The following video (duration 23:32) forms part of Eddie Woo's article in Scan, Volume 43, Issue 1.

Eddie Woo

Mathematics Teacher, Cherrybrook Technology High School; Leader, Mathematics Growth, NSW Department of Education; Professor of Practice, University of Sydney

Video transcript

It is a real pleasure to be able to present to you a session that I've titled, ‘Stories that count: how maths and literacy enrich each other’. I don’t have a long time to present with you, but I do want to cover a few big ideas with you.

Firstly, to address the elephant in the room. I know speaking to a bunch of people who care deeply about libraries and reading, maybe the first question you'll mind is, Really? Maths? Is that what we're going to be talking about today? So I want to make sure I start off with that. And then I want to talk about how mathematics and literacy really do actually have a wonderful, symbiotic overlapping relationship. And so, we're going to talk about how stories are full of maths, how maths is full of stories, and then I will try to tie up everything in an echo at the end of this.

So, let's begin by having a think about maths. Now, like I mentioned before, I am expecting that a lot of people here in the room who are watching and listening in are the kind of people who think about maths like this. It's a source of anxiety and confusion and it's something which, actually, probably a lot of you have spent many, many, years – decades even – actually running away from as far as possible.

Now, to explain why in fact mathematics has a deep connection to literacy, I want to tell you a very brief story that comes from my time at Cherrybrook Technology High School. This is where I've been a classroom teacher for the last 10 years, and Cherrybrook Technology High School in Sydney's leafy north-western suburbs is a really large school. We have a campus that was originally designed for 800 students, but actually right now, hosts over 2 ,000 of them.

Now, as a consequence of us having so many students, we have a lot of teachers, and that's why our staffroom is so large. This [image of a staffroom] is actually only one of the combined staff rooms that you find around the school. Something like 80 teachers sit in this room, and the other KLAs who don't fit in here, because we have about 135 teaching staff, do have to occupy other spaces. Now, one of the things I loved about being in this staffroom for many years is that being a combined staffroom, there are lots of different key learning areas mixed in together, and for a long time, maths was right next to CAPPA (creative and performing arts). So, all the dance and drama and music teachers, they were right beside us, and oftentimes, as any of you who've worked in an open plan environment can attest to, I would overhear conversations from my colleagues when I was busily trying to work and concentrate on some important task.

Now, one day, I was overhearing a conversation between two visual arts teachers, and I knew they were art teachers because I recognized their voices, I knew who they were. But in their conversation, despite being art teachers, I noticed that they were using all these mathematical words in their conversation. And I was very perplexed by this. So, after a few minutes of listening in, I sort of had my curiosity got the better of me. I wanted to find out why on earth they were talking about maths. So, I got up, went around to their side of the table, and on their desks, I saw this [referring to image of a tiled pattern]. Now, I don't know if you've seen this kind of tiling pattern before. It's the sort that's located in mosques all around the world. And you might be able to guess some of the mathematical words that my art teacher colleagues were using as they described these patterns. They were using words like symmetry, polygons, angles, tessellation – all of these words that I had originally thoughtof as belonging to me, but I recognized actually belonging to all of us.

Because Mathematical concepts and ideas are found everywhere, It's not just art, it's also things like music. In fact, music is, someone once said, the joy that people feel when they are counting, but they don't know it. And music is deeply mathematical when you're thinking about the rhythms or the melodies or harmonies. Everything within it is mathematics made audible.

Now, in order to To explain why I'm spending some time talking about this, I'm trying to sort of widen what your idea is of mathematics. A lot of people, when they hear ‘mathematics,’ they just think numbers, formulas, equations. And true enough, number of those formulas and equations are full of mathematical ideas and maths is full of them. But there's more to maths than just numbers. And I want to give you an example of one of these kinds of objects that's really important for our topic today about literacy and maths.

In the mathematics standard course, which is the most popular HSC course actually in the entire HSC, not even English, any of its individual courses, despite English being compulsory, none of the individual levels of English has more students than mathematics standard every year. And one of the best topics within mathematics standard is something called networks.

Now networks are exactly what they sound like. They're a collection of interrelated objects that have some kind of connection or relationship that can be quantified numerically and understood, analysed mathematically. Now, maybe when you hear the word network, you might picture a literal computer network or perhaps a train network. But actually, there are networks all around us. And if you open your eyes, you'll recognise this mathematical object, which you might not have even thought of as mathematics is literally just hiding in plain sight. For instance, you've got something like a food chain. So, I remember studying these when I did, you know, Year Seven and Eight biology. And this is a mathematical network. You can trace who eats what and where the calories are flowing within the diagram. Or say, for instance, over the last three or so years, we've all become kind of collectively obsessed with these kinds of networks. This [referring to image] is an epidemiological network that tracks the spread of a disease. These kinds of objects here are mathematical, even if we don't realise how mathematical they are.

