Making Your Own Sense

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

Tag: life

  • Ten years

    On the 23rd of July 2008, I started my first day as coordinator of the Maths Learning Centre at the University of Adelaide. Today is the 23rd of July 2018 – the ten year anniversary of that first day. (Well, it was the 23rd of July when I started writing this post!)

    So much has happened in that time. I have given hundreds of hours of revision seminars, I have written/drawn on tonnes of paper, and used miles of sticky tape and chalk in mathematical artwork, and I have talked individually to over ten thousand students. I can’t possibly distill it all into one blog post, but I can talk about why I believe I am meant to be in this job and still meant to be in this job.

    When I went to the interview for the MLC coordinator position, I thought it would be a pretty cool job to have. At the interview, I had the epiphany that it was not just a cool job but it was in fact the perfect job for me, the job I really needed to have. Travelling home from the interview, the thought that I might possibly not get the job made me cry almost the whole train journey. I remember praying to God that I would find out soon. They called me that very night to say I had won the position!

    I still believe that this is the job I was destined to have. In no other job could I have been able to indulge my dual interest in both university pure maths concepts and fundamental maths concepts you meet in primary school. In no other job could I simultaneously help students overcome their crippling fear of mathematics and (sometimes the same students) become research mathematicians. In no other job could I make mathematical art and play an actual legitimate part of my work. Admittedly, I may have made some of those things part of my job when they weren’t part of it before, but it was being here in this role at this university that has allowed me to do so.

    There are parts of the job that are annoying – interminable meetings, lecturers who take my offer of support as an affront, constant requirements to convince the establishment that what I do is important, semesterly reminders that we just don’t have enough funding to provide the level of support I think is necessary – but overall it is a most wonderful and amazing job.

    When I started ten years ago, I already knew the pleasure in helping students learn, but since then I have learned the even greater pleasure of letting students help me learn. I have barely scraped the surface of learning first hand about how people think about maths and how they learn maths, and I don’t think I never get to the end of the wonder of it.

    Thank you to the other MLC lecturer Nicholas and all my casual tutors for coming along for this ride of teaching at the MLC, for listening to me as I talk through my crazy ideas and plans, and for pushing me to be a better teacher and leader. Thank you to all the other staff of the university that have worked so graciously with me, especially those nearest in the other student development and support roles. Thank you to my new colleagues I have met through Twitter, who make me better as a teacher and a mathematician in so many ways. Most of all thank you to my wonderful wife and daughters for always believing in me, and tolerating my mind ticking over on work things most of the time – I could never do this without your love and encouragement.

    It’s been a wonderful ten years at the MLC. I hope the next decade is just as wonderful.

  • Fairy Bread

    Fairy bread, in case you don’t know, is an Australian children’s party food.

    A tray of fairy bread triangles. That is, bread spread with butter and with hundreds and thousands (tiny ball shaped coloured sprinkles) sprinkled on top.

    Here’s how to make fairy bread: take white bread, spread it with margarine, and sprinkle with hundreds and thousands. Now cut into triangles and serve.

    Notes:

    • It has to be white bread. If you try to make fairy bread with wholemeal bread, or multigrain bread, woe betide you!
    • It has to be margarine, not butter. Butter may just be acceptable only if it’s the kind that is spreadable directly from the fridge. It may be that “margarine” means something different in other places in the world, so just in case, what I’m thinking of the butter-like spread made of plant oils that is spreadable directly from the fridge and can spread very thinly.
    • Hundreds and thousands are a kind of brightly-coloured sprinkles that are shaped like very tiny balls. If you use chocolate sprinkles, or sprinkles shaped like little sticks, or coloured sugar, then it’s not fairy bread.
    • It has to be cut into triangles. Don’t ask me why. Triangles are more magical than rectangles I suppose.

    When I went to Twitter Math Camp in the USA in 2017, one of the lunchtimes I made fairy bread for everyone and passed it out. It was heaps of fun seeing people’s reaction to it, which was mostly good, though mixed with various levels of surprise and confusion.

    A Twitter post from Heather (Kohn) Russo @HeatherRusso99 on 30 Jul 2017 with text and a photo. The text says: Fairy bread from Australia is delicious! Thank you @DavidKButlerUoa #TMC17 The photo contains: Six people smiling at the camera. Behind us is a big room with chairs and tables and lots of other people. I am the second person from the left, holding a tray of fairy bread. The other people are all holding a triangular piece of fairy bread.
    https://twitter.com/heather_kohn/status/891339803056275456 

    For me, fairy bread is strongly linked to memories of my childhood, and every time I eat it I am surprised again at how good it is. I mean, it’s the stupidest thing: bread and margarine with sprinkles. Yet somehow all the more awesome for that.

    And here is where I am supposed to make a point about maths or teaching or maths teaching. But that might ruin the whole thing. Like those horrible people who try to make fairy bread “more healthy” by using wholemeal bread. Honestly people! It’s a party food – just own it!

