Making Your Own Sense

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

Tag: movies

  • Jack Frost’s Centre

    On the weekend I watched the film “Rise of the Guardians” by Dreamworks Pictures, and it is a very enjoyable film. In it, Jack Frost is enlisted by the Man in the Moon to join the Guardians of Childhood—who already have Santa Claus, the Easter Bunny, the Sandman and the Tooth Fairy in their ranks—and together they fight the evil Pitch Black, who is the Bogeyman.

    There is a scene in the film, where Santa Claus (called “North” by the other Guardians) gives some advice to the new recruit Jack. He tells Jack that he needs to find his centre – that part of him that guides how he will guard the children of the world against fear.

    Spoiler alert! Jack’s centre is fun. His great epiphany is when he finds himself saying the phrase: “Don’t be afraid, we’re just going to have a bit of fun instead.” He realises that for hundreds of years he has been warding off the darkness of winter by helping children have fun in the snow. Because they are having fun, they forget to be afraid.

    And then it was Monday. And not just any Monday either! It was the first day of O’Week – one of the busiest days in the year for the MLC. From 8am it was printing handouts and setting up the drop-in-centre and visiting preliminary lectures and playing Numbers and Letters in the Hub Central welcome centre.

    This year we had PASS leaders helping us out in the welcome centre and I must say they were a great bunch of people who leaped into the role of seeking out students with cheerful fervour. Georgia in particular was super enthusiastic about getting people involved in the games, and indeed playing the games herself.

    Interestingly, Georgia started the day saying she wasn’t all that good at calculations, and stood back letting others do it. But I persevered with her, encouraging her to have a go, asking for any ideas, writing down her slightly wrong solutions so we could work together to tweak them to make them work. By the end of the day she was our greatest champion for the numbers game, itching to rub it out and start a new one every time we drew the last stroke of the previous solution.

    That night when thinking about this MLC success story, I suddently made the connection to “Rise of the Guardians”. Georgia had forgotten to be afraid because she was having fun. She had forgotten to be afraid of calculations, forgotten to be afraid of failing, forgotten to be afraid of looking stupid in public – all because what we were doing was playing a game.

    Of course this is precisely why we have a mathematical art and play program at the MLC, but I had never so clearly realised the power that it actually had to change someone’s perspective.

    And I never realised how much of the time that Jack Frost’s centre is mine too. Any number of times a day, I will do something to distract a student from their fear so that they can get on with learning the maths they need to learn: wear a maths-themed t-shirt, pull out the play dough, draw their diagram in texta or crayon, ask about their lecturer’s lovable quirks, or just simply yell out “That’s so COOL!”. In all of this I am saying to the student, “Don’t be afraid of the maths, let’s just have a bit of fun instead.”

  • Elsa’s Freedom

    Disney’s Frozen came out on DVD last week and my family and I watched it on Saturday. It’s a very good movie with an excellent theme about the real nature of true love which is not usually seen in a “princess movie”. There are also two different stories about freedom, which is pretty common in a princess story (consider Rapunzel in Tangled and Jasmine in Aladdin). It’s this I want to talk about today.

    In case you don’t know the story of the film it starts something like this: Princess Elsa is born with the ability to create snow and ice, and while playing with her younger sister Anna there is an accident and Anna is blasted in the eyes with ice. The trolls are able to cure her but warn that Elsa will need to learn to control her power. The King and Queen take this to mean she needs to try not to let her power out at all and so Elsa spends much of her time locked in her bedroom, trying not to feel. Well this all comes to a head at Elsa’s coronation where it all gets too much for her and she lets it out spectacularly and runs off into the mountains. Cue the Oscar-award-winning song Let it go.

    The song is all about how, now that everyone knows about her powers, Elsa is free to let it go and really see what she is capable of. This is where I want to draw my parallel to maths.

