Making Your Own Sense

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

Tag: life

  • 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 Road to Royalty

    Last week, I met His Royal Highness Edward the Duke of Kent. I’d like to tell you the story of how this came about.

    His Royal Higness was in Adelaide because he is the patron of the Royal Institution of Australia and was presenting an award to a scientist there. But it just so happened that the Hyperbolic Crochet Coral Reef exhibition was still on display at the Royal Institution during his visit, so he dropped in for half an hour to see it.

    “How nice for him,” you might say, “but how did you get to be there while he dropped in?”

    Good question! Well, less than a week before, the curator of the exhibition Julie had emailed me to ask if I would like to attend afternoon tea with His Royal Highness in the Reef exhibition. She said that I was one of the very few men who was involved in crocheting the reef, and moreover she would greatly appreciate the knowledge I would bring about the mathematical aspects of the exhibition. After making sure the students in the Drop-In Centre would be looked after, I said yes – and that’s how I got to be there.

    “But David,” you might continue, “how did you get involved in crocheting the reef in the first place?”

    Another good question! Well, let’s see… another RiAUS staff member Cobi who I happened to know dropped in to my office in February asking me if I knew anything about hyperbolic geometry, and also if I happened to have any 3D models that might be used as part of an art exhibition. And of course I knew about hyperbolic geometry, and I had a couple of ready-made models of hyperbolic quadrics rigt there.

    That was the start of a year-long involvement in the project. During the course of the year I wrote a poster for the exhibiton to explain the geometry, learned to crochet, crocheted about forty corals, and ran three crochet coral workshops. I was probably the most involved of the very few men who were involved.

    “Wow! You really committed yourself to this, David,” you are probably saying. “But how did you happen to know Cobi?”

    Ah! Yet another good question! Well Cobi had once worked as a tutor for a course called Research Methods in Media at the University. The very first tute was supposed to be refreshing the students’ memories of statistics, and she had come to me as the coordinator of the Maths Learning Service for some help running that tute. I jumped at the chance and we had a great time getting the students to draw graphical representations of data on the windows. It’s one of my first memories of working at the Maths Learning Service.

    “Cool!” I’m sure you are saying. “But why did she think you would know about geometry and have 3D models?”

    You are full of the great questions today! Well if you know me at all you’d know that I can’t help being excited about maths in general and geometry in particular, and also that I also have a collection of models of geometries that I pull out at every opportunity. So it shouldn’t really be a surprise that I did talk excitedly to Cobi about geometry, and show her the models when we met, even though my task was to help teach statistics.

    “But,” you must certainly say, “that doesn’t explain why you happened to have the models of quadrics there.”

    That is an excellent point. Well, I’ve always been a model-maker (I remember making things even in primary school). So it was a natural thing for me to try to make models of the quadrics I was studying when I came back to Uni to do my PhD. Towards the end of my first year of PhD I spent a few weeks making paper-mache models of quadrics, constructing the underlying structure with carboard and string. I have fond memories of sitting in the School of Maths tea room with my hands covered in maper-mache glue and paper and cardboard all over the table.

    Later, towards the end of my PhD, I ended up on a team designing interactive activities for open-day and the string quadrics seemed like a reasonable thing to get passers-by to engage in. When I went to the Maths Learning Service, I took the string models with me.

    Now you probably have more questions at this stage, but our conversation has been going on for some time now, and I think I’d better make some sort of point, don’t you?

    If you trace the story back, you’ll find that there are two reasons I ended up meeting His Royal Highness. The first is that I never shyed away from doing things that would be considered play – things like paper-mache and crochet. Other people were too busy or too embarassed to do this sort of thing, but that never stopped me. The second is that I was always willing to share my love of maths – with Cobi, with Cobi’s students, with the passers-by on Open Day, with the visitors to the reef, and finally with His Royal Highness himself.

    If you want to learn anything from this, then learn what I did: never shy from playing, and never give up sharing the things you love with others. You really never know what good may come of it if you do.