    Actually this reminds me of people who are always trying to get me to make a mathematical moral to my play. Yes there are times when the mathematics people do is deeply meaningful or useful for solving real world problems, and there are other times when it’s just for fun and there is no other purpose to enjoy myself and spend time with good people. Sometimes I need to be left to simply enjoy it, thank you very much.

    Oh look, I did make a point. I hope it didn’t ruin the experience too much.

    This comment was left on the original blog post:

    David Roberts 10 July 2018

    As I’m sure you know, David, Dutch people love sprinkles of all kinds on bread, and for some reason especially for breakfast. When I was in the Netherlands a few years back, at a supermarket, there were (at least) two whole shelving units for different kinds of sprinkles. I do wonder if fairy bread was introduced via some widely-sold party-food cookbook a few decades back (edit: well, it’s at least 90 years old, according to https://en.wikipedia.org/wiki/Fairy_bread  !), where the author/compiler was inspired by this cultural phenomenon.

  • Mr Johnson’s Rainbow

    I love reading and writing, and the way that people use words to express ideas fascinates me. So it is no surprise that when I was in Year 12, I studied the highest level of English available. My English teacher was called Mr Johnson and I hated him. (It wasn’t really, Mr Johnson – I’ve changed his name to write this.) The reason I hated him is expressed in this poem I wrote at the time:

    MR JOHNSON’S RAINBOW

    The afternoon sky was fretted
    With cotton shades of blue
    And the rainbow came, inspiring us all
    And on some old scrap paper
    My thoughts and feelings grew
    Some lines of verse upon the page did fall

    And then I took the poem
    A work all of my own
    And to my English classmates did I show
    That my poem was Quite Good
    To me it was made known
    Because my fellow classmates told me so

    But the teacher, oh my teacher
    Said: I know it is Quite Good
    But it is not what I would call My Way
    Your verses on the rainbow
    Are not the way I would
    Ever say the things that I would say

    For I, yes I my student,
    Am like the poet Donne
    As you are like the other poet Keats
    You like to write, like he,
    On emotion by the ton
    Where I do so much higher mental feats

    He went on by relating
    All the things that he would write
    And prattle from his open mouth did flow
    He said: the rainbow is
    All the colours making light
    So there must always be thingy, you know

    And I was quite inspired
    By this brilliant oratory
    And thought:
    Why don’t you write your own bloody poem if mine isn’t good enough for you?

    The same theme appeared in all of his feedback about all of my creative writing: he disapproved of the content I chose to write about, often saying that it wasn’t clever enough. He never gave me feedback on my expression of those ideas – no discussion of flow or characterisation or word choice or metaphor – only ever that the ideas themselves were not to his taste. One notable example was when we were asked to write a short story about a Far Side comic involving butterflies from the wrong side of the meadow, and so I wrote about the flowers sending rogue butterflies to attack the flowers on the other side of the meadow. I was marked down because I didn’t instead do something more clever, like write about some completely other thing only tangentially related to the theme of the comic. As you can imagine, I did not choose to study creative writing at university, and to this day I still have quite a fear of sharing my writing.

    Thinking about how this applies to my maths teaching, I wonder how often we tell students in maths “but it is not what I would call my way”. For example, those times when a student does a perfectly wonderful and correct solution to a problem, but then we tell them it has to be done this way instead. Or those times when we discount their excitement of maths applying to something that interests them to tell them they should be interested in the beauty of the maths itself. Alternatively those times when we get annoyed at the student who wants to understand the ideas behind a method and tell them to just do it and not worry about that. When a student asks me to check their work, do I critique their execution or do I criticise their ideas? What about all those times when I ask the class for what they notice/wonder and then wait until I get the one I was really hoping for? I am worried about students choosing to stop studying maths because we always judge them on their ideas.

    As usual, I don’t know what to do about this other than just be aware of it. Just yesterday when this was on my mind I was careful to say to a student how awesome I thought their Quarter the Cross solution idea was, before talking to them about how they might be more precise in their execution so other people could also be sure it was a quarter. I only hope I can have it on my mind a bit more often as I work with students on the everyday stuff in the MLC.

  • Childhood memories

    Two books I’ve read recently have encouraged me to investigate my memories from childhood. In Tracy Zager’s “Becoming the Math Teacher You Wish You’d Had“, she urged me to think about my maths autobiography to see what influenced my current feelings about maths. In Stuart Brown’s “Play“, he urged me to think about my play history to see what influenced my current feelings and tendencies about play. In the spirit of those two, here are some of my earliest memories about maths and play.

    In primary school, I have very few memories of actually being in a maths class, and all of them are negative. I’ve related two of them already in this blog. One was my memory of doing a maths assignment about one million dollars, where the financial aspect distressed me to tears. Another was my memory of my Year 6 teacher attempting to teach us averages using cricket.

