Making Your Own Sense

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

Tag: television

  • The Zumbo (hypothesis) Test

    Here in Australia, we are at the tail end of a reality cooking competition called “Zumbo’s Just Desserts “. In the show, a group of hopefuls compete in challenges where they produce desserts, hosted by patissier Adriano Zumbo. There are two types of challenges. In the “Sweet Sensations” challenge, they have to create a dessert from scratch that matches a criterion such as “gravity-defying”, “showcasing one colour” or “based on an Arnott’s biscuit”. The two lowest-scoring desserts from the Sweet Sensations challenge have to complete the second challenge, called the “Zumbo Test”. In this test, Zumbo reveals a dessert he has designed and the two contestants try to recreate it. Whoever does the worst job is eliminated.

    I find it very interesting that the Zumbo test is the harder of the two tests. In the Sweet Sensations challenge, the contestants can choose to use whatever skills they are already good at, and design their dessert in a way that they can personally achieve. In the Zumbo Test, the contestants have no control over the techniques that are required, and must try to do things they are not familiar with in ways they may not have seen before.

    And why am I talking about this? Because my medical students find themselves in similar situations. Our medical students have two projects to do as part of their research curriculum during their third year. One project is a research proposal: they work in a group with a supervisor to plan a hypothetical research project, including ethics, literature review and (this is where I come in) statistics. The other project is a critical appraisal: they work in pairs to analyse a published article, including where it fits in the research, the writing, the importance and (again where I come in) whether the statistics is appropriate.

    I have noticed over the years that in terms of statistics, the critical appraisal is harder than the research proposal. A meeting with students about the critical appraisal usually takes twice as long as one for the research proposal, and twice as much preparation for me. Many more students come to me to talk about the critical appraisal, and the ones who do come are more worried about the statistics they find in the critical appraisal than the statistics they need in the research proposal. Why is this?

    When watching Zumbo’s Just Desserts, it occurred to me that the reason why is the same as the reason the Zumbo Test is harder than the Sweet Sensations challenge.

    When doing your own research you can choose to only investigate questions in such a way to use the statistical methods that you understand. Even if you need a new statistical method, you just need to learn that one. Either way, you have complete control over your own decisions and know the things you are measuring and what they mean. It’s just like in the Sweet Sensations challenge the contestants get to make all the choices and use methods they are familiar with.

    On the other hand, when reading someone else’s research, you have no control over the wacky statistical methods they choose to use. Even if they are the appropriate ones (they often are in medicine, actually), the paper almost never describes how the researchers decided to use them – it just says what they used. And they often measure new things in new ways that you don’t deeply understand. It’s just like in the Zumbo Test the contestants have to do things that are new to them in ways that are new to them.

    It’s much much harder to understand the statistics in someone else’s research than it is to make your own.

    Let’s just hope we don’t eliminate all the students by asking them to do it with less support.

  • Sleeping through Miss Marple

    My wife and I like to watch mystery shows together like Poirot, Midsomer Murders and Miss Marple. Unfortunately I have a slight problem: when watching television in a comfortable position, I tend to drift in and out of sleep, no matter how interesting the show might be. This can be quite disasterous for mystery shows, especially ones with major unexpected plot twists.

    Just yesterday we were watching an episode of Marple called The Pale Horse and I woke up from a doze at the scene where everyone was gathered in the dining room to reveal the killer. And I had not the slightest clue what was going on.

    Later I went back to see the bits I had missed and it turned out I had missed a total of about three minutes of viewing in small snippets, but these were precisely the key moments I needed to be able to follow that final revelation.

    This morning it occurs to me that some students I have helped in the MLC have been in a similar position with their maths courses. A particularly common example is in Maths 1A too with the word “span”. It is mentioned in passing in one of the early Algebra lectures, with the discussion lasting for a total of about a minute, and it doesn’t seem related to the content of the course at the time. But then later it becomes one of the most important ideas and is talked about as if they already know what it is. If they “slept through” the first mention, they’d be most confused! It happens in our own bridging course too, with the idea of a “unit vector”. It’s mentioned on precisely two pages in our course materials, and is very easy to miss. Students almost always completely ignore the word in their assignment and then struggle to get what we are asking them to do. (This is one of the reasons we hope to rewrite the resources in future.)

    As teachers, we need to remember that a maths course is not like a murder mystery. In a murder mystery it’s the fact that working out the case hinges on small details that makes it mysterious and fun. But maths courses don’t hinge upon small details, they hinge upon big ideas. We need to make sure that anything pivotal is mentioned several times and discussed deeply so that even if their attention wanders for a minute once, they can still pick it up again and still follow the story.

  • Jamie Oliver’s teaching lesson

    This is a guest post by MLC lecturer Nicholas Crouch

    So it has to be said that I do like what Jamie Oliver does. I have always liked watching his shows and some of the messages that he aims to get across to the community are ones that I believe in. However when it comes to following his recipes and repeating what he does on television, well I figured it was like any other cooking show: the steps are there, but it required being a competent cook to begin with before you would get anything edible from doing what he said to do.

