Making Your Own Sense

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

Tag: identity

  • Who is worthy to ask stupid and smart questions?

    This post was going to be part of the Virtual Conference of Mathematical Flavours, which you can see all the keynote speakers and presentations here: https://samjshah.com/mathematical-flavors-convention-center/ . The prompt for all the blog posts that are part of this conference is this: “How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?” In the end, it didn’t end up being there, because my computer started dying painfully at the critical time, but I still want to highlight the Virtual Conference anyway because it was a great idea.

    There are many things I could have written about this, but I think I will choose one thing that is about my approach in the MLC to student questions. In the MLC everyone is worthy to ask both stupid and smart questions.

    My Maths Learning Centre is a place where any student doing coursework at the Uni of Adelaide can visit to talk about their maths learning with a tutor (often me). People come to talk about all aspects of their maths learning in all sorts of places where maths appears, from dividing whole numbers by hand to understanding proofs about continuity of functions between abstract metric spaces. My point here today is that people from both ends of that spectrum and everywhere in between are allowed to ask questions that are about basics and questions that are about deep connections.

    Imagine a student who has always been good at maths, who finds things easy and quickly grasps abstract definitions. It is natural for such a student to fold their goodness at maths into their identity, which often means they become extremely embarrassed to show any sign of struggling. They’re supposed to be the smart student and this simple stuff is supposed to be obvious for them. So if they have a question about the basics, they hide it and hope it will come clear eventually.

    The thing is, having a question about something simple doesn’t make you stupid, and it doesn’t even make you not smart. Having a question about how to get from line 3 to line 4 is at the very least a sign that you’re paying close enough attention to wonder about that step; having a question about the definition is a sign that you know definitions are important; and having a question about some random bit of algebra or notation you happen to have never seen just shows you want to learn. In my Maths Learning Centre, I try to make it a place where everyone can ask a “stupid” question. Where stupid questions are treated with respect and answered clearly, with encouragement to make sense of what is happening.

    Now imagine a student who has always struggled with maths, who just never seems to understand the explanation the teacher is giving the first time, and who struggles to get through the first few of the exercises. It is natural for such a student to fold their badness at maths into their identity, which often means they don’t even try to understand things and just look for some step-by-step instructions they can follow so it will be over with as quickly as possible.

    The irony is, they never finish their exercises, so they never get to be part of that part of a maths class where the early finishers ask the deep and involved questions about theory and beyond-curriculum interesting stuff – the very stuff that can make maths a lot more fun. I know for a fact that students who feel they are bad at maths are intelligent people capable of logical and creative thought, and they deserve to ask their deep questions. So in my Maths Learning Centre, I try to make it a place where everyone can ask a “smart” question. If a student who is struggling asks about infinity or quaternions or what my PhD was about, I will damn well discuss it with them. If they look at the work they’re doing and ask how it is connected to some other bit of maths, we’ll explore that together. That curiosity is a treasure to be prized and I will not squash it by saying we have to get on with the assignment now.

    And you know what, it turns out that many a basic question is actually a deep and clever question after all. Recently a student who was struggling asked why it was ok to add two equations together. Not one student in my ten years of working at the MLC has ever asked that question! There must be something really special about the person who asks this question, right? And it’s a really deep question about the nature of equality. I want my Maths Learning Centre to be a place were it is okay for everyone to ask a question that is simultaneously stupid and clever.

    That’s all I have to say. I believe everyone deserves the chance to ask stupid questions and to ask clever questions and to ask questions that are simultaneously both. They are worthy to have their questions taken seriously and the answers discussed with respect for the humanity and intelligence of the asker. I have to always remind myself to give students the chance to ask these questions when I’m with them, especially students who are struggling to articulate the questions for whatever reason. And maybe if they’re not asking, I’ll sometimes ask the questions for them and we’ll answer them together.

    How will you welcome all people in your learning spaces to ask all kinds of questions?

  • TMC17 Reflections a year later

    A year ago, I went to Twitter Math Camp (TMC) and it was a wonderful experience. TMC is a great conference full of all sorts of opportunities for maths teachers to learn from each other in many ways.

    Here are three reflections on my experiences there.

    You can read this blog post, along with later posts on the same theme, in PDF form here. 

    The titles of the posts in the series are:

    • TMC16 reflections from someone who wasn’t there (2016)
    • TMC17 diary (2017)
    • Fairy Bread (2018)
    • My Favourite is my favourite (2018)
    • TMC crochet coral quietness (2018)
    • The TMC Attitude (2018)

  • Book Reading: Choice Words

    This post is about my reaction to the book “Choice Words: How Our Language Affects Children’s Learning” by Peter H. Jonston.

    (You can read this blog post and all other Book Reading posts in PDF form here. )

    I was lent the book by Amie and I am very grateful to her because it really is a good book (though it was tough to read with the forest of sticky notes marking her favourite pages 😉).