    I have been a mathematician from a very young age – my mother says at the age of five I was playing number and letter games in my head. But it wasn’t too long before I realised that a love of maths attracted resentment and even hostility in others. I soon learned that the only way to enjoy maths was in my head, all by myself. I had to work hard to turn off my natural instinct to see the mathematical in things when I was with others for fear of getting the wrong sort of attention.

    In my first year at university, the people I spent time with expressed resentment at being forced to learn useless and boring maths, so even then I felt I had to hide. It wasn’t until my second year at university that I found others who shared a similar joy in maths and was fully free to be myself with them and “let it go”.

    Strangely, I had to go into hiding again as a maths teacher in a high school. Despite the fact that my job was to teach maths, I was looked upon as strange by the other teachers for my love of it. And worse, the many and burdensome responsibilities of day-to-day work in a school meant that I did not have time to play with the maths I was teaching and I struggled having to hold it all in. Coming back to University was like Elsa escaping to the mountains – I felt a great relief that I could play freely.

    Of course, this story is a little sad because there are still throngs of people who don’t share my love of maths and I shouldn’t have to feel trapped when I am with them. Well I’m happy to say I learned a long time ago that it’s not worth worrying about what others think of me, and I am actually free to be myself no matter who I am with. As long as I’m not getting in the way of their joy, I should be able to express mine. (Incidentally this allows me to publicly express my love of other strange things like childrens fiction and singing.)

    The key point I want to make is that it was being part of a community where it was ok to love maths that helped me realise this, and I found that community here at University. There must be scores of students with a similar experience to mine – those who have a love they’ve had to hide and who discover the freedom to express it here at University (and not just maths either). This is much better than Elsa’s so-called freedom, where she still had to be alone to express herself.

    I dare say, however, there are many other students who still don’t find that freedom here because for whatever reason they don’t connect with the right community. Like me in first year, they still feel like they have to hide their love. This is one of the reasons we do public puzzles and sculpture, and talk excitedly in the Drop-In Centre about maths beyond the curriculum. Who knows who might find the freedom to let it go?

  • Good movies, bad movies

    I went to the movies a month or so ago and saw two movies. I get to go to the movies very rarely, so when I do I like to see movies that are very good. Of course, you can’t know in advance whether they will  be very good, and based on last month’s experience the reviews in the paper are no help whatsoever.

    Anyway, the movies I saw were “The Lucky One” and “The Five Year Engagement”. In my opinion, the first was good and the second was bad. Let me tell you why…

    “The Lucky One” is very good mainly because it is a well-constructed movie. The story it told was simple, but with enough complexity to keep you interested. The characters were well-drawn – both the good and the bad. There were many subtle things to take away from the film, but none of them clouded the overall message, which nevertheless was not rammed down your throat. There was plenty of stuff in it to talk about afterwards. It was a good movie.

    “The Five Year Engagement” was just bad. The story it told should have been simple, but it was made unnecessarily complicated by random plotlines. The characters jumped from nice people to complete wackos in the course of single scenes. There were some nice messages to take away about faithfulness and finding the love of your life, but they seemed to appear all of a sudden when someone thought the movie ought to end now. All in all it seemed like a random collection of stuff that someone thought was vaguely connected to the title. And the thing that made it the worst was that it really could have so much better. The idea had such scope for a great film – I really wanted it to be a good film – but it just wasn’t.

    My feelings are the same about university courses, especially maths courses. Some have a small number of grand messages that all the ideas fit into neatly; others just seem like random collections of stuff to do vaguely with the title. In some courses each concept is discussed well and the connections between it and the rest of the course are made clear; in others everything seems half-done before you move on to some new and seemingly unrelated topic. Some lecturers give the sense that they have a plan and a story to tell; while with others you feel they just had to do this course today with the materials they had to hand. Finally, some courses leave you with a sense that it was worthwhile being there; while others leave you thinking it was all sort of interesting, but it could have been so much better.

    I commend all those lecturers who already know that good course design is like good movie-making – these lecturers have a story in mind to tell, and a plan for telling it well. They know that students need to feel that it was worthwhile turning up.

