Tag: teachers

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, I 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.

21 January, 2021
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)
14 July, 2018
Leaving the most important teaching to chance

Something is bothering me about teaching at university: we are leaving the most important teaching to chance.

In most tutorials, there is an opportunity to try out things with a tutor there to talk to about it, or deep discussion of course content, or at the very least worked examples of using the ideas in practice with a higher chance of asking questions. In a lot of ways the tutorial is the place where the majority of the classroom learning actually happens in a university course. Indeed, students often say that tutorials are the most important part of their learning at university and will go to them even if they don’t go to lectures. I talked to a student just the other day who was still catching up watching the lectures online from two months ago, and yet has been able to do his assignments because he has been attending the tutorials.

So, if the tutorial is the most important class for student learning, then you would think that the tutorial would be the class where you put the most effort into making sure it was as good as you could achieve. Yet in so many disciplines in so many universities, the tutorials are given to their current postgrad students to teach, with minimal or no training. (Not to say the postgrad students can’t be great teachers, just to say they don’t have much teaching experience yet.) By not carefully considering our tutorials and training the tutors, it’s like we’re leaving the most important teaching to chance.

Even more than this, most initiatives to improve teaching at university focus on the lecturers. We give support for designing what happens in lectures and online, but somehow we don’t provide any time or resources for training the hundreds of tutors running the thousands of tutorials. Again, we spend all this effort improving lectures, but leave the most important teaching to itself.

This really surprises me, and I really wish there was something I could do about it. What I wish for is a funnelling of funding into designing effective teaching in tutorials, and even more importantly, funnelling funding into training tutors in effective teaching in tutorials. I think this might have a huge impact on learning at university.

25 May, 2018
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)
4 August, 2017
Book Reading: Becoming the Math(s) Teacher You Wish You’d Had
This post is about Tracy Zager’s most excellent book, Becoming the Math Teacher You Wish You’d Had.

(You can read this blog post and all other Book Reading posts in PDF form here. )

I actually finished reading it back in January, and I live-tweeted my reading as I went. The process culminated with this tweet:

https://twitter.com/DavidKButlerUoA/status/824183955012415495

That’s what I thought about it at the time, but I haven’t sat down to organise my thoughts on it. Until now.

I was first drawn to the book based entirely on its contents page. Check this out:
- Chapter 1: Breaking the Cycle
- Chapter 2: What Do Mathematicians Do?
- Chapter 3: Mathematicians Take Risks
- Chapter 4: Mathematicians Make Mistakes
- Chapter 5: Mathematicians Are Precise
- Chapter 6: Mathematicians Rise to a Challenge
- Chapter 7: Mathematicians Ask Questions
- Chapter 8: Mathematicians Connect Ideas
- Chapter 9: Mathematicias Use Intuition
- Chapter 10: Mathematicians Reason
- Chapter 11: Mathematicians Prove
- Chapter 12: Mathematicians Work Together and Alone
- Chapter 13: “Favourable Conditions” for All Maths Students
Is this not awesome? Here was a list articulating things about maths that I know are important and yet that I’ve struggled to articulate all my life as a mathematician and maths educator. Many of them cut straight to the heart of the difference between how I experience mathematics and how it usually is experienced in a classroom.
- “Mathematicians use intuition” you say? Well, yes. Yes we do.
  But many a maths classroom is about following rules and avoiding the need for intuition.
- “Mathematicians work together” you say? Well, yes. Yes we do.
- But so many students think maths is only a solitary activity.
- “Mathematicians make mistakes” you say? Well, yes. Yes we do.
  But mistakes are feared and avoided in most maths classes.
- “Mathemaicians connect ideas” you say? Well, yes. Yes we do.
  But so many maths curriculums are just so many piles of disconnected procedures, even here at my own university.
The contents page promised a book about the most important aspects of mathematical work and thinking, and a hope that it would give ways to bring these into the experiences of students in all maths classrooms.

And the hope was made real.

Each chapter starts out comparing how mathematicians talk about what they do and what students’ experience of it is. Then it moves on to detailed examples of the aspect of maths thinking in action in real classrooms, as well as strategies to encourage it both in your students and in yourself as a teacher.

I didn’t expect to see this last point about encouraging these attitudes and thinking in yourself as a teacher. Yet it is the most compelling feature of the book for me. Indeed, I don’t think the book would have had nearly the impact it had on me (or the impact I see it having on others) without this constant message that to help your students experience maths differently, then you yourself need to experience it differently too. More than this, Tracy doesn’t just make this need clear, but actively and compassionately empowers us to seek out ways to fill it.