    The only other maths class memory is of a test I did in Year 3. I had been sick with asthma for a couple of weeks and came back to school on the day of a test. I dutifully did the test and actually got almost full marks. The only thing I got wrong was the meaning of the word “net” in the phrase “net weight” as you might see listed on a packet of food. I distinctly remember it being a multiple choice question and ruling out two of the answers as ridiculous, but basically having to guess between the other two. I was angry because how could I possibly know that? Everything else was just logic and so I could figure it out for myself, but you can’t figure out the meaning of a word without more context. Eight-year-old me was an astute little person.

    Across my primary school career, I do remember a strong feeling of pleasure and fascination associated with construction toys. I remember absolutely loving the MAB blocks, in particular the moment when I replaced ten units with a long, and ten longs with a flat and ten flats with a block. Interestingly, my memory is only of the blocks themselves and I can’t pinpoint a year level or a teacher that goes with this. I also remember loving playing with polydrons and attribute tiles, but again the memory is just about the fascination of playing with them, and not about any particular maths class. In fact, thinking carefully about what is around me in these memories, I seem to be in a hall or a library, rather than in a classroom.

    Outside of school, I remember playing a game in each new playground, where I would try to do every part of the play equipment exactly once without crossing my path. Would I have to interpret the slide as both a sliding down and a climbing up in order to do it? Would I end up trapped on the top, or could I finish on the ground where I started?

    At home, we’d build elaborate maze-like cubby houses out of spare mattresses and sheets (we lived in a house where visitors often stayed over). I remember planning these out with my brother with explicit conversations of how we would fit more rooms and pathways into the space of our shared room. I also remember spending hours making designs with a ruler and compass. Or by folding paper several times and cutting out holes then unfolding and sticking on a contrasting colour.

    It seems that for me, geometrical play holds the strongest positive mathematical memories from my primary school years.

    Indeed, my very first memory of primary school is about geometrical play. It’s the moment I walked into my kindergarten classroom for the first time. We walked into a carpeted play area, and the desks and blackboard were some distance away at the other end of the classroom. Here in the play area was a bookcase filled with big thick brown blocks. Some of them were on the floor being made into a car track by some other children. I remember immediately wondering about how the various straight and curved pieces might fit together. I have some vague memories of tying various combinations on other days in kindergarten.

    Earlier than this, one of my only memories of Happy Days Pre-School was getting out the giant foam blocks from the store room under the building and playing with them on the grass.

    It’s funny that so many of my positive mathematical memories are geometrical when now I also have such a love of the structure and behaviour of numbers. Maybe that came later, though my mother says as a very young child I was always “playing number and letter games in my head”. I myself can’t remember doing that, but my mother is a very astute person and I am not about to doubt her observations.

    My earliest memory of any kind is of a cool hard flat greenness. My mother says this is probably a memory of the back verandah at the house we lived in before I was two years old – it had a green-painted concrete floor. I wonder if other people’s earliest memories are about feelings of space and colour. If so, maybe it means we’re all geometers from birth. Or maybe it’s just me.

    What is clear is that it’s hardly surprising that I ended up doing a PhD in finite geometry even though the original undergraduate degree I enrolled in was mathematical physics. I think the fundamental pull towards that geometrical play was calling me all along, considering how strongly I gravitated towards it in primary school despite the rest of maths not being so inspiring.

    If you’re reading this, I don’t know what you might learn from my story. But for myself I realise I am right where I belong.

    This comment was left on the original blog post:

    V Lakshmi 27 September 2017:

    Nice article! Infact, childhood memories have something to learn and plays an important role in future they are like the learning stages check this peace very interesting http://www.publicdebate.in/childhood-happiest-part-life-agree/ 

  • Actually, I am a maths person

    I am a mathematician and a maths teacher. Therefore it is an occupational hazard that any random person who finds out what my job is will respond with “I’m not a maths person.” The most frustrating people are my own students who I am trying to tell that my actual job is to help them learn maths. I used to tell them that there was no such thing as a “maths person”, but I have recently come to the conclusion that this is a lie. There is definitely such a thing as a maths person because I am a maths person.

    Let me explain.

    I used to think that the phrase “maths person” meant “a person who naturally finds maths easy and without working can do all the maths”. I’m pretty sure a lot of people do mean this when they say they are not a maths person, as if I’m going to force them to knuckle down and learn complex differential geometry at any moment.

    But it occurs to me that a more literal interpretation of the phrase “maths person” would be “a person who is maths”. That is, a person for whom maths is part of their identity. And in that case, there is absolutely no denying that actually, yes, I am a maths person.

    Maths is a huge part of my identity as a person. I have a favourite fraction (3/8), and a favourite fraction fact (1/3 + 1/6 = 1/2). I love the classification of quadrilaterals. I can’t help but see shapes in a building, or try to tell if a friend’s age is a prime on their birthday. I actively seek out puzzles to try. For goodness’ sake I wear home-made maths t-shirts to work every day!

