are about basics and questions that are about deep connections.

    Imagine a student who has always been good at maths, who finds things easy and quickly grasps abstract definitions. It is natural for such a student to fold their goodness at maths into their identity, which often means they become extremely embarrassed to show any sign of struggling. They’re supposed to be the smart student and this simple stuff is supposed to be obvious for them. So if they have a question about the basics, they hide it and hope it will come clear eventually.

    The thing is, having a question about something simple doesn’t make you stupid, and it doesn’t even make you not smart. Having a question about how to get from line 3 to line 4 is at the very least a sign that you’re paying close enough attention to wonder about that step; having a question about the definition is a sign that you know definitions are important; and having a question about some random bit of algebra or notation you happen to have never seen just shows you want to learn. In my Maths Learning Centre, I try to make it a place where everyone can ask a “stupid” question. Where stupid questions are treated with respect and answered clearly, with encouragement to make sense of what is happening.

    Now imagine a student who has always struggled with maths, who just never seems to understand the explanation the teacher is giving the first time, and who struggles to get through the first few of the exercises. It is natural for such a student to fold their badness at maths into their identity, which often means they don’t even try to understand things and just look for some step-by-step instructions they can follow so it will be over with as quickly as possible.

    The irony is, they never finish their exercises, so they never get to be part of that part of a maths class where the early finishers ask the deep and involved questions about theory and beyond-curriculum interesting stuff – the very stuff that can make maths a lot more fun. I know for a fact that students who feel they are bad at maths are intelligent people capable of logical and creative thought, and they deserve to ask their deep questions. So in my Maths Learning Centre, I try to make it a place where everyone can ask a “smart” question. If a student who is struggling asks about infinity or quaternions or what my PhD was about, I will damn well discuss it with them. If they look at the work they’re doing and ask how it is connected to some other bit of maths, we’ll explore that together. That curiosity is a treasure to be prized and I will not squash it by saying we have to get on with the assignment now.

    And you know what, it turns out that many a basic question is actually a deep and clever question after all. Recently a student who was struggling asked why it was ok to add two equations together. Not one student in my ten years of working at the MLC has ever asked that question! There must be something really special about the person who asks this question, right? And it’s a really deep question about the nature of equality. I want my Maths Learning Centre to be a place were it is okay for everyone to ask a question that is simultaneously stupid and clever.

    That’s all I have to say. I believe everyone deserves the chance to ask stupid questions and to ask clever questions and to ask questions that are simultaneously both. They are worthy to have their questions taken seriously and the answers discussed with respect for the humanity and intelligence of the asker. I have to always remind myself to give students the chance to ask these questions when I’m with them, especially students who are struggling to articulate the questions for whatever reason. And maybe if they’re not asking, I’ll sometimes ask the questions for them and we’ll answer them together.

    How will you welcome all people in your learning spaces to ask all kinds of questions?

  • TMC17 Reflections a year later

    A year ago, I went to Twitter Math Camp (TMC) and it was a wonderful experience. TMC is a great conference full of all sorts of opportunities for maths teachers to learn from each other in many ways.

    Here are three reflections on my experiences there.

    You can read this blog post, along with later posts on the same theme, in PDF form here. 

    The titles of the posts in the series are:

    • TMC16 reflections from someone who wasn’t there (2016)
    • TMC17 diary (2017)
    • Fairy Bread (2018)
    • My Favourite is my favourite (2018)
    • TMC crochet coral quietness (2018)
    • The TMC Attitude (2018)
  • Fairy Bread

    Fairy bread, in case you don’t know, is an Australian children’s party food.

    A tray of fairy bread triangles. That is, bread spread with butter and with hundreds and thousands (tiny ball shaped coloured sprinkles) sprinkled on top.

    Here’s how to make fairy bread: take white bread, spread it with margarine, and sprinkle with hundreds and thousands. Now cut into triangles and serve.