    To the rest of them I say it’s not good enough to have a lot of stuff to say that is good stuff. There has to be a story that draws it all together, and some big ideas you can walk away with. Without these you end up with a course that should be good but just isn’t – you end up with a course like “The Five Year Engagement”.

  • “Helping” Hands

    In recent weeks, a new artwork has appeared on the walls of Hub central. They used to have people’s faces, and now they have people’s hands in various poses.

    For some reason this reminds me of a particularly fascinating scene in the most excellent film “Labyrinth”, which you can check out on YouTube here:

    Here is a description of what happens in case you can’t or don’t want to watch it yourself.

    The main character Sarah tumbles down a well and is caught by a multitude of hands growing out of the walls of the well. She screams, “HELP!!!” and at that point several of the hands move together to form a face, which says, “But we are helping – we’re Helping Hands.”

    A face made of hands with a hand made into a circle for each eye, a fist for the nose, and two hands making a movable mouth.

    Sarah says, “But you’re hurting me!” and the hands respond by saying, “Would you like us to let go?” at which point they do let go and let Sarah fall for a second before catching her again.

    The hands then ask Sarah which way she wants to go: “Up or down?” They badger her until she finally decides she wants to go down. At this there are peals of laughter and yells of “She chose dooown!” as the hands help her smoothly downwards.

    Sarah asks, “Was that wrong?” and the only response is, “Too late now!” before she is dumped in the darkness of the Oubliette.

    Now this scene made me think of teaching staff I have known (and been). Students are given a task to do, with what seem like deceptively simple instructions, and they do what they think is best in response. And yet they still get disappointingly low marks. Often the person marking their work gives no indication of what the person did wrong and how to make it better.  The student says “Was that wrong?” and the teacher silently replies through their lack of feedback “Too late now!”.

    And yet so many of these same staff think they’re actually helping the students. They think it’s somehow wrong to tell students what the teahcer’s actual expectations are because then they are “spoonfeeding” them. “They have to learn how to do these things themselves,” say the teachers.

    It makes me angry to think that through just a few simple words we as teachers can make a big difference to the students’ lives, and yet we don’t say them because we think we’re being “helpful”.

    Having the title of “Helping” Hand does not mean that what you are doing is helping.

  • Rapunzel’s Epiphany

    We bought Disney Studio’s newest film “Tangled” on the weekend and I have to say it’s one of my favourite movies ever. It’s certainly Disney’s best movie since “Beauty and the Beast”, and I dearly loved “Beauty and the Beast”. I should warn you now that in order to say what I want to say I’m going to have to reveal a bit of the plot, so let this count as your spoiler alert.

    OK. So Rapunzel grows up in her tower thinking that the old lady is her mother and not knowing who she really is. During the film she escapes and goes to the town where there are a lot of sun-shaped motifs. She brings one home to the tower with her on a piece of cloth to remember her experience.

    We see her lying on her bed staring at the ceiling, which she has completely filled with painted pictures during her life in the tower. She looks at the sun-shape and notices something remarkable about her painting: the sun-shape from the cloth is there in her paintings, and not just once, but over and over and over, and the repeating pattern sparks a memory of seeing the shape when she was a baby. The music swells as she realises who she really is. In short, the cloth and the paintings spark an epiphany.

    But it occured to me that she would never have had this epiphany without two important factors. Firstly, she had to bring the sun-shape home with her on the cloth. Secondly, and more importantly, if the sun-shape had not been in her paintings so many times, she may not have noticed the connection.

    And here’s where it relates to learning maths:

    We want the ideas we show our students to connect together so that the students realise the true nature of things and the realisation changes them. In short, we want them to have “learing epiphanies”.

    I’ve seen it happen for students when learning about subspaces in first-year maths. There are a lot of ideas but they are all highly connected, and sometimes while they are trying to solve a particularly difficult problem they suddenly realise that they’ve been seeing the same pattern over and over and that it all just makes sense.

    I want this experience to happen for all my students.