  • The Pied Mathematician of Hamelin

    Have you ever been in a situation and felt like you were reliving a scene from a book or movie? Well it happened to me the other day when I went to visit my daughter’s school. I felt exactly like I was the piper in the Pied Piper of Hamelin, because an ever-growing crowd of children followed me across the oval as I walked in.

    And why were they following me? Well I had brought a Stage 4 model of the Sierpinski Sponge with me for my daughter’s Show and Tell. She had come with me to university the day before to help me make Stage 6, and we thought the other kids would be interested – and my goodness they were!

    At this point I should probably tell you more about the Sierpinksi Sponge Project…

    The Sierpinski Sponge is a fractal constructed in the shape of a triangular pyramid. It has a giant hole in the centre, and each of the corners around this hole is a copy of the whole thing. This means that each corner is a pyramid with a big hole in the middle, and each corner of those pyramids is a pyramid with a hole in the middle, and each … and you go on like this forever until you have an object with a great number of holes (infinitely many in fact) – hence the name “sponge”.

    Of course, you can’t make a real Sierpinksi Sponge because it goes inwards forever; you can make a decent model though. What you do is you get four small pyramids and you join them together at the corners to get a bigger one with a hole in the middle. Then you take four of these bigger pyramids and you join them together to get a bigger one with a hole in the middle. And so on. The individual small pyramids are called Stage 0, then when you join four together you get to Stage 1, and then Stage 2, and so on. We made a Stage 6, which contained 4096 individual pyramids.

    (To see video of the Stage 6 Sponge and us making it, check out the YouTube videos: http://youtu.be/A7YbmITSck8  , http://youtu.be/W0uLbhRR-Hw  .)

    So back to the story… on the day after we made Stage 6, I walked through the school yard with a Stage 4 Seirpinski Sponge, and all the kids crowded around to see this remarkable thing and ask questions. And then in the classroom, the kids just couldn’t keep quiet with the questions and fought over who would be first to hold the smaller models. Their little eyes lit up as they imagined standing inside Stage 6, and imagined the awesomeness of Stage 7, Stage 8 and Stage 100.

    But it did make me think: We made our Stage 6 in a public place in the Uni where hundreds of people walk past a day. Several people looked at it as they walked past, and a few came close to touch and ask questions, and a handful of those actually stopped to help make it bigger. Before construction day, I had spent every train journey sticking pyramids together, usually reaching Stage 4 by the time I got to my destination. On one particular day I finished a Stage 5 on the train and carried the metre-wide pyramid it through the crowds. Not one person stopped to look or ask about it. Yet the schoolchildren couldn’t keep themselves away.

    When did all the adults lose their sense of wonder? Because even the the Stage 4 Sponge is truly wonderful to me (and to hordes of children too).

    What would it take for adults to crowd around like the children in the Pied Piper of Hamelin?

  • Dagwood Dogs at the Gawler show

    I went to the Gawler Show with my family the weekend before last, and it was a wonderful day. We had camel and pony rides, patted the animals, looked at all the stalls, bought some toys, got given balloons and generally had a most excellent day.

    And as we left, we decided to indulge in some show food. One of the food vans was selling what they claimed to be “The best Dagwood Dogs in the land”. And you know what? They were! If hadn’t already left the show and walked halfway down the street to our car when we had finished, we would have bought another one.

    But even as I ate this faboulous Dagwood Dog, I wondered, “Sure it’s good, but why is it so much better than any other one I’ve ever had?” And soon I had quite a list:

    • It had just the right level of salt. Most Dagwood Dogs are way too salty, but this one was just right.
    • The batter wasn’t greasy. Instead it was fluffy and light.
    • The batter had corn and peas mixed into it! I have never seen this before but I’m amazed no-one has ever thought of it.
    • The flavour was so good I wanted to keep eating it even after the bit with the tomato sauce was gone.
    • The stick they used had a wider bit at the bottom so you could properly hold onto it.