    Of course, maths is not the whole of my identity. I am a Christian, a husband and a father. I love to read children’s books aloud, and to write stories, and to draw and to sing. I design board games for fun. It’s just that maths is a big part of who I am. I simply would not be me without my love of maths.

    So when I hear a person who says they’re not a maths person, maybe they mean that maths is not a part of who they are. Which is perfectly acceptable, to be honest. Maths doesn’t have to be an overtly obvious part of everyone’s personality!

    Still, I suspect a lot of people actually see not liking maths as a part of who they are. I wish they maybe allowed themselves to have a tiny corner of themselves to be a maths person. Maybe a maths little toe, perhaps. If only so that they can incorporate approaching maths into their study of, say, nursing or economics or teaching. What frightens me most is how difficulut it is to help people when they don’t see something as part of their identity. I know I can be gentle and calm and patient and encouraging, but I still worry how much of a difference I can really make.

    I am also afraid that they might look at me – clearly a maths person – and be intimidated by that part of my personality. Yet I can’t stop being who I am. I can only hope that my playful approach to it might alleviate some of that identity threat. Maybe seeing it as play will allow them to do it without seeing it as a change to their identity?

    That descended a long way into despair in only a couple of paragraphs, I’m sorry. But once I noticed that there was such a thing as a maths person, it really did create this spiral of doubt. I’d love to hear some words of wisdom from the people out there, so please do leave a comment or join in the conversation on Twitter.

    These comments were left on the original blog post:

    John Rowe 8 June 2017:

    Such a nice post, David, I really enjoyed reading this. I also see myself as a maths person but have great difficulty in describing it in that way for perpetuating a fixed mindset towards learning maths. One thing I still hear some people say, which I resent, is having a “maths brain”, which I think is much different to being a maths person. I do think, and worry, that when people see me as a maths person, some think it’s because I have a “maths brain”. Not sure if that made much sense… haha

    Great post – it resonated with me significantly.

    David Butler 9 June 2017:

    Thanks for the reply John. I agree completely about the idea of a “maths brain” being unhelpful. In fact, there’s a blog post on my list waiting to be written all about that. It looks like I’d better do that one next.

    Telanna 8 June 2017:

    I wonder if by the time we become adults with jobs and families of our own, our identities feel like they all the pieces of them fit together like a puzzle. And after all this painful teenager/young adult self-exploration it feels comfortable. Changing something that you alreasy settled upon might not be as fast and would require multiple experiences.
    It took me about 2 years of hanging around #MTBoS and actively seeking engaging mathematical experiences to turn from “definitely not a math person” to “becoming a math person”. But I had intention; what if someone doesn’t?

    I think you are right about playful and enjoyable experiences that can nudge people to looking at math differently. My workshop with most engagement this year was about manipulatives when even self-identified “not math people” had fun with hands on puzzles. I remember one of the comments, “Think I’ll get some wine and continue on the weekend.” I think the math/play/art events that you organize at MLC are great way to invite people in. Maybe “math person” will never become a big part of their identity. But then maybe “not a math person” will stop being a part of it. Like, I am not a mountain biker, but I do enjoy taking my bike to the mountains on the nice summer days and stick to the easier trails with beautiful views.

    David Butler 9 June 2017

    Thanks Lana. Even if I can only help people who are seeking, I think I can take heart that the seekers can be helped! The people who do visit me in the MLC are at least seeking to not be unmaths people, and you’ve given me hope that I can help them on that journey.

    John Golden 8 June 2017:

    I also self-identify… I guess the majority of those who read this will be, though it would be great to hear from others. Maybe we can share on FB where we intersect with a more general audience?

    I tend to think of this as the result of a kind of abuse. Not to minimize other forms of abuse, but convincing someone through repeated messaging that they lack a capacity which they really do have (in my belief) is really cruel. That it is done with often the best intentions of a teacher is deadly irony.

    My usual response is to ask what they do or enjoy and then share some of how that is like math to me, and if they were taught in a way that emphasized connections, they’d see that they are doing maths already.

    David Butler 9 June 2017:

    Thanks John. The cowering people do when they hear I teach maths certainly is consistent with a response to abuse. I wonder even more about how I can be a little positive experience on the day I meet them, rather than reinforce their abuse. Asking them about what they enjoy sounds like an interesting approach, and actually I have had some success with that sort of discussion too. That is, helping people realise that my ability with maths uses all the same skills as their ability with, say, poetry. There’s a blog post upcoming about that.

    Gregory Taylor 9 June 2017:

    There’s sort of an interesting distinction there, “doing” maths versus “being” maths. Being a teacher myself, and more to the point having personified something like 50 graphs into people, I can hardly deny having it as a part of myself too. On the flip side though? I am pretty terrible at finance.

    Like, I can calculate a tip… but budgeting, income tax, even knowing my own income, I’d much rather go to the dentist. I guess what I’m saying here is, “maths” is a huge umbrella. People can dislike part of it, even while accepting that other pieces are an integral (ha ha) part of themselves or other people. Trouble is most don’t get past the “dislike part of it” stage, assuming everything under the umbrella is the same, and hence being intimidated. Well, there’s a random thought, any way.

