Making Your Own Sense

Reflections on maths, learning and the Maths Learning Centre, by David K Butler

Tag: learning environment

  • Space to enter

    This is a photo of the entrance to my Maths Learning Centre. What do you notice?

    Maths Learning Centre entrance. In the foreground on the floor is a big cross made of yellow and blue coloured tape.

    There are many many things to notice in that photo, and if you ever want to ask me about any of them, please do. Today, the thing I want to focus your attention on is the empty space right at the front as you walk in. Every so often someone asks me why I leave that space empty and I don’t put an extra table there, and there are a couple of very good reasons why.

    First, the space isn’t empty: it has the floor graph in it. The floor graph used to be at the back between the % and the 3 on the wall, but one day I realised that I could have a bit of extra space for it if I put it in the entrance. I also hoped it might send the message to people arriving not only that maths is a thing that happens here, but also that we do things a little differently to your regular university maths classroom. One day I will write about the floor graph to tell you all about how we use it, but there is one purpose I want to tell you today: the floor graph helps us to break students out of staring forlornly at their page or screen. The open space on the floor graph gives a sense of physical freedom, which can translate to a sense of mental freedom.

    The openness of the floor graph space was the main reason I moved it to the entrance, actually, because it makes the space easier to enter, for several different kinds of students:

    We regularly get tours of new students or prospective students come past the MLC, and with an open space in the entrance, we can bring those tour groups right into the MLC, rather than standing outside and pointing. The experience is so much realer if you can come right in and stand surrounded by the art and whiteboards. They can remember that we asked them to come all the way in. Without the space in the entrance, we’re just pointing from outside and they miss so much.

    Students who are familiar with the MLC stand on the floor graph for a moment when they arrive and look around to find a good table, or other students they recognise. The empty space allows them to take a moment to make a choice, and to prepare themselves for working in the space.

    Students who are not familiar with the MLC have a place to stand looking lost. (We tutors even call it the “lost soul zone”.) When there was a table in the entrance, people wouldn’t want to be too close to the students already studying there, so newcomers would do their unsure dithering stance outside where we couldn’t see them, and more often than not they would just leave without us ever knowing. The emptiness of the space now means that they can come in without feeling like they’re encroaching on the work of the students and staff already in the room. Just like our regulars, they can prepare themselves for asking for help while actually being in the room. And since they’re in the room, we can see them and go up to them to ask what they are looking for.

    Without an empty space in the entrance, we would not be able to welcome as many new students to the MLC as we do. The emptiness is important to provide space for the complex process of deciding whether and how to engage with us. I am so happy I managed to created the space to enter.

  • The MLC Date Blocks

    This blog post is about a piece of the MLC learning environment which is very special to me: the date blocks. It’s a set of nine blocks that can be arranged each day to spell out the day of the week, the day number, and the month. I love changing them when I set up the MLC in the morning, so much so that since the face-to-face MLC closed due to COVID-19, I brought them home and have been changing them each morning here in the dining room. The story of how this object came into the MLC is the reason it is so special to me.

    You can read the rest of this blog post in PDF form here. 

  • 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)

  • 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!

  • 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?

  • Kindy is awesome

    My younger daughter started kindy last week, and I got to actually be there for the beginning of her first day. It was one of those moments only a parent can understand as I realised with both excitement and sadness that my little baby was not a baby any more.

    But this is a maths learning blog, so as much as the above point really is all that needs to be said, I will make just one more: kindy is awesome!

    Of course I already knew it was awesome – my wife is a kindy teacher and director and anything she is involved with is definitely awesome – but the true awesomeness of it was brought home to me once more as I stood there in my daughter’s own kindy.

    I looked around, and everywhere I looked was something specifically designed for learning, and learning was actually happening there.

    The activities chosen allowed each child to choose to learn in their own way: Some activities were quiet and some were loud; some required social interaction and some were individual; some involved running, some hand-eye coordination, and some sitting still; some needed deep thought and some creativity – and every activity was encouraging learning.

    The free-form structure allowed each child to choose what to learn at their own pace: children decided what to do as the whim took them, and didn’t need to wait for anyone else to tell them it was ok, and didn’t need to wait for everyone to be ready. They just started playing, and therefore just started learning straight away.

    The staff were in the thick of it helping learning to happen: they moved from one place to the next, talking to the children and turning ordinary moments into teaching moments. It was clear that at some point they would move to the “group time” areas and help the students draw together the ideas they had encountered in their play. And finally, they were also constantly setting up and re-setting up the environment so that new children could keep learning there.

    I was in total awe of the whole thing, and it made me wish again that we could make uni more like kindy – a place where the staff choose learning environments and materials that students could interact with in their own way and still learn, but where staff are always ready to help make learning happen.

    I have been accused in the past of making the Maths Learning Centre too kindy-like. But in my mind, I could never make it too much like kindy.

    Because kindy is awesome.

  • The Bare Drop-In Centre Walls

    I took down all the posters in the Maths Drop-In Centre on Friday and the effect is startling.

    (The reason I took them down is that the Drop-In Centre is moving to a new location in under two weeks and I needed to feel like I was doing something before the boxes arrive and we can pack properly.)

    It’s all gone: the Greek alphabet, the regular and semiregular polyhedra, the characters from the phantom tollbooth, the families of number, the picture of me teaching maths as drawn by my daughter, the “solving maths problems” flowchart, and the aims of the Drop-In Centre – and now the walls look as bare as when I arrived.

    I almost cried.

    It made me realise what a difference all those posters made to the learning environment of the Drop-In Centre. Without them it’s just like any other classroom that never meant anything to me – a place people occupy rather than live in – a dead place.

    Even the students commented on it. When I took down the “solving maths problems” flowchart, one said, “Where will we get our inspiration from now?” and another commented that there won’t be anything to talk about without the interesting posters.

    I never knew as surely as now what an effect the environment has on the students. It has helped them to engage with their own learning and to interact with us and each other.

    I can’t wait to move so I can put it all back up in the new Drop-In Centre – I want a living classroom again!

    This comment was left on the original blog post: 

    David Roberts 17 Jan 2011:
    Ah, those wonderful posters. They certainly helped brighten up our office in the old maths building, when David and I were PhD students. We never quite saw eye to eye about what sort of ‘things’ should have gone in the families of numbers posters. 🙂 But David is right – at some point they stop _being_ numbers.