    This thin little book is about how words have power to help children learn about reading, writing, learning, themselves and their place in the world. The majority of the book is a list of sentences spoken by teachers followed by an analysis of what those words mean for children’s learning. The focus is mostly on helping children learn to read and write successfully, but don’t let the “children” or the “read and write” fool you – I have so many thoughts swirling in my head about how this might possibly apply to my own teaching, and indeed my life.

    Unfortunately, “swirling” is the appropriate word for my thoughts right now. The fact that the book is structured around analysing specific utterances by teachers made it all very concrete, but on the other hand it is making really hard for me to process the information coherently. At the moment it’s just a big cloud of things to think more about, a lot of which overlaps. I’m finding it hard to tease things apart to find something I can apply first, or a way for me to consistently apply it so it’s useful for my students. I’ve decided the best thing to do is to write this post so I can attempt to process it all.

    The chapter titles might be a good place to start. Here they are:

    1. The Language of Influence in Teaching
    2. Noticing and Naming
    3. Identity
    4. Agency and Becoming Strategic
    5. Flexibility and Transfer (or Generalizing)
    6. Knowing
    7. An Evolutionary, Democratic Learning Community
    8. Who Do You Think You’re Talking To?

    Even just listing those titles is helping me focus a bit more. While I was reading it, it might have helped me to keep a bookmark in the chapter heading so I could look back and remind myself what the big idea of the chapter was. Instead I found that I got a bit bogged down in some of the details as I went along and lost the focus. Now that I can look back from a higher vantage point, I reckon I might be able to pull out some bigger ideas…

    Chapter 1 is about how much our language has power to create reality, in particular the reality of the listener’s identity. If I were to hold on to just one thing from the whole book then maybe this message would be it: I can make the world different for another person by choosing the words I use.

    Chapter 2 is about how in order to learn and know what you have learned, you need to notice things. You need to notice how things are similar or different, how they are related or not. And then, things need to be named, so that it is possible to talk about them. This is remarkably similar to the Notice and Wonder idea from the Math Forum people, and to Chris Danielson’s way of getting to geometry ideas via Which One Doesn’t Belong. But here, Peter goes deeper than this. He suggests that you can notice and name not just content, but also your processes as you work as a group, your thoughts about yourself as a learner, the things you have learned so far, and your behaviour. It is a fascinating idea to me that you can apply the same noticing and naming to mental and social processes as you can to the properties of quadrilaterals. Something to hold onto from this chapter is that my words can draw attention to features worth noticing, and the act of noticing itself.

    Chapter 3 is specifically about identity. Peter talks about how we construct a narrative with ourselves as one of the characters and the words we use to tell this story shape the sort of person we see ourselves as. We as teachers can make a difference to identity by the words we choose. Something that struck me most strongly was using words that don’t give people a choice to opt out of the identity. For example, the question “What problems did you have?” assumes that there must have been problems, and asking someone what choices they made assumes they made a choice. This is what I want to hold onto from this chapter, that I can give someone courage to be a writer or mathematician by using words that put them into that character.

    Chapter 4 is about agency, and in a way is an extension of the previous chapter on identity. The identity in question here is that of a person who has power over their own choices. This chapter spoke to me most strongly as a maths teacher, since maths is a subject where so many students feel they have no choice and that choice isn’t even a thing that people ought to have (as evidenced by the constant request to tell them what to do). Peter advocates talking to students as if they did make a choice, and analysing the choices they could have made. This is one of the biggest ideas in the whole book to me, and I want most to hold onto this one as I go forwards.

    Chapter 5 is about transfer, that holy grail of teaching where students are able to apply what they learn in one area to another. Peter pulls together the agency and the noticing/naming from the earlier chapters as the main mechanism for this. More explicitly, the questions listed here focus on noticing explicit connections between things and also exploring the “what if” questions. He ends with a comment about the importance of play, which of course resonates strongly with me. The thing I want to hold from this chapter is the focus on connections, over and above answers.

    Chapter 6 is about knowing, and in particular about who holds knowledge and who decides when we know something. In many teacher-student interactions, the assumption is that it’s the teacher who knows and the teacher who decides what is true and when we are correct. Yet really one day when they leave our care, our learners will need to know how to be sure of things for themselves. The thing I want to hold onto here is that I can give my students the power over knowledge. This is especially important in maths, which is set up so that you actually can be sure of things through your own arguments, rather than having to rely on the authority of others.

    Chapter 7, while it has a very long title, is really about how our words can help people learn to work together. Peter has a lot of examples where teacher words encourage learners to consider the feelings and ideas of others, and to choose shared goals. He reuses the noticing and naming power of words to help learners notice their own group processes, and the identity-forming power of words to help learners put on the mantle of people who care about others. The thing I can hold onto from this chapter is that words can make group social and cognitive processes explicit in a way that makes them learnable.