    David Butler 9 June 2017:

    Thanks Greg. That’s a really interesting point. Would I claim I’m not a fruit person because I don’t like all fruit? Or does being a [insert thing here] person mean you have to like all of it all the time? I certainly don’t enjoy all maths all the time, having a similar aversion to things financial as you do. Thank you for the thought.

    Mike 9 June 2017:

    G’Day from the USA,

    I am not a maths person. I say that from the experience of never having found maths to be an easy subject throughout my academic career. I like to joke that I was okay in maths class until letters made their appearance.

    This is not to say that I don’t, at this stage in my life, appreciate the application and use of maths in my life and the world around me. I am profoundly fascinated by the scientific facts that humanity has and continues to uncover thanks in large part to maths. I’m also very fond of using maths and logic to my own advantage in my personal and professional life.

    After reading your blog post, you definitely sound like a maths person; which I would define as someone who is fascinated with and enjoys thinking about and working with mathematics separate from its applications. I don’t share that fascination. Advanced maths to me remain a bit of a mystery. I can grasp the concepts that the maths operate on, or understand what the maths are trying to prove, but it is the how of maths that eludes me.

    To use an analogy, for a non-maths person it’s like being a traveler in a foreign land. It’s fascinating and exciting, but I don’t fully understand it. I can’t speak the language, I don’t understand the culture, I’m not used to the social and physical environment.

    A maths person is like a native of that land. They have an understanding and a feel for the culture. The language comes naturally to them. They can navigate the land of maths with confidence, if not ease. I may, through time and effort, come to understand maths to a level where I am more comfortable, and can get by okay, but I don’t feel as though I can ever assimilate to the point where I will have the same experience as a native of mathsland.

    My educational journey took me on a much different path. I am a lawyer by trade and education, and a philosopher at heart. That’s the land I feel home in. I enjoy thinking about and working through logical dilemmas, moral questions, and the why of human nature and human existence. Like you, I find myself pondering such things after a conversation, or while reading a book or news article, or even while washing the dishes. It’s endlessly fascinating and a significant part of my personal identity.

    I think this is true for everyone. We all have something that truly fascinates us, and for some those things come more naturally than others. For you it’s maths, for me it’s law and philosophy, for others it’s music, or poetry, or science, etc. Like you, I like to share my interest with anyone who has the patience to listen. It’s important that the “natives” share their interests with the “non-natives.” It makes us all better as people, and deepens our shared knowledge as a species.

    Thanks for sharing your perspective.

    David Butler 9 June 2017:

    Thank you so much Mike for sharing your thoughts on this! It’s a really interesting perspective to me.

    The comparison to a native of a country is making me think of immigrants. I would like people who have come to live here in Australia to see themselves as Australians, even if they weren’t born here. How can I, as a native, make them feel welcome? Even more, I’d like people who are only visiting to maybe not see themselves as Australian people, but maybe at least see themselves as “Australian people people” – people who like being around Australians even if they don’t fully understand them. It sounds to me like you’re happy to be a “maths-person person” and for others to be “philosophy-people people”.

    On that note, I would have to say that while I certainly wouldn’t consider myself a philosophy person, I definitely wouldn’t say I’m a non-philosophy person. That particular handle seems to me to be an unhelpful way to see yourself. From what you say about your appreciation of maths’s place in your life, I wouldn’t consider you a non-maths person at all! Somehow I think we need a middle-of-the-road word that doesn’t sound like it excludes all maths.

    Michael Way 9 June 2017:

    I am a maths person. I remember a co worker ( also a maths person) once say ”we as mathematician (teachers) like to count in our moments of idleness.” Yeah I find my self counting between light changes at an intersection, time between TV commercials, etc. That was one of he first moments I recall calling my self a mathematician and not just a teacher of math and not feeling afraid to say it.

    David Butler 9 June 2017:

    What a simple and lovely idea “counting in moments of idleness”. For me it’s drawing figures in my head. Thank you for sharing.

    Sally 10 June 2017:

    David’s original pat and the ideas of everyone here have made me stop and wonder: Am I a maths person?
    I enjoy thinking about maths, wondering about maths, playing with maths, teaching maths. Is this enough?
    My background is in philosophy which is lucky: thinking about thinking let’s you try on many hats. Sometimes I like wearing my mathematician hat and thinking about maths. Other times I wear my scientist hat and plan experiments; or my artist hat and create new things. There are many hats I wear, but always for me, the attraction is in the thinking that underlies each discipline.
    Perhaps the most important thing about the labels we give ourselves – “maths person” “not a maths person” “becoming a maths person” – lies in the activity of making the distinctions. We discuss what each one means to us and to others; we make distinctions and give examples in our quest to convey our feelings and desires, the things that give us joy (and the things that don’t). This conversation is so important because the same label can mean different things to different people and then lead to all sorts of misunderstandings!
    Thanks David for a post that helps us explore our own definitions and how they interact. Am I a maths person in the way you are? Sometimes? Maybe…. I don’t know yet – but I loved the opportunity to think this through some more!