    With this in mind when I saw his show on how to make pasta, I was keen to give it a try as I have always loved the idea of making my own pasta. In fact I had given it a shot in the past. My pasta took a very long time and really turned out rather ordinary (and for 3 hours of cooking there was about 5 mins of eating).

    This time, however I listened carefully to what Jamie told me, created myself a mental list and believed that he was not going to lead me astray (and when I listened carefully, he did say pretty much don’t bother trying unless you have a pasta machine, which might be a lot of the problem with my first attempt). I followed his instructions and in very little time at all I had beautiful pasta which those who tried it all commented on in a very positive way. So why was this attempt so much more successful than the first?

    Well in thinking about that question I felt there could be some lessons that all who aim to pass on their knowledge could learn from. Jamie’s shows could be considered like a lecture, where he can talk about a topic, but there is no opportunity to give feedback on what the student has done. What did he do that was worthy of note?

    Firstly he was clear about what exactly to do. Most cooking shows are, but often get distracted by other less important details. He told me just what to do.

    Next he sign-posted. “If this is the situation you find yourself in at this point, this is your problem, and this is the solution.” Or “Do this until these conditions are met”. For example, I think he mentioned that if your pasta is too dry you can add more water to make it softer (but not too much). However, do not over complicate it with all possible cases, just the important ones. He also gave some explanation as to why we would do something in that way.

    Lastly he inspired me to believe that I could do exactly what he had done and achieve a similar result.

    So what are the lessons about teaching?

    Firstly, be clear, don’t overcomplicate something. You probably know a lot more than is required about your topic. It can be very difficult to cast your mind back to a time when you didn’t know that topic extremely well. However this is what you need to do to distil the essences of what you are trying to teach.

    Secondly, signpost (OK I should know the proper pedagogical term for this but I don’t). By this I mean, talk about the reasons for making the decisions that you have, not just the steps that need to be taken! For a lot of what I do, this comes down to trying to state the connections between what is being asked and what I am doing. Even to the point of listing my options and then saying why I would chose this option.

    As for inspiration, well that can be hard to give people advice on. I personally sound excited when talking about certain topics, and it is infectious. Other things that work are giving your topic some historical significance, or talk about how it is used.

    The last part is keeping the goal in mind. In Jamie’s case, we want to eat what we are working on. In the case of teaching we want the student to have a greater understanding. So look back at what you have done. (I know about this term – the cognitive closure) But this also can be a time where we talk to students about how they could re-order the concepts for themselves so that they don’t just have the linear connections in their head. The way the material has been presented to them, we want them to do more than that with it. So perhaps connect the dots for them, even mind map it for them if you have to!

    So next time you are in front of a class, sound excited and have pasta!

    If you are the student in the class, create your mental list and have confidence in your instructions!

    Thanks for your time

    Nicholas Crouch

  • Too much time on his hands

    On the train a while ago I overhead some people talking about Heston (the celebrity chef). Apparently he had been doing a series on giant food. It involves him trying to figure out the physics and logistics of trying to produce food on a giant scale – for example, a three-metre tall soft-serve ice-cream cone.

    After describing all the care and effort Heston took to produce this giant ice-cream, the first person declared, “He’s very clever.” Her friend’s response was, “He has too much time on his hands.”

    Clearly this person could easily do a better job than Heston if she wanted to, but she chooses not to because she has so many more important things to do with her time. Apparently Heston’s not clever, he’s just idle.

    I had a strong desire to lean over and ask her if JK Rowling had too much time on her hands, or if Stephen Spielberg had too much time on his hands, or Michaelangelo had too much time on his hands. If you think about it, what they did was more or less for their own enjoyment too and wasn’t “important” either.

    Of course, it wasn’t Heston I was really indignant about. The statement brought up several unpleasant memories when people have said this to my face when they have seen me making models of fractals, crocheting hyperbolic coral, drawing digits of pi on the pavement or solving puzzles, or even just doing maths in my own time. They seemed to feel that they needed to make those things seem trivial.

    Perhaps they felt cheated that they don’t spend more time doing things they actually enjoy. Perhaps they felt like I was making them look stupid and they needed to make me feel bad for it. Or perhaps they are just grumps who are unable to share in others’ fun.

    Now that my indignation has faded a little, I feel sorry for them. I remember what it was like to be in a situation where I felt it was somehow wrong to choose to do things I enjoyed, and it wasn’t a pleasant place to be. It can colour your view of the world and frankly it does make it difficult to enjoy other people’s fun.

    Still, it’s no real excuse for making people feel bad about things they have spent a lot of time acheiving. Sure, they may have a lot of time on their hands, but at least they are using it well!

  • Australia’s Got Dedication

    In the MLC Drop-In Centre, it sometimes happens that students succeed quite well at their maths, and yet somehow they manage to actually feel bad about it. They say that they only succeeded because they worked hard, and not because they are “good at maths”, implying that somehow natural talent is more worthy of praise. Well I’m here to say this is the most ridiculous thing I have ever heard.