Somewhere inside you is a child who used to play with numbers, patterns and shapes. Reconnecting with your inner mathematician will improve your teaching and benefit your students, and it will also benefit you.
– Tracy Zager, Becoming the Math Teacher You Wish You’d Had, p39

These comments were left on the original blog post:

Tracy 10 May 2017:

Misting up over here, David. You’ve cut right to the heart of it. Thank you so much. I feel incredibly lucky to learn with you.

David Butler 10 May 2017:

And I am lucky to have been able to sit and talk with you by reading your book. I really felt like you were there with me, encouraging me to be more.

Susan Jones 10 May 2017:

I’m still reading it. Your post makes me realize my privilege in not majoring in math 🙂 I never did lose the “play with the numbers” thing.

David Butler 10 May 2017:

Sadly, you don’t have to major in maths to lose the play-with-numbers thing. A good dose of standard high school maths teaching can safely banish that tendency, as Tracy described in the first chapter of the book!

For me, my maths university degree is what actually freed me to play. I took Discrete Maths II in second year of university and it felt like all we were doing was playing with these ideas, and it was play encouraged by the lecturer.
10 May, 2017
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)
25 July, 2016
My cat’s bottom

Did you know that cats have scent glands just inside their bottoms that are constantly being filled with liquid and are squeezed as their poos come out, and if their poos are too skinny the glands are not squeezed enough and get over-full making them very painful and inflamed? Neither did I, until my cat Tabitha Brown started bleeding out of her bottom.

The vet literally reached into Tabitha’s bottom and squeezed the glands, making scent-liquid squirt all over his face (I have very great respect for vets, especially this one!). Then he told us some very useful things about how to look after our cat properly, such as the fact that many cats need Metamucil (yes, human Metamucil) every so often.

The point of this story is that we would never have known about how to look after our cat properly if she had never been in this pain. Because of her bleeding bottom, we now know for her, and for any future cats we might have in our home, to keep an eye on the size of their poos and give them Metamucil if the poos are consistently a bit skinny. All because of her bottom.

As always, my life makes me think about my teaching…

Students often say that I am a better teacher than their own lecturer, and it has become clear to me that the main reason this might be true is because I spend so much time with students. I am there when they have problems, and so I am able to see the problems students might have, and thus I am better equipped to help future students. There are so many things about the way people learn or don’t learn that I would never know if not for me being there when the students were in pain. Not that I wish anyone pain of course! I’m just saying their pain helps me prevent unnecessary pain for future students.

So thank you to all the students who were in pain and let me be there when they were. You make me more able to help others.

9 May, 2016
Out-of-body teaching experience

I have had a couple of new staff start in the MLC this semester. As part of the selection process they have to do a trial session in the Drop-In Centre, with me observing how they teach in order to give them feedback.

Every time this happens, it has a very unusual effect on my own teaching in the Centre – I start having out-of-body experiences! I find myself watching myself as I’m teaching. I’ll be sitting there working with a student, and simultaneously watching and listening to what I’m doing. A constant undercurrent of questions is flowing beneath my words and actions: Are you really listening to what the students’ understanding is? Was that a good question to ask them? Why haven’t you gotten them to write this instead of you? Did you stop to check if they knew they learned something they can use on their own?

In some ways, it’s disconcerting to have an experience like this – to feel so consciously aware of my teacher conscience as if it’s another person. But in other ways I like it. Most of the rest of the time, I only get to think about what I’m doing with students later when it’s too late to do anything about it (and I mentally kick myself), but when I have this self-awareness, I can change for the better while I’m still with the student.

I wouldn’t wish it on anyone all the time, but I do wish I could more easily give others this sort of out-of-body experience sometimes, because it really is beneficial I think. Perhaps we should all spend more time observing other people teaching where we have the responsibility to give feedback on others’ words and actions. It might make us think about our own actions more.

This comment was left on the original blog post:

Lyron 4 September 2015:

This happens to me quite rarely, but its invariably been a positive experience whenever it has — although I agree, I would not want it to happen all the time, but I would like if it happened more often. I have no idea how to induce such a state in myself though, it just… kinda happens, occasionally, for no apparent reason. Almost always only when I am in a good mood. 🙂

3 September, 2015
Moses loved numbers

Many traditions hold that Moses wrote the first five books of the Bible. If we assume this is true, then there is one thing I think is clear about Moses, based on the things he wrote: he loved numbers. I’m pretty sure he was a mathematician at heart, or at the very least an accountant, because his books are littered with numbers which are not entirely necessary to get his overall point across.