  • Money and me

    In the online resources for Becoming the Math Teacher You Wish You’d Had, Tracy Zager provides information about the benefits of writing a “math autobiography”. I really have tried to do this, but I am having a lot of trouble organising my thoughs and memories. However, I reckon I can track some of my memories about one particular application of maths: money.

    As a child, I hated money. My mother says as a young child I would actually cry if someone gave me money as a gift. She thinks it might have been related to having to make a decision about what to spend it on, which was way too big a responsibility for little me to handle.

    This sounds right, based on a very specific memory to do with making decisions. I don’t know how old I was, but I wanted to buy some lollies at the local deli. I talked to my older brother and sister about the process and had a well-formed plan. I could go up to the counter and ask the man for 5c worth of lollies, he would give me lollies and I could go home with them. I walked to the deli with my 5c and went in the door. I reached up to the counter and placed my coin on top and asked “Can I have 5c of lollies?” The man asked me “What would you like…” and proceeded to describe about five options. I couldn’t cope. He was just supposed to give me a selection of lollies and I could have them and go! I wasn’t supposed to have to make all these decisions! I left my money on the counter and ran all the way home. It turns out that using money meant making a whole lot of decisions on the fly and I did not like having to have that sort of pressure.

    At some later time, I remember plucking up the courage to try and buy lollies again. I went to the school canteen and put my 20c coin on the counter and asked for 10c of lollies. The canteen lady looked at me and said, “You’ve given me too much.” I said, “But that’s all I have.” After a pause, she reiterated, “You asked for 10c and you’ve given me 20c.” I looked at her, not knowing what to say. I was certain that if you gave the lady more than you needed, they could just give you whatever was leftover. I don’t think I knew the word “change” to describe this, but I certainly knew how the process worked. Still, I wasn’t sure how to explain the concept to the canteen lady on the fly. She stared at me. Acutely aware of the line of people behind me, I took my coin and left. Looking back on this as an adult, I wonder if she simply assumed I didn’t know what the value of the coin I gave her was. Clearly it never occurred to her that I didn’t actually want to spend my whole 20c. I learned that sometimes people treat you like an idiot when you use money.

    Later again – I think it was during Year 4 – the teacher had set us an assignment asking us what we would do to spend one million dollars. I couldn’t do it. I had done absolutely nothing on the assignment right up until the very last minute, because I simply couldn’t face it. My mother sat me down to talk to me about it and tears streamed down my face as we tried to figure out what the problem was. I described all the examples the teacher had given, which were about cars or houses or things that people might want for themselves, but I didn’t want any of those things. Cars didn’t interest me, I liked the house I lived in, and I simply couldn’t imagine wanting to spend that huge amount of money entirely on myself. When my mother realised what the root of the problem was, she encouraged me to think about how I might spend the money on someone other than me. How could you use the money to make life better for someone else? In the end, I wrote my assignment about using a million dollars to start an animal shelter in order to look after lost animals. Not until now do I realise this assignment was actually about the size of the number one million. For me at the time, it was about money and spending, which were emotional topics and not maths at all.

    This aversion to money-related maths never really went away. In High School, I found topics on compound interest intensely uninteresting. I could “do” them, and I understood their application to my future life, but I never cared about them. When teaching financial maths to high school students, the explanations of which numbers in the graphics calculator had to be positive or negative were never natural to me. Even now I can’t process explanations of probability which define probability as “how much you’d be willing to pay” for something. How much I’m willing to pay for something is such a complex issue, which requires me deciding if I actually want the thing and is dependent on how much money I actually have to spend and my emotional state, not to mention the horror of having to manage the interpersonal minefield of actually negotiating a price.

    I don’t have any particular goal in relating all of this and I wonder if it will mean anything to anyone else. For me, it has helped me realise just how much of my like or dislike of particular applications of maths has to do with emotional and interpersonal things. It makes me aware that there will be internal battles inside my students that affect how they respond to maths and its applications that I can’t see or even they can’t see.

    These comments were left on the original blog post:

    Paula Krieg 19 April 2017

    One thing that’s really powerful about this story,David, is how a person can be struggling so intensely with a problem has little to do with the problem that is presented. About the canteen lady, it’s easy to think that she was being a jerk to little David, but the fact is, she really may not have known how to make change. Hard to know if in that case she was the one that was struggling with problems that were hard to pinpoint. A good reminder to ask questions of the person who is befuddled. but what a great string of stories. thanks.

    David Butler 19 April 2017

    Thanks Paula. It was a tough thing to write.
    That may possibly have been true about the canteen lady. Still, 6- or 7-year-old David could hardly have helped her understand at the time!
    I guess a lesson for 37-year-old David is indeed to ask and listen to people.