    Notes:

    • It has to be white bread. If you try to make fairy bread with wholemeal bread, or multigrain bread, woe betide you!
    • It has to be margarine, not butter. Butter may just be acceptable only if it’s the kind that is spreadable directly from the fridge. It may be that “margarine” means something different in other places in the world, so just in case, what I’m thinking of the butter-like spread made of plant oils that is spreadable directly from the fridge and can spread very thinly.
    • Hundreds and thousands are a kind of brightly-coloured sprinkles that are shaped like very tiny balls. If you use chocolate sprinkles, or sprinkles shaped like little sticks, or coloured sugar, then it’s not fairy bread.
    • It has to be cut into triangles. Don’t ask me why. Triangles are more magical than rectangles I suppose.

    When I went to Twitter Math Camp in the USA in 2017, one of the lunchtimes I made fairy bread for everyone and passed it out. It was heaps of fun seeing people’s reaction to it, which was mostly good, though mixed with various levels of surprise and confusion.

    A Twitter post from Heather (Kohn) Russo @HeatherRusso99 on 30 Jul 2017 with text and a photo. The text says: Fairy bread from Australia is delicious! Thank you @DavidKButlerUoa #TMC17 The photo contains: Six people smiling at the camera. Behind us is a big room with chairs and tables and lots of other people. I am the second person from the left, holding a tray of fairy bread. The other people are all holding a triangular piece of fairy bread.
    https://twitter.com/heather_kohn/status/891339803056275456 

    For me, fairy bread is strongly linked to memories of my childhood, and every time I eat it I am surprised again at how good it is. I mean, it’s the stupidest thing: bread and margarine with sprinkles. Yet somehow all the more awesome for that.

    And here is where I am supposed to make a point about maths or teaching or maths teaching. But that might ruin the whole thing. Like those horrible people who try to make fairy bread “more healthy” by using wholemeal bread. Honestly people! It’s a party food – just own it!

    Actually this reminds me of people who are always trying to get me to make a mathematical moral to my play. Yes there are times when the mathematics people do is deeply meaningful or useful for solving real world problems, and there are other times when it’s just for fun and there is no other purpose to enjoy myself and spend time with good people. Sometimes I need to be left to simply enjoy it, thank you very much.

    Oh look, I did make a point. I hope it didn’t ruin the experience too much.


    This comment was left on the original blog post:

    David Roberts 10 July 2018

    As I’m sure you know, David, Dutch people love sprinkles of all kinds on bread, and for some reason especially for breakfast. When I was in the Netherlands a few years back, at a supermarket, there were (at least) two whole shelving units for different kinds of sprinkles. I do wonder if fairy bread was introduced via some widely-sold party-food cookbook a few decades back (edit: well, it’s at least 90 years old, according to https://en.wikipedia.org/wiki/Fairy_bread  !), where the author/compiler was inspired by this cultural phenomenon.

  • TMC17 Diary

    Well I did it. I went to Twitter Math Camp 2017 (TMC17) in Atlanta, Georgia, USA.

    You can read this blog post, along with later posts on the same theme, in PDF form here. 

    The titles of the posts in the series are:

    • TMC16 reflections from someone who wasn’t there (2016)
    • TMC17 diary (2017)
    • Fairy Bread (2018)
    • My Favourite is my favourite (2018)
    • TMC crochet coral quietness (2018)
    • The TMC Attitude (2018)
  • TMC16 reflections from someone who wasn’t there

    This post is about my response to TMC16. For the uninitiated, TMC is short for Twitter Math Camp. This is a conference designed by teachers for teachers with teacher speakers, organised through the collective efforts of the Math Twitter Blog-o-Sphere (MTBoS) – a group of people who blog and tweet about their experiences teaching math(s). That description is not the best description of the MTBoS, but I’ll get to that later.

    You can read the rest of this blog post, along with later posts on the same theme, in PDF form here. 

    The titles of the posts in the series are:

    • TMC16 reflections from someone who wasn’t there (2016)
    • TMC17 diary (2017)
    • Fairy Bread (2018)
    • My Favourite is my favourite (2018)
    • TMC crochet coral quietness (2018)
    • The TMC Attitude (2018)
  • Give good teaching a go

    It was the Uni of Adelaide Festival of Learning and Teaching last week, and as always there was a string of people telling us about the great things they’re doing with their teaching. As much as it can get a bit weary sitting through presentations all day, I really do love seeing that there are people excited about doing their best for student learning.