Now, you might say to me, ‘Eddie, sure, all of these examples that you've just given me, of course, they have connections with mathematics’, because these examples, I haven't chosen them arbitrarily. They're all from what we might call STEM, science, technology and engineering. These are often lumped together with mathematics, but I want to kind of tease out for you the fact that it's not just these traditionally connected to mathematics subjects that have these links to mathematics and numeracy.

For instance, we were talking before about music, right? Are there networks in music? And the answer is, absolutely. This [image], for instance, is a diagram of a new series of musical acts that were just sort of bursting onto the scene in California last year and you can see all of the different genres that connect each of the different bands and performers together. Musical genres are a collection of interrelated objects whose connections can be quantified and analysed mathematically.

What about thinking about languages? I am sadly monolingual, even though my parents could speak many, many languages when they moved here to Australia in the 70s. But even if, like me, you only speak one language, you probably recognize that all the languages are connected one to another. And so, there's a mathematical network underneath all of these different languages. In fact, it's not just the languages as a whole. Even every individual word is actually connected to words in other languages. So, when you pick up a book and you start to read different words in there, we can actually quantify mathematically how those words are connected to other cultures and societies throughout time and space.

So that was my kind of introduction for you to help you see that mathematics is broader probably than what you first took it to be. This is how mathematics and literacy can be deeply connected. If you start to widen your idea of how you define mathematics. Now, I've spent a lot of time talking about this idea of a network. It wasn't just by accident. This is my segue into explaining how stories are full of maths. Think about that network, for example, and keep it in the back of your mind as I tell you the story of one of my favourite kinds of books to read when I was younger.

I remember very distinctly being eight, nine, ten years-old and having my mum give me my first choose your own adventure story, and for those of you who have read these, if you're a similar vintage to me, you know the joy and the exhilaration of getting to the end of the page and not just turning the next page but actually having the choice of determining what the protagonist will do. Climb the ladder then you turn to page seven, or you're going to descend into the dungeon then you turn to page 39. And I don't know if you were anything like me, the kind of thing I did when I was a kid is I would, you know, put my finger in at the current page and then I would flick forward to page 39 and then I'd look and I'd say, ‘Oh no I died’ and then I would flick back and I would try again.

Now, what I love so much about these stories, and you will too if you've read them as well, is that there are so [many] different endings to every story. Each choice sends the protagonist on a different path and in fact these paths are networks. You can see that same mathematical idea is hiding underneath the storytelling here. Now you might say, ‘Oh, of course that's quite unusual’, though like this is what we call a non -linear narrative and such stories are a little unusual.

What about like your regular page one to page 500 kind of stories? Do they have networks and mathematics underneath them? And if you're a Harry Potter fan then you know absolutely they do because a family tree is a network and one of the key things about the Harry Potter series is who's a muggle, who's a pure blood; all the different connections and relationships are a large part of what drives the story forward.

Now, I'm conscious of the fact that the Harry Potter series is a little bit dated now. I mean, some of those books were coming out when I was in my early years of high school, so let me try and modernize this example for you. This is not a book per se, but it is a story and it's a great example of this principle that I want to use to illustrate how mathematics is woven into stories, even in ways that you wouldn't expect.

I don't know if you or any of your students have heard of this little film series that's made a splash over the last 10 years called the Marvel Cinematic Universe. you can see the poster there [referring to image] for Avengers Endgame on the left-hand side and, even if you've never seen any Marvel movies, you can appreciate the challenge faced by the Russo Brothers, Joe and Anthony, the directors of this movie, you can appreciate the challenge the Russo Brothers had just by looking at the poster. You can see how many main characters this story has and that's because this particular movie served as the bookend, as the conclusion, to more than 20 films that had come up in the previous 10 years.

Now my question to you is, how did the Russo Brothers plot a story, a narrative thread, that wove together all of these immense characters with their own background and things that they care about and put that into one coherent storyline?

How did they manage all of these competing narratives? And the answer is, I think you're about to guess right, they created a network. You can see this diagram here, it actually plots the last 20 plus movies and how they're all connected one to another, how it can appear and reappear, how these very specific objects called the Infinity Stones sort of weave their way through time in the Marvel Cinematic Universe. So, you can see that mathematics is actually a deep part of how to write a good story and not just how to read one.