    Nicola Petty 2 May 2017

    Kia ora David
    An interesting story, and almost the opposite of many people, like my father, who felt he could only do maths if it involve money.

    I have an aversion to stars and anything much to do with space. The size of it all makes me feel uncomfortable. I know for many people, space is really interesting, but I would rather not think about it. I don’t know why I feel like this, and I have a hard time seeing why other people are so interested in space. We just don’t know what will make people uncomfortable!

    David Butler 4 May 2017

    That’s really interesting Nic. Another fine example of how we can never really predict what might be going on inside our students’ hearts.

  • Mansplaining

    A few months ago, I learned a new word: “mansplaining”. You may have heard it before, but I never had until this year.

    The general idea is that very often, a man will explain something to a woman in a way that seems to be based on the assumption that the woman is incapable of understanding the concept themselves and requires the man to rescue them from their misunderstanding. Often it is very explicitly patronising or condescending. This is a mansplanation.

    In recent weeks, I have seen people I greatly respect being treated this way in the online space, and they have called out the man in question by telling him that he was mansplaining. Quite often, he has responded with quite a bit of vitriol, claiming that the word “mansplaining” is in itself sexist and they were just “trying to help”. This very vitriol is of course really not supporting the man’s case, and tends to show that his assumptions actually are that the woman did need to be rescued from her ignorant state. You can see some classic examples of this sort of assumption in Fawn Nguyen’s excellent blog post “Baklava and Euler “.

    I had formed the idea that mansplaining was really just assholesmanplaining, and it didn’t have all that much to do with your general everyday respectful man.

    But then something happened that hit me in the guts. Megan Schmidt started a conversation on Twitter about notation, and it had a flurry of responses, all from men, one of whom was me. She tweeted separately that “the mansplaining game is strong right now”. I was not consciously responding from an assumption that Megan needed to be rescued from confusion, and yet the conversation was called mansplaining. Clearly Megan’s use of the word didn’t fit with my understanding that only assholes mansplain.

    It was time to get to the bottom of this, so I asked Megan to help me understand what she meant and how she felt about it. I have to thank her a hundred times for the thoughtful and gracious responses that she gave. I hope I will do justice to what you taught me, Megan!

    I learned that there are times when offering an explanation at all is actually mansplaining. Not because the explainer is an asshole, or because they meant to be condescending or sexist, but because the explainer is unwittingly playing to a wider cultural assumption that the woman needs an explanation at all.

    When a woman expresses frustration or anger or worry at something, a man’s common response is to offer an explanation to clear up confusion. Do you see the disconnect there? The man is rescuing the woman from confusion, but the woman wasn’t expressing confusion. She didn’t need an explanation – she didn’t need to be “rescued”. It’s most likely that she actually does understand the nuances of the concepts involved. Indeed, she would usually have to understand in order to have the emotional response she is having.

    An unfortunate part of it is that the majority of men in this situation, especially in a professional setting, actually do realise that the woman does have the same or greater experience and training. It’s just that they are culturally conditioned to offer explanations in response to frustration. Indeed, it seems to be that men in professional settings are expected to engage in more “academic” conversations than “emotional” ones. Yet by doing so, we are still mansplaining.

    The problem is that it opens the door for assholemansplanations, which are sure to follow. Even worse, it is adding to the hundreds of tiny  sexist events that occur for a woman every day. And it reinforces the very cultural norm that produces those daily tiny sexist events. It’s important to give the experience a loaded name like mansplaining to make sure that those of us who do care have our attention drawn to these problems.

    But how, as a man, can I fight back? Well, I can certainly call out others when they are mansplaining. Assholemen need to hear it from other men to have a chance of hearing the message – they’ll never listen to a woman. Ordinary men need to know about the damage they do unintentionally.

    And what about my own daily actions? All I can think of is to be more aware. I can listen to the actual words people are saying and notice the emotional part of what they say. I can choose to respond by asking for more information first, rather than launching into an unwanted and unnecessary explanation. It takes a lot of energy to watch your own words and actions, and sometimes I will slip (sorry in advance) but with practice I’ll get better at it. And then one day maybe I’ll find I never offer a mansplanation again.

  • Do you get tired of the same topics?

    In the Drop-In Centre, the majority of students visit to ask for help learning in a very small number of courses, mostly the first-year ones with “mathematics” in the title. Of course, any student from anywhere in the uni can visit to ask about maths relating to any course, and we do see them from everywhere, but the courses called Maths 1X have between them a couple of thousand students per semester and that’s a lot of people who might need help to learn how to learn.

    Anyway, the upshot of this is that I help people with the same topics semester after semester, year after year. Sometimes people ask me this question:

    Question:

    “Do you get tired of the same topics?”

    Short answer:

    No.

    Long answer:

    I actually really love the topics in first year maths. Row operations and the fact that they help to solve equations and decide independence and find inverses are fascinating. Nutting out how to do an integral is a fun game. Eigenvalues are the Best Thing Ever. And don’t get me started on conics and quadrics. To me, seeing them every semester is like watching the Muppet Christmas Carol every December. I get to be reminded of a story I love, and notice something little I had never noticed before every time.