    But is it possible to set up these learning epiphanies in advance? It could be argued that epiphanies are highly personal and can’t be engineered. But I think perhaps we can make them more likely by putting certain things in place…

    Firstly, the connections between the ideas have to be there all along, just like the sun-shapes in Rapunzel’s paintings. If they weren’t already there, the realisation wouldn’t have been so powerful. We need to make sure that there are patterns in what we do and say from the very beginning.

    Secondly, the connections have to be there many times – so many times that once they have been noticed you wonder why you didn’t notice it before. It gives a huge sense of sureness to the realisation that you have, so you don’t just discount it as your imagination. So in our examples and explanations, we need to repeat and repeat the same pattern over and over and over.

    Finally, there needs to be an event to start it off, something to help you notice that first connection. Just like Rapunzel’s cloth – she needed the shape to be marked out simply so she could notice it in her own work. So we need to stop and point out the pattern in what we’ve said every so often, and get the students to do activities that hold the patterns up close to each other so they can notice.

    I think keeping these things in mind as we choose what examples to show our students, and choose how to present them, and choose what activities to get them to do, may just make it possible to help them have an epiphany like Rapunzel’s.

    This comment was left on the original blog post:

    “Humane Pain” 26 March 2013
    I agree (with both your opinion of *Tangled* and with the learning strategy), but wanted to add an additional benefit besides helping students to grasp the concept: epiphanies also add the element of excitement, that “aha!” or “Eureka!” emotion that is such a rush, such a natural high, that they want to study and learn more and more, in essence, the epiphany becomes a vehicle for motivating the students as well as grasping concepts, and this makes them lifelong learners. It makes maths *fun*.

  • Pushing your own “Dawn Treader”

    I went to see the new movie version of The Voyage of the Dawn Treader on my birthday and I was sorely disappointed. I liked The Lion the Witch and the Wardrobe and I was a little disappointed with Prince Caspian – if the pattern continues I wonder what depths of disappointment I might sink to if they ever make The Silver Chair.

    But my disappointment itself is quite another matter – the point of this post is why I’m disappointed: I’m disappointed because they removed most of the wonder and innocence of the book. They decided their version would be more exciting or interesting or mysterious, but in the end they just made it less than it was before. Many of the scenes of the book with the most meaning and feeling for me were cheapened by the film-maker’s agenda. And as to some of my well-loved characters – like the Dufflepuds – the film-makers thought that merely including them somewhere was the important thing, but I think it would have been better not to include them at all rather than the half-hearted cameo they got.

    *sigh*

    But what has this rant got to do with Maths or Learning or living in the Maths Learning Centre? Well here’s my thought – how often do we, with our students, do the same thing to the subjects we teach?

    In order to serve some agenda – say the usefulness of a particular bit of maths to some obscure application – we remove the wonder and innocence of our subject. The joy of discovery and learning, and the meaninfulness that comes from an encounter with something rich and wonderful are lost in the agenda we must keep.

    And we keep some things in our courses in order to appease the people who say it must be there, but it would be better to leave it out entirely than leave behind the shameful passing wave they have – like “informal induction” in the current South Australian year 12 maths curriculum.

    But what are we to do?

    If we have the choice to change our curriculum we are like the writers of the film – we have a responsibility to capture the wonder of the original and not push our own agenda.

    If we must teach the curriculum we have, then we are like the actors in the film who have to do the best we can with the script they’re given, even if it is only a hollow copy of the original story. We can put as much emotion and feeling as we can into our delivery.

    And if we are neither and like me aren’t directly involved in the curriculum at all, what then? Well the film did remind me of the book, and made me think of all those things I did love about it (even if they weren’t in the film), and it will probably inspire many who have never read the book to read it now. In the same way, maybe I can work with those students who are involved. I can tell them about the story I remember that is similar but so much better than the version they have seen; I can encourage students to have their own moments of wonder; and I can encourage them to investigate the half-hearted cameos further and gain a true love for the characters they missed out on the first time.