Okay so I've been talking about networks a lot, let's go in another [direction] and show you how stories and narratives and all different kinds of literature are actually full of maths. I remember when I was at school studying Shakespeare and studying a lot of him, right? We had Shakespeare play every single year that I was in Year 7 to 12, and I think they often still do. And when you have a look at this line, one of Shakespeare's most famous, perhaps you know why this line is so famous. It's because it's in a poem that is written in something called iambic pentameter. Now I didn't know what iambic pentameter was until I went to I taught at a school where one of my good friends was the head teacher English and he explained to me what this was all about. You see, an iamb is a unit of English language and maybe I'm telling you something you already know, but to me this was a whole sort of flash of inspiration when I realized how deeply mathematical these objects were. And iamb is about a pair of syllables where the first syllable is not stressed and the second syllable is stressed. So, you can see or maybe you can hear the iambs in this sentence when I say it aloud: ‘Shall I compare thee to a summer's day?’ When I say ‘compare’, if you contrast it to saying compare; compare that's a whole different word, right? ‘Compare’ means something very specific compared to that. So, you can see where the syllables are emphasised and if you count along with me how many iambs there are, there are five. And that's why it's called iambic pentameter, like a pentagon. Pentameter just means a measure of five, and of course Shakespeare's genius was that he didn't just write one line in iambic pentameter, he could write in iambic pentameter for days and he could make it rhyme in this really rigid structure with groups of four, which we of course call quatrains followed by a couplet a pair of rhyming lines at the end. And you're probably aware, this is what we call a sonnet and Sonnet number 18 is one of Shakespeare's most famous and delightful.

Let's go another direction. I don't know how many of you are familiar with the American author Kurt Vonnegut one of the things that he was famous for was talking about how different stories and narratives often follow archetypes, despite how different the stories may be. Now, as an example of this, and I wonder if you can see where the mathematics is, he talked about plotting stories along a graph. His graph had two different axes. The horizontal axis was from the beginning to the end of a story and the vertical axis was about whether the main character was experiencing good or ill, were they having health and prosperity and money and power or were they down in the dumps, sick, defeated – all the rest of the things you would experience at the bottom.

And Vonnegut talked about these three particular kinds of stories that come up over and over again. He said firstly, there's the love story, right? You've got a person or a pair of people, rather, who are in the middle, they’re just kind of, life is normal; they meet each other, they're excited, it's really a fantastic relationship, they're both discovered and then something goes wrong. There has to be a tension, there's some conflict where they, you know, one character realises the other one is not exactly whom they seem and the relationship goes through a dip, but then of course there has to be a happy ending so you can see [on the graph] that blue curve coming back up again. And then there is what Vonnegut called the man in a whole story. Someone starts off okay and then they discover?, some series of terrible events happen to them and the story is all that – how they kind of claw their way back out of it and you have to end off better than you started.

But Vonnegut's favourite was the one you can see there [on the graph] in green and he called this the most popular story in Western civilization. If you know about the monomyth and the hero's journey, these probably look familiar to you. You've got someone who's actually really, really low down, perhaps they're an orphan, they've lost their parents, or they're someone who's hated, they're completely unpopular in their school or they're weak, they have no powers. But then there's a call to action, they get thrust into this new world where they grow and grow and they develop new skills and there's a training montage and they reach this high point only then to perhaps meet the archvillain of the story to be defeated. They suffer a major setback, they lose their friends and this massive sharp dip in the middle there [on the graph] and then they have to overcome that through some sort of change and some synthesis of new ideas.

Now, you might say, okay, three stories, I can hear some of the similarities there, but you can't possibly come up with just three archetypes that describe every story in the world, and you'd be right. There are more than three, but some scientists, some data scientists had a look over a series, hundreds and thousands of stories that they borrowed from public libraries, and they plotted a lot of Vonnegut's sort of archetypal story shapes, the geometry of the story, and noticed that there were several different stories that fit these basic patterns of things getting better or things getting worse, or these ups and downs that you saw before.

I like to call these the geometry of narratives. There's mathematics as we think about how time and the fate of a character throughout a story is plotted. Now, for my last favourite example, or last maybe, of how you find mathematics in stories, I want to talk about time travel. I love a good time travel story. Yes, I am a Doctor Who tragic, I won't tell you who my favourite doctor is though, because everyone's got their favourite, and you just end up in arguments about it, right? So, I'm just going to talk about the fact that any story that has time travel in it needs to be very carefully thought about, because when people are going backwards and forwards, it can be quite easy to lose your way and, what comes to the rescue – answer, mathematics. You can think about all the different kinds of time travel stories that we have read and we've watched down the years and how they fit into one of these different kinds of patterns. How, you know, does going into the past affect the future, or does it make a whole new future, or do you end up meeting yourself from the past, or does future ‘future you’ come back to stop future you from doing things? All of these are different mathematical shapes that you find in storytelling.