    There are two of these people that I want to hold up high as a shining example, and they are Catherine Snelling and Sophie Karanicolas from the School of Dentistry. They have won all these awards for their good teaching, but this is not what I think is the exciting thing. The exciting thing is that they did it through good old fashioned giving it a go.

    They thought it would be a good idea to have videos for their students to view, and they didn’t wait for a professional to shoot it for them or to have professional voice training, they just set up a camera and recorded themselves at the whiteboard. They thought it would be a good idea to have students talk to them online, and they didn’t bother to build a whiz-bang tool to do so, they just found out where their students already were on Facebook. Finally, they thought it would be good for the students to see detailed diagrams of dental anatomy, and they didn’t go out to buy fancy state-of-the-art teaching tools, but simply drew really good diagrams in colour on the board.

    When you listen to these two people speak you can tell they love to help students learn and that they believe that anything is possible. It was impossible for me not to be inspired by their infectious can-do attitude.

    You can do good teaching. Just give it a go!

  • Classroom archaeology

    At the combined MERGA/AAMT conference in 2011, one of the keynote speakers was Matt Skoss, a high school maths teacher in the Northern Territory. I talk a lot about how much we at uni have to learn from schoolteachers and Matt was case in point: he had a lot of most excellent stuff to say. But the thing that stuck with me the most – and is still with me more than 15 months later – was the concept of viewing your own classroom as an archaeological dig.

    This concept originally came from maths education researchers Zevenbergen and Flavel.
    [ Zevenbergen, R., & Flavel, S. (2007). Undertaking an archaeological dig in search of pedagogical relay. In: B. Sriraman (Ed.) The montana mathematics enthusiast. Monograph 1: International perspectives on social justice in mathematics education (pp. 63–74). Missoula, USA: Department of Mathematical Sciences—The University of Montana. ]
    They talked about how, as a maths education researcher, you can tell a lot about the sort of learning that goes on in a classroom by simply observing the artefacts left behind: the students’ work on the wall, the arrangement of the desks, what’s left on the whiteboard, etc.

    Matt took this concept and turned it upside-down: if someone were to perform archaeology on your classroom, what evidence would they find of learning? He encouraged us to think about deliberately leaving artefacts behind for the archaeologist to find. Of course, not all of us will be in the position to let an education researcher into our classroom, but Matt’s point was that an “archaeologist” is anyone who sees our classroom: the potential students who visit on Open Day, the teacher who uses it after you, the students who use it after you, your very own students a week from now, and finally yourself at some point in the future.

    All of these people glean information about what goes on in your classroom simply from the things you leave behind, so it makes sense to be purposeful in what you choose to leave. Matt in particular pointed out that your own students will benefit from seeing evidence of their own past learning, especially if you want to use that past learning for future learning. Two examples he gave were to get students to write on butcher’s paper when doing group work and then stick it on the wall; or to get them to write on the whiteboard, then take photos of what they do and post them online.

    So, what evidence will you leave behind?

  • Things I didn’t learn from OZCOTS 2012

    A couple of weeks ago I found out that OZCOTS (Australian Conference on Teaching Statistics) was being held here in Adelaide. I thought that I should go to it, since I seem to be spending rather a lot of time teaching statistics these days. And so I went.

    As it turned out, I didn’t learn all that much I didn’t already know. But this is a good thing: It’s always nice to have the things you knew instinctively confirmed by those with more experience than you. So, here is a list of things I didn’t learn from OZCOTS 2012:

    1. “Real life” examples are good for teaching stats, but much more important is to have MORE examples.
    2. Successful stats courses depend on all the staff who interact with the students having the same goals.
    3. Statistical software often distracts students from the real learning.
    4. The reason students find maths boring is because they don’t understand it – being useful is secondary.
    5. Students like to have the option of talking to someone about their learning, no matter how many other resources you give them.

    Of course, there were a few new things I DID learn (such as all about how to measure ESP, and the behaviour of badgers under pressure), but they can wait for some other time…