Making Your Own Sense

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

Category: Reflections

Reflections on learning and teaching and research and 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.

  • Happy Photographers

    Once upon a time at my place we used to watch “New Zealand’s Next Top Model” and “America’s Next Top Model”. They were a bit of light fluff that we could have on while doing something else.

    Every week in the show, the remaining models had a photoshoot. This involved some famous photographer taking photos of the models, after dressing them up in themed costumes, or painting them in mud, or dunking them in water, or getting them to jump on trampolines etc.

    And every week the same thing happened: as the photographers took the photos, they displayed very clearly in their demeanour that they were happy with some of the models, and unhappy with others. When the photographer was happy, they smiled and they looked like they were enjoying themselves; when they wre unhappy, they had a steely look of determination as if they just couldn’t wait for the whole thing to be over.

    And what was the reason the photographers were so happy with some of the models? Well, they said it was because the models actually listened to their instructions. They did what the photographers asked them to do even if it sounded silly, and even if it meant admitting they didn’t know how to do it without being given instructions. Other models, on the other hand, just continued to do whatever they thought was best regardless of what the photographers said and how unhappy the photographers became.

    And every so often I am reminded of these photographers when I am working with students in the Maths Learning Centre – I too have times when I am happy or unhappy because of the behaviour of the people I work with.

    I don’t mind in the slightest if the students don’t understand my first explanation and I have to try another and another – that’s all part of the job. What I mind is when I ask them to do something that will help them learn – like looking up something in their notes or writing down a particular fact on their page – and they flatly refuse to do it. It makes me so angry!

    On the other hand, some students happily take all suggestions. They are willing to give anything a go, and when they’re in the same situation next time they give it a go again without needing the sugesstion. Just like the happy photographers, I come away from these interactions with a smile.

    And I get something else from this that the photographers don’t: These students who listen, usually succeed in understanding their maths. And who wouldn’t be happy about that?

  • 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”.

  • Can I take a cheat sheet?

    The first maths exams for the year are tomorrow, so recently I’ve been talking to more and more students about exams. To be clear, I’m not complaining about this! It’s a really important part of the MLC’s role to give students advice about exams, since they have such a huge impact on the students’ experience of learning maths at uni. We can make a big difference to people by simply helping them cope with this stressful time.

    Anyway, one question that keeps cropping up is, “Can we take a cheat sheet into our exam?”, and the answer for the regular maths courses here at Uni of Adelaide is no. I’m not complaining about this either, because I believe that the process of memorising things strengthens connections in your brain that you will need for problem-solving. Moreover it’s easier to figure out how to do new things if you have a good stock of old things you are really familiar with.

    I’m not even complaining about the fact that students ask the question in the week before the exam. It’s perfectly reasonable to start looking around for ways to reduce your stress when you are in a stressful situation, even if your hope for relief is based on the slim chance that you just happened to miss a vital piece of exam administrative information.

    No, what I am complaining about is this: no-one seems to be teaching students skills to help them remember things while they’re teaching the maths! It seems obvious to me that if you expect students to remember things, you should support them in learning how to remember things. This is especially true if you know full well that they don’t have these skills already because the majority of them were allowed to take cheat sheets into all their exams in high school!

    Of course, it doesn’t change what my response is to the “Can I take a cheat sheet?” question. The response is to say no, and then give them some advice for how to remember things and talk to them about how it will help them do problem-solving if they do. I just wish more of that sort of thing was done at the moment they first learned the maths.

    Ok. My complaining is over. Now it’s off to the MLC Drop-In Room for the last day before the exam…

  • “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.

  • 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.

  • Statistics and Insomnia

    Some years ago, I saw a snippet on the ABC science show Catalyst about insomnia – in particular, the flavour of insomnia where a person has trouble falling asleep at all. They reported on a trial study investigating the effectiveness of a tortuous new treatment for chronic insomnia. (You can find the published research here: Click here to go to insomnia article .)

    The usual way to cure insomnia is to retrain your brain and your body to associate the bed with sleep rather than wakefulness. What they recommend is to only go to sleep when you’re really really tired, and if you don’t fall asleep in quarter of an hour, to get up and go to some other room until you feel tired enough to go to sleep again. Eventually, you’ll fall asleep in bed. Then you try again tomorrow night, and the next night, and the next night… Usually it takes a month.