Just look at this passage from Genesis (NIV):

When Adam had lived 130 years, he had a son and he named him Seth. Afer Seth was born, Adam lived 800 years and had other sons and daughters. Altogether Adam lived 930 years, and then he died.

When Seth had lived 105 years, he became the father of Enosh. And after he became the father of Enosh, Seth lived 807 years and had other sons and daughters. Altogether Enosh lived 912 years, and then he died.

When Enosh had lived 90 years, he became the father of Kenan. And after he became the father of Kenan, Enosh lived 815 years and had other sons and daughters. Altogether, Enosh lived 905 years, and then he died.

When Kenan had lived 70 years, he became the father of Mahalalel. And after he became the father of Mahalalel, Kenan lived 840 years and had other sons and daughters. Altogether, Kenan lived 910 years, and then he died.

When Mahalalel had lived 65 years…

And this one:

He spent the night there, and from what he had with him he selected a gift for his brother Esau: two hundred female goats and twenty male goats, two hundred ewes and twenty rams, thirty female camels with their young, forty cows and ten bulls, and twenty female donkeys and ten male donkeys.

The emphasis on numbers is striking.

Now I’m pretty sure Moses didn’t mean to place such an emphasis on numbers in his writing. Presumably his main aim was to let his readers know about the history of Israel, and the nature of God and his relationship with humankind in general and Israel in particular. But still, the numbers are there. Why?

I argue that the reason the numbers are there is because Moses himself loved numbers. I think he couldn’t help the numbers appearing in his writing because he wasn’t even aware he was doing it. He liked numbers, so he thought about them a lot, and so they just turned up in his head when he was writing his books.

And if it can happen to Moses, then it can happen to anyone. I know myself that I can’t help references to childrens literature turning up in my lectures, and I can’t help maths turning up in my everyday conversation, just because I love those things. And I can’t help turning every discussion about maths into a discussion about problem-solving, because I think about the process of problem-solving a lot and it just happens.

But the danger is when the things we are interested in distract from the message we want to get across. For example, what if a teacher absolutely loved sport to such an extent that every example in class was about sport, and some of the students who disliked sport were turned off because of the association? And what if the thing a teacher most loved in the solution to a problem was the fancy trick? Then when they presented the solution they couldn’t help getting excited about the trick and it would seem to their students that fancy tricks were what problem-solving was all about.

But what can these teachers do, since they can’t help the things they love coming through in their communication? Well I think they can simply be aware of it. Then at least they can make sure that even though the things they love are there, the overall message isn’t obscured by them. (Of course the ultimate would be to love the thing you are trying to teach!)

21 May, 2013
Don’t clean the whiteboard

In the previous post, I talked about classroom archaeology: the concept that we leave behind evidence of the learning that goes on in our classroom for others to find, and since people will see this evidence whether we like it or not, we should leave some useful artefacts on purpose.

This post is about one simple idea I have for an archaeological artefact we can leave behind: a full whiteboard.

Your typical university classroom is woefully bare – there is little or no evidence that learning has happened in them at all, letalone what learning it actually was. In general we don’t have topical posters to inspire questions in our students, we don’t have a list of this semester’s topics marked to show where we’re up to, and we don’t put the students’ work on the wall for people to see. The main reason for this bareness is that the classrooms we teach in don’t “belong” to us – everyone shares them and classes traipse in and out of them all day.

And this is precisely why I think the full blackboard is such a great idea! If you leave on the blackboard what you did in your class, then the next person who uses it can see what learning was going on there. If they are from a different discipline, then they might just get a kick out of knowing that your topic is actually taught at your university. (Indeed, just yesterday a lecturer in Media expressed this exact opinion about seening Physics on the whiteboard when he enters his lectures. And I myself enjoy walking through Hub Central and seeing the intricate diagrams and calculations left behind on the whiteboards by the students studying overnight.) Not only this, but if you have the good fortune to have no-one else use the blackboard between now and your next class, your own students will have the benefit of seeing right there what you did last time.

Now I know that it is many a teacher’s pet peeve to enter a classroom to be faced with a “dirty” whiteboard, but I think the benefits far outweigh a little bit of annoyance. And anyway, if everyone did this, you’d just clean the whiteboard at the beginning rather than the end of the class, and so everyone would still doing the same amount of cleaning overall wouldn’t they? (Possibly less cleaning if you think about it, because if you don’t plan to use the whiteboard at all, you won’t have to clean it!)

So in the spirit of having a healthy sense of classroom archaeology, please: don’t clean your whiteboard!

7 November, 2012