    Later that day, it occurred to me that I very naturally evaluated my Dagwood Dog. It was so easy for me to make the decision of whether it was good or not, and to come up with a list of reasons why it was good.

    So why is it so hard to do this when it comes to teaching and learning? When I have a particularly good class, do I stop to think about why it was good so I can achieve it again? When my students fill out a SELT for my seminar, they quickly decide if it was good or bad, but do they give me a list of things that made it good or bad, so I can do better next time?

    Yet, it was such a natural thing to do this for my Dagwood Dog. I reckon we could all start using our natural food-evaluation instincts on our teaching and learning, and then perhaps we could claim we have “The Best Teaching in the Land”.

  • Charlotte’s Sudoku

    The other night I was doing a Sudoku, and my two-year-old daughter Charlotte decided she wanted to help, as she always does at any time when I have a pen and paper she could steal.

    So she bent over the paper concentrating very hard and a while later she threw her hands in the air and declared in her loudest voice, “I did it!!!”.

    And sure enough, she had. Every single box was filled with a letter-like squiggle.

    And isn’t this the most basic rule of Sudoku, when you really get down to it? Sure, the symbols in the boxes are supposed to be the digits from 1 to 9 and you’re supposed to have one of each in every column, row and box, but really if there’s not one symbol in every box, you just haven’t finished have you?

    I was extremely impressed that she was able to figure out that rule just by watching me for a few minutes!

    And, as usual, it made me think of my students. Often they latch on to one idea from their lectures and do their maths problems following that one idea, even though there are quite a few important details that make it actually work. But should I really be upset? They’ve picked out the most important idea and that in itself is impressive. Next time I’ll try my best to let them know how impressive it is before telling them how to be better.

  • Plastic bag CPR

    There is a saying that goes “practice makes perfect”, but I’ve had several people point out to me that a truer statement is “practice makes permanent”. If you do something over and over, it will stick — whether it is the right thing or not.
     
    This principle was brought home to me very clearly by some stories that my instructor told during the First Aid training I had at the beginning of the year (provided by Red Cross).
     
    The first story involved a person who went to the aid of a shopper who had collapsed in a shopping centre. After ascertaining that the person was not breathing, they proceeded to put a plastic bag into the patient’s mouth and then performed CPR. Needless to say, the patient died.
     
    The second story involved a teacher coming to the aid of a student who had gone into anaphylaxis due to an allergic reaction. The teacher fished the life-saving epipen out of the student’s bag and quickly jabbed it into her own leg instead of the student. I never did find out what happened to the student in this situation.
     
    The question is: what on earth possessed these people to do these strange things when clearly it wasn’t going to help their patients?
     
    Answer: that’s how they had practised it during their training.
     
    You see, during our training, we practise CPR on plastic dummies. Part of the mechanism is a plastic bag that goes inside the dummy’s throat and holds the air as we breathe into the dummy’s mouth. In the extreme stress of the moment, the poor first-aider from the first story simply reverted to doing what she had done in her training. The situation is similar for the second story — the teacher had practised putting the dummy epipen into her own leg and so did exactly that with the real-life epipen. (Our instructor had the presence of mind to make sure we used the dummy epipens on each other.)
     
    Of course, these stories came home to me as a teacher because I see the principle in action all the time. I see so many students doing practice exams with all their notes handy, when they are not going to be able to do that in the real exam. I also see students being sloppy with their writing and saying they’ll do it properly for the exam, even though I know full well that they will write sloppily in the exam despite their best intentions.
     
    But the students don’t just inflict this upon themselves — we teachers do it too. We show students a short cut to do something in a particular case, hoping to fix it by showing the “proper way” later, only to find that they keep trying to do the short cut even when it’s not appropriate. And we also find it so hard to avoid doing things for the students — thus forcing the students to practise letting someone else do it for them.
     
    I’m hoping the message of the plastic bag CPR helps me remember to get the students to practise what I want to make permanent, rather than something else!