    The big problem with it is that people just don’t have the stamina to put themselves through all this for four weeks. Here’s where the radical treatment comes in: you compress the month of practice into 24 hours. The poor participant is put in a windowless room and practises going to sleep, and when they finally do fall asleep, they only get four minutes to sleep before they are woken up to try and fall asleep again. In this way you fit a month’s worth of falling-to-sleep practice in one day. Imagine how desperate you would have to be to sign up for this sort of thing!

    Recently, it occurred to me that there are a lot of other skills that take a lot of practice to learn and this practice is usually drawn out over such a long period that people just don’t get through it all. One of these is statistics – in particular, the process of deciding which statistical procedures should be used to analyse your data.

    In your standard stats course, the approach to teaching students to make decisions is to get them to do a project. This gives them practice at making decisions a grand total of once. And so students need a whole degree’s worth of projects, and probably years of working as a statistician, to learn how to make decisions. Hence, very few people ever get very good at making them. It’s just like the poor insomniac trying to cure their own insomnia once a night.

    But what if you could, like the new insomnia treatment, compress all that practice into a short amount of time? What if you could pick out just the part where you make the decision and get students to make a lot of decisions all at once? Then they might get the necessary experience rather more quickly than the standard approach.

    I tried it out last year with the med students. I gave them a quick lecture about how you make the decision of which hypothesis test to use. Then, I gave them 30 research questions and got them to make a decision for each one. They seemed to get the idea of how it worked. So much so that they actually had intelligent questions to ask afterwards!

    I’m trying again this year, only this time the Medical School is letting me help design the whole stats teaching program, not just one lecture. Here’s hoping that a little bit of torture for a short time can alleviate months of pain later…

    Theis comment was left on the original blog post: 

    Richard Knowling 27 January 2012:
    This is an awesome idea David! I only wish Mike Roberts had still been alive to hear about it!

  • Mathematical collocations

    There is a phrase people use when talking about statistics that really bugs me. It’s “non-parametric data”. I see it all the time in statistical teaching materials and I hate it because I know what they mean, but what they’ve said is simply wrong. Whoever writes this phrase has a tenuous grasp of what the word non-parametric means. If they really understood what it meant, they would realise that the word non-parametric can only be used to apply to a statistical procedure, not to the data itself; the words “non-parametric” and “data” just can’t be put together like that.

    Ok, so now I’ve had my rant, let me tell you about the word collocation. I was looking at what was on the other side of our scrap paper recently (this is always a good way to procrastinate), and I found myself  reading drafts of the PhD thesis of Julia – one of the Writing Centre team. The bit I was reading concerned whether people understand certain idioms and how you might include information on what these idioms mean in a dictionary. As is appropriate for a scholarly work, Julia spent quite a bit of time discussing what is meant by an idiom, and here is where collocation comes in.

    One of the features of an idiom is the fact that it contains certain words which need to go together in a certain order. For example, the phrase “a piece of cake” has to contain both the word “piece” and “cake” or it just doesn’t mean the same thing. This phenomenon is called a collocation – some words just go with other words, and other combinations either just don’t happen or have a different meaning.

    Julia pointed out that part of learning a new language is learning which words go with which words in order to make a collocation. For example, you need to know in English that “piece” collocates with “cake” in this way, but that you can’t say “a slice of cake” and mean the same thing. As another example, you need to know that the word “hand” can be used in collocations such as “hand in”, “hand up”, “hand over” and “hand out”, but not “hand under”. And as a final example, you need to know that the word “fro” can’t stand on its own as a word but must be used in the specific collocation “to and fro”. These are difficult things to learn because most native speakers don’t even realise they are doing it; it’s just natural to them. And the native speaker can often tell there’s something wrong with what a non-native speaker said, but sometimes can’t quite figure out why it sounds wrong. So the teachers of language have to point these things out explicitly as new words are learned.

    And it occurred to me while reading this that collocations are really important to know about when learning maths too. In geometry we say that a point is “on a line”, but we say a line is “in a plane”. In set theory we say that an element is “in a set”, but a smaller set is “contained in a set”. (We even use different symbols for element-in-set, and set-contained-in-set.) In calculus we say that this is the Taylor series “for this function”, not “of this function.” And in statistics  the word “non-parametric” collocates with the words  “test” and “statistics”, but not the word “data”.