Now, this one is the last one. You might notice there [referring to image], Harry Potter. I talked about it before when I showed you that family tree and network, and in Prisoner of Azkaban is it's a time travel story – sorry spoilers. I mean, it's like decades old now, so I feel like I'm okay to say that. But one of my last favourite examples about Harry Potter is about how you can plot the characters of a story across different axes. Let me give you an example of what I mean here. If you think about the characters in a story as to whether they're good or they’re evil it's usually not that difficult to pick out the people who are working for the side of good, the people who are working for the side of evil, and then often you will find characters somewhere in the middle – people who maybe do a bit of both or they seem to be on one side or the other. And you know I didn't come up with these specific examples, by the way, so if you disagree with where I put them on the graph then that's okay – have an argument with the person online who came up with this scheme.

But you might notice I don't just have a vertical axis of good and evil, I also have a horizontal axis and maybe you've heard of this. This is about – are the characters lawful? Do they follow the rules or are they a bit chaotic and unpredictable?

And you don't have to use these axes, you can choose any qualities that you like and you can see how different characters occupy different parts of the narrative and provide foils for each other and it's a really wonderful way to analyse how the characters interact with each other and also how to create a new story for yourself.

Okay, we're coming towards the tail end here. We just talked about how stories are full of maths. Let me very briefly share with you some great literature recommendations for how maths is full of stories. Some of the stories I love that help our more inclined students and young people to interact with books because they see the maths in it.

Let me give you some general examples first. Alex Bellos started his career as a journalist and he wrote Alex's Adventures in Numberland as well as numerous other stories, books rather, which are full of stories of how mathematics weaves its way into our culture and history– a delightful set of tales. And because he's a journalist – he's an excellent writer – Simon Singh put together The Simpsons and their Mathematical Secrets., many of the writing staff of The Simpsons down the years weirdly have full -on advanced mathematics degrees and so they've smuggled all of these little mathematical jokes into Easter eggs and storylines within The Simpsons across many, many seasons and this book unpacks a lot of them.

A good friend of mine is a mathematics professor from Cornell University called Stephen Strogatz and he wrote a series of columns in the New York Times that are all very bite -sized and talk about different aspects of mathematics. Again, like we were talking about before that you wouldn't even think are necessarily mathematical, but then he sort of collated them all into this book called The Joy of X and it is just an absolute delight to read.

Now all of these examples? are quite general. They talk about various different areas and fields of mathematics, but to be a little more specific let me introduce you to Hannah Frye. Hannah wrote a fantastic book called Hello World which is all about how data and algorithms are governing our world, but the story is about how we need to understand that and also be cautious about it.

Another book that I really love which deep dives into a specific mathematical concept is called Change is the Only Constant and author Ben Orlin, isa mathematics educator in the United States, he did a wonderful job not only writing but illustrating this book so it's very accessible to a wide range of students.

Another is Once Upon a Prime by Sarah Hart; also a mathematics educator. And what I love is she talks about how mathematics and literature are connected so some of the ideas that we talked about before and just a much wider range.

Now, as a final note, my publisher would be really upset if I didn't talk about the fact that I've written some books about mathematics, so Woo's Wonderful World of Maths is the Australian title of It's a Numberful World, which is which was released in North America. And much like those first books that I talked about, it just talks about all the places that mathematics is found in everyday life. In fact, the 26 chapters of this book are basically composed of all of the times that a student asks me, ’What does all this math? have to do with anything in my life?’ And every chapter of the book is one of my answers to that question. And if you want to look at the question route, then I've got a couple of books that are for younger readers, primary school aged, which are about me, 12-year-old me, who is much more brave and popular than actual 12 year-old me, but he goes on a series of adventures with his friends and solves mysteries where mathematics is the hero. So, like I said, just some brief recommendations for you to stock in your libraries.

I hope after reading this you are able to see, number one, mathematics is broader probably than one you think; it's more than just numbers and symbols. Secondly, stories are full of maths if you know what to look for, and when you see the mathematics in a story, I think that that actually enriches your understanding and appreciation of that story. And lastly, if you want to help your more mathematically inclined students to absorb the world of stories and places to go.

[End of transcript.]

How to cite

Woo, E. (2024). Stories that count – how mathematics and literacy enrich each other. Scan, 43(1), 11–12.