    Also, it’s not just the topics I get to see each semester, it’s the students learning the topics. So many of them have a perfectly appropriate and successful way of understanding it that never occurred to me and these make the topics fresh again. Who ever thought of checking vectors are parallel by making sure that cos of the angle between them is 1 or -1? Not me until yesterday when a student did it.

    And then finally, I get to be there at the moment everything clunks into place and see the light in their eyes as they feel the buzz of understanding it for the first time. And that never gets old!

    Short answer:

    Hell no.

  • My cat’s bottom

    Did you know that cats have scent glands just inside their bottoms that are constantly being filled with liquid and are squeezed as their poos come out, and if their poos are too skinny the glands are not squeezed enough and get over-full making them very painful and inflamed? Neither did I, until my cat Tabitha Brown started bleeding out of her bottom.

    The vet literally reached into Tabitha’s bottom and squeezed the glands, making scent-liquid squirt all over his face (I have very great respect for vets, especially this one!). Then he told us some very useful things about how to look after our cat properly, such as the fact that many cats need Metamucil (yes, human Metamucil) every so often.

    The point of this story is that we would never have known about how to look after our cat properly if she had never been in this pain. Because of her bleeding bottom, we now know for her, and for any future cats we might have in our home, to keep an eye on the size of their poos and give them Metamucil if the poos are consistently a bit skinny. All because of her bottom.

    As always, my life makes me think about my teaching…

    Students often say that I am a better teacher than their own lecturer, and it has become clear to me that the main reason this might be true is because I spend so much time with students. I am there when they have problems, and so I am able to see the problems students might have, and thus I am better equipped to help future students. There are so many things about the way people learn or don’t learn that I would never know if not for me being there when the students were in pain. Not that I wish anyone pain of course! I’m just saying their pain helps me prevent unnecessary pain for future students.

    So thank you to all the students who were in pain and let me be there when they were. You make me more able to help others.

  • But I don’t like cricket

    When I was in primary school, one of my teachers once tried to teach us averages using cricket, and it is one of my strongest memories of being thoroughly confused in maths class.

    I’m pretty sure my teacher thought that using cricket to teach averages was a great idea, but (for me at least) it was a very bad idea, for three main reasons. First, I didn’t actually know the all rules of how cricket was scored. I had played cricket before, but this amounted to hitting when I was supposed to hit, running when I was supposed to run, and trying to catch when I was supposed to catch. I had never actually scored anything or been told how this was done. So all his discussion of average scores was basically meaningless to me. Second, there’s this technical detail in cricket batting averages that has to include “not out” somehow, which makes it not like normal averages. He spent most of his lesson discussing this detail and I ended up not knowing what a traditional average was, letalone a cricket average. Third, and most importantly, I didn’t like cricket. As an exercise-induced asthmatic, the running wasn’t pleasant. As someone with low coordination, I tended to be out pretty quickly as a batter, and so spend a lot of time just sitting on the bench. And as a fielder, well, the chance of actually interacting with the game as a fielder in primary-level cricket is quite low. So the mere mention of cricket turned me off. If cricket is what averages are for, then I really didn’t want to know about averages.

    And this story embodies the dangers of using “real life applications” to teach maths:

    • Students don’t know the context: If students aren’t familiar with the context of the application, the discussion will be meaningless to them, which often leaves you teaching the context itself rather than the maths.
    • The context is too complex: Most contexts are more complex than the thing you are trying to teach, and to deal with this complexity, you often cloud whatever it was you were trying to teach (or end up changing the context so much it doesn’t make sense any more).
    • Students might be turned off by the context: The application itself has a high chance of simply not being interesting to the students at hand, and they will transfer this disinterest to the maths.

    All three dangers are real and present in every classroom, especially the third one. Yet I have lost count of the number of people who have responded to the question of “how do I motivate my students to learn topic X” with “just tell them about application Y”. No-one seems to recognise the possibility of disengaging students by telling them about application Y.

    I’m not entirely sure what to do about it, unfortunately. If you have a group of students at university who are all studying the same degree (say Mechanical Engineering), then you have a good chance of picking an application they will be interested in, but even then almost always you have the second danger of complexity getting in the way. You could conceivably get the students themselves to seek out applications of the concept to things they personally are interested in, but some maths concepts simply aren’t used in varied enough places. And you could just show them a huge number of different applications so that they are sure to be interested in at least one of them (a linear algebra lecturer recently did this with eigenvalues). But of course, you yourself would have to know all these applications.

    In the end, I think we need be aware of the dangers so we can keep an eye out for students disengaging. Also, I think we need to make sure that the students are comfortable with the maths itself, and we need to be excited about the maths itself, whether we use a real-life application or not. Then the students who don’t like cricket might be able to be interested in just the maths.