    If you did well at maths because of your hard work, then you should feel proud! You should feel proud because that outcome is the result of your own personal effort – you were the one personally responsible for your own success.

    On the other hand, if you were born with a natural talent for learning maths concepts, if you always found it easy to solve maths problems and if you don’t have to work to get high grades in maths, then the best you can feel is lucky. If you really were born with a talent, then none of that success is really your fault at all, and you have no right to feel proud about it. You might as well feel proud of the colour of your eyes.

    Even in the TV show “Australia’s Got Talent”, if you listen closely you’ll find that the finalists are not there because of their so-called talent. No, the judges are giving them praise because of their bravery and hard work and in fact they deal out criticism for simply riding on raw talent. In short, perhaps a more accurate title for the show would be “Australia’s Got Dedication.”

    So start giving yourself some credit and stop beating yourself up for not being “naturally good at” maths! You’ve got something you can legitimately feel proud of – you’ve got dedication!

    These comments were left on the original blog post:

    David Butler 5 November 2013:
    Oh and PS: The concept that some people are “good at maths” or “not good at maths” is a myth anyway: http://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad… 

    Trang Nguyen 5 November 2013:
    http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-geniu… 

  • The seven doll’s houses

    There is an episode of the TV show “Friends” where Phoebe makes a doll’s house out of boxes. The other friends are most impressed with this doll’s house, especially with the candy room, aroma room and bubble-blowing chimney (except Monica of course, who still wants to play with her historically accurate mansion). Unfortunately, the cardboard doll’s house burns down, the fire seeming to originate in the aroma room.

    It was a cool episode, but it was made all the cooler after I watched a “making of Friends” show in the special features on the DVD. This featurette chronicled the making of a single episode of Friends, and the work of hundreds of people who made it happen. There were writers, set-builders, camera operators, editors, costume designers, sound editors, music composers, foley artists, live audience herders, actors, and props managers, all working sixteen-hour days just to make half an hour of television.

    The ones that most opened my eyes were the props managers. They make sure that everything the actors hold or touch works and looks the way it should. In particular, they made Phoebe’s doll’s house. In fact, they made SEVEN of Phoebe’s doll’s house: that’s SEVEN candy rooms, seven aroma rooms and seven bubble-blowing chimneys, all exactly alike. They had to make so many in order to get the scene right where the house burns down.

    Yet to us the viewers, there was only one house and it was only in the episode for a total of three minutes. You wouldn’t dream that there would be SEVEN doll’s houses to produce these three minutes of television.

    And it got me thinking about one of the major difficulties of my job: it seems easy. The students turn up to the MLC or our seminars or art events and we talk to them; they go to our website and find resources to use. It all seems so easy. But what people DON’T see the hours of other work: the data entry, the meetings with casual staff, the workplace safety training, the fiddling with web links, the data entry, the editing of videos, the painting, the design of posters, the printing, the laminating, the dishwashing and the data entry.

    Well finally someone recognised all that work. Yesterday we got a Commendation for Excellence in Support of the Student Experience from the Vice Chancellor. While we would never stop doing all this behind-the-scenes work (because we really do love working with students), it is nice to know at least a few other people appreciate how much goes into making it look easy.

  • 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?

  • 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!”)

  • The Fairyland Clickety-Clock

    This post is again inspired by the television show The Fairies (you have been warned!).

    In Fairyland, there is a peculiar procedure you have to go through in order to find out the time. The following sequence is played out several times across different Fairies episodes:

    RHAPSODY: I wonder what time it is.
     
    HARMONY: Well there’s only one way to find out the time in Fairyland…
     
    CUE MUSIC.
     
    ALL SING (with appropriate actions):
    Fairyland Clickety-Clock we need to know the time.
    Please show yourself in Fairyland and let us hear you chime.
    Tick tock Clickety-Clock,
    Tick tock Clickety-Clock,
    Tick tock Clickety-Clock,
    Chime!
     
    ENTER CLICKETY-CLOCK to tell everyone the time.

    You can understand why they lead such a carefree existence in Fairyland: if you had to do this every time you needed the time, you wouldn’t find it easy to stick to a timetable!

    Anyway, while watching the little sequence above, I was reminded of the Gramm-Schmidt Process, which the students doing Maths 1B in Summer Semester have been studying recently. It’s pretty much the only surefire way to create an orthonormal basis for a vector subspace. (If any of the words “orthonormal”, “basis”, “vector” and “subspace” are not familiar to you, then I wouldn’t worry about it too much – the point is that the Gramm-Schmidt Process is the only way to do a particular task.)

    The problem with the Process is that it can take quite a lot of calculation, especially if you’re working with long vectors. This of course inspires the students to ask if there is an easier way, or at least a short-cut sometimes. It usually takes some convincing for the students to believe that in fact this is the only way and they’re going to have to get used to how long it takes. Sometimes there really is only one way to do something, and it does take a while.

    RHAPSODY: I wonder what an orthonormal basis would be for this subspace.
     
    HARMONY: Well there’s only one way to find an orthonormal basis in Fairyland…