    Chapter 8 is about the interplay between your beliefs and your words. As a teacher, if you believe your students are not capable of learning something, your words (and your silences) will reflect this. However – and this is the big thing I want to hold on to here – if you choose to change your words, then some of your beliefs might follow. I see this in using SQWIGLES with myself and my staff where choosing to ask open-ended questions changes the ways that students respond to you and therefore ways that you respond to them. Your beliefs about what students have to say can change through this change in your words.

    I think I’ve achieved my goal in writing about this book, in that I have a much clearer idea about how I want to respond to it in my work. I have clarified how much of an impact my words can have on learners’ realities, which I knew, but not to the level of specific detail I did before. In particular I think I want to hold on most strongly to the idea that I can help learners to see themselves as having choice and capable of making that choice, changing both their view of mathematics and of their place in it.

    These comments were left on the original blog post:

    Simon 8 August 2017

    Well, that makes me want to read it – thanks for taking the time to review it David.

    Nic Petty 8 August 2017

    Thanks for this David. I am really interested in how this fits with the ideas on helping people to think more positively about mathematics and to think of themselves as mathematicians. Language empowers or disempowers people, and we really want the former.
    I have just bought the book. (Thanks to one-click on Amazon, I can have instant gratification.)

    David Butler 10 August 2017

    Thanks Nic. I’d love to hear your journey as you read it too.

    Mark Pettyjohn 8 August 2017

    It sounds like you are at the beginning of a tremendous journey. My book probably looks a lot like Annie’s. This thin book spawned so many thoughts.

    I see Nic commented above about identity. It looks like he teaches stats, which probably means high school students. That puts you two in a basket teaching students whose identities in mathematics have already been forged for a good portion of their academic careers. So while the end goals may be the same as someone like me working down elementary, I think you two have a much tougher go of it.

    Not that you shouldn’t! Last year I worked with a professor who was teaching a university course of mathematics for college students studying to be elementary teachers was enlightening. There were some serious challenges to developing a positive mathematical mindset, but I also saw some good progress.

    I know you will be keeping us updated, and I am looking forward to following along in the coming months and years.

    David Butler 9 August 2017

    Thanks for the comments Mark. It was motivating to think that my words might be enough to help people *change* their identities, as opposed to *form* them. I felt a lot of these things already, but the book helped me know them.

  • 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/ 

  • The Arts student’s maths brain

    Yesterday I talked about one of the common responses to people finding out I am a mathematician/maths teacher, that of saying, “I’m not a maths person.” The other common response I get is, “I don’t have a maths brain.” (John Rowe mentioned this in his comment on the previous post.)

    This is how I reacted last time someone said this to me:

    A screenshot of two tweets from DavidKButlerUoA on 5 Jun 2017. Yesterday at church the youth pastor responded to learning what I do with "I don't have a maths brain". I fear I may have been a bit rude when I almost yelled "There is no such thing as a maths brain!" https://twitter.com/DavidKButlerUoA/status/871637804916195329
    https://twitter.com/DavidKButlerUoA/status/871637804916195329 

    It may not have been the best response, but I stand by the sentiment. I strongly believe there is no such thing as a maths brain. Or at least, that all brains are maths brains. I believe all human brains are wired in such a way to be able to learn and do maths, not least because I observe babies engaging in mathematical thought long before they can talk, so that capacity is there in all of us from the beginning. But more than this, I believe that the skills that I use to be good at maths are the same skills that other people use to do other things that they wouldn’t call maths.

    I have one specific story to tell about how I helped an Arts student to believe that maybe she did have a maths brain after all.

    Earlier this semester (a few months ago now), several student services were invited to an orientation event for Arts students, to make sure they knew about what was available for them. So I went along with a Writing Centre staff member to do our usual joint activity of Numbers and Letters.

    A student came along to see what we were doing and happily engaged with the Letters game. She then glanced over at the Numbers game and I asked if she’d like to join in. With a rather green look on her face she said, “I don’t have a maths brain!”

    I said, “I’m not sure I believe there’s such a thing as a maths brain.” Then I asked her what she was studying, and she revealed it was mainly poetry. “That’s really cool!” I said. “I reckon the skills you use to analyse and create poetry are tha same ones I use to do maths. Did you want to try a different sort of activity?” She graciously agreed and so I wrote this haiku on the board:

    Word points, letter lines:
    Fur ute you oft try fey roe.
    My geometry

    “What do you notice?” I asked.

    “It really is a haiku. And there’s a lot of really interesting words in that middle line.”

    “Yeah I know right? I particularly like the concept of fey roe. What else do you notice about the words in that middle line?”

    “Well, they’ve all got three letters…”

    Following this was a most wonderful conversation about the letters they start with and end with, and which letters appear and how many times, scribbling notes on the board. This all culminated in the beautiful moment where the student realised the symmetrical nature of the words and the letters here and made an “oh!” of satisfaction.

    “That was cool,” she said, after declaring she had to go. “Maybe I have a maths brain after all.”

    This was one of the greatest moments of my entire teaching career, right then.

  • 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!