    Yet somehow we expect our students to pick this up all on their own. I think we need to learn something from our esteemed colleagues teaching language…

  • Bathelling in assignments

    The Deeper Meaning of Liff by Douglas Adams and John Lloyd  defines the word bathel like this:

    bathel (vb.) To pretend to have read the book under discussion when in fact you’ve only seen the TV series or movie.

    I do not like to bathel, and in fact it is one of my life’s ambitions to find and read the books on which the TV series and movies I have seen – especially those I saw as a child. This ambition has inspired me to read Tom’s midnight garden, The Children of Green Knowe, Anne of Green Gables, The Hundred and One Dalmations, Babe (aka The Sheep Pig), Archer’s Goon, Jumanji, Dot and the Kangaroo, Peter Pan, The Wizard of Oz, The Last Unicorn, Halfway Across the Galaxy and Turn Left, Finders Keepers and I’m sure several others I can’t think of right now.

    I was talking about the word bathel at the AUMS barbecue yesterday, and Nicholas called me to remind me that I had lost track of time and what I should be doing was helping students in the MLC Drop-In room. So off I went to help people with their t-tests, conics and subspaces. And it occurred to me while doing this that a small number of the students I was talking to were attempting to bathel about their coursework.

    These few students were attempting to use information they’d been told in their lectures to talk knowledgeably about a problem, without having tried to organise and connect the ideas first. They hadn’t sat down with their notes and some problems and tried to grapple with how these ideas can be applied. They had only seen the movie and not taken the time to read the book.

    (I should say at most students I talk to have a very positive attitude and do try to think through their course content deeply, using the MLC to help them learn to do this thinking!)

    A movie presents the ideas in a book most pertinent to the film-makers’ intepretation of the overall theme. And it does so in a small window of time without any pauses or breaks for thought. On the other hand, when you read a book, you can savour a particular page for quite some time, and flick back and forth as you read to check something you might have missed. And you can think about what the book means to you in the gaps between reading sessions.

    In the same way, the lecturer presents the ideas of a particular area of learning most pertinent to the overall themes of the course. And you don’t get the chance in the lecture to think through what it means to you and how these ideas are connected. To really understand you need to sit and savour it like you do when reading a book.

    I’d like to hope that I can encourage students to take the time to savour it, but if not, I’d at least like to teach them that bathelling is not the best way to go. Lecturers are pretty good at spotting people bathelling on assignments!

  • Quick Iggle Piggle! Catch Makka Pakka’s Og-Pog before it hits the Ninky Nonk!

    The CLPD head administrator Cathy told me a story the other day about an experience she had on the train: She was sitting opposite a pair of students, and one was helping the other prepare for a test. The first student was reading out words from a stack of cards and the second was trying to correctly say what they mean. After listening to this for a while, Cathy leaned over and asked what it was they were studying. The students said “pure maths”.

    This completely surprised Cathy, because not one word they had said in all that time seemed to be related to maths in any way, and some of them she had never even heard before. Now Cathy has worked in many different areas in her life, many of which were in academic institutions, not to mention her own experience with maths in the past. So it was quite a shock to her that she had never heard these words associated with maths before. “It was like a completely different language,” she said.

    My response to this statement was, “Quick Iggle Piggle! Catch Makka Pakka’s Og-Pog before it hits the Ninky Nonk!” And Cathy immediately knew what I was talking about because she, like me, has a young daughter, and therefore watches ABC2 rather a lot.

    You, however, may not regognise or attach any meaning to any of the words in that sentence at all. The question is: do you feel like an idiot for not knowing what I’m talking about? Of course not – it’s just that you happen to have never seen the TV show “In the Night Garden”.

    So why do so many people admit to feeling stupid for not knowing specialised maths words? If you happen never to have come across that particular area of maths in your life up till now, that doesn’t make you an idiot. It just means you’ve never come across that area of maths in your life up till now.

    If you feel stupid when you hear someone using unfamiliar words, just think of a phrase from some other area if life or learning where you’re pretty sure the other person won’t know any of the words. (Such as, “Quick Iggle Piggle! Catch Makka Pakka’s Og-Pog before it hits the Ninky Nonk!”)