Talking Maths in Public Podcast - Episode 1: Cardboard Boxes, Russell’s Paradox and a Sense of Belonging
Full transcript
Welcome to the Talking Maths in Public podcast, a community podcast for members of the Talking Maths in Public network, which is a UK organisation bringing together maths communicators of all kinds. My name is Katie Steckles, and I'm a maths communicator and member of the Talking Maths in Public team.
In this podcast, we'll be hearing from various members of the community, sharing their maths communication projects, discussing how we communicate maths, recommending their favourite bits of maths-comm, and looking into the research behind how to communicate effectively. In this episode, we'll be hearing from science communicator and project manager Hana Ayoob, who's running Matt Parker's mega grant project for 2024 number city. We'll also hear about some recommended popular maths books, discuss mathematical explanations, and find out about some maths comm research. To see links to things discussed in this episode and to find more episodes, you can visit talkingmathsinpublic.uk/podcast.
---
Section 1: My MathsComm Project - Number City (1:20)
Okay. So we're talking to Hana Ayoob, who is a project manager for the Number City project. So Hana, tell us about this project.
So for Number City, we are going to be building a cardboard city along a number line, where we have cardboard boxes that represent the prime factors in each number. Okay. Does that work as an explanation?
Like, yeah, I mean, this makes sense. So for full disclosure, I am also partly involved in this project, so I'm aware of mostly how it works. But I guess it's, it's about prime factors and- like, what scale are we talking here?
So, we are going to- we are going with a number line that goes up to 128, and we are using 50cm cube boxes, which means that we are looking at a 64m by 64m sort of pitch area of space to work with. So, when we say city, it is sort of not quite on the scale of a city, but it is going to feel like quite a big build.
Yeah, and it's the kind of thing you can walk around, I guess, like walk around between the boxes and explore. Yeah, so this is- I guess this has originated out of a, a slightly different project, I guess. So tell us about where this has come from.
So the, this project has come from an application that Maths Communicator Paul Stevenson put into the MEGA Grant. so you probably know a lot more about actually what the original project looked like.
Yeah. Well, so the MEGA Grant has come out of- so, myself and Matt Parker have done quite a lot of what we call ridiculous public maths projects where we have these large scale daft ideas, and try and do something very hands on, very interactive. And Matt is keen to carry on these things happening, but, I mean, I guess it's not technically that we've run out of ideas, but we've done a lot of things and we feel like it's someone else's turn to have some ideas and do some things. so the mega grant, I guess, is an attempt at carrying that on. And Matt is going to try and award this every couple of years to someone - we'll take submissions. And if someone has a good idea for something in this sort of same, same style that we can do. And there will be, I guess, depending on the project and the year, there'll be other people involved. So Hana's involved as a project manager for this one - partly because you're good at that. I guess we've brought Hana on as someone with a lot of experience of this kind of thing. But also, cause I guess this is going to be quite a creative thing as well, right?
Yeah, so we're- I mean, the act of building something like this itself feels like quite a creative project, but we're also going to have members of the public helping us with the build as part of a family day at the Orkney International Science Festival. And our plan is to get people to decorate the boxes that they are building and placing within the city, according to the number factor, so if they are placing a sort of 'two' box, you know, they could add two of something, or they could draw a massive two on the side, or something like that, and the same would go for sort of three, five, seven, and all the way up, in with the primes.
Yeah. So kind of picturing this, you've got the number line going off in one direction. This is great material for a podcast. If anyone is listening, you can picture this in your mind. So the number line goes off one way and then the other way we've got like the prime factors and then lined up against each of the numbers on the number line are all the boxes representing the factors of that number.
Yes.
And then if it's the same factor repeated, they go in a little stack. I say a little stack. I mean, if we've got 128 in there, that's a stack of like, you know, what's that, seven boxes?
Seven boxes I think is as high as we'll be getting, yeah.
Yeah, and that's three and a half meters tall, so it's not a little stack in some cases, but yeah. The theory is that I guess it will give a sort of sense of the shape of numbers?
Yes, yeah. In terms of their factors. So I, I'm going to resist saying 'I'm not a mathematician'. I- I don't have as much mathematical training as everyone else involved in the project. And when I sort of built a mini version of this myself, I really started to see like those shapes and to see patterns and sort of almost seeing like, especially even just looking, say, along the two line, you know, you can almost see these like waves or undulations as you have sort of, you know, just a 2, or there's 4, there's 8, or 16, etc. Um, and I think there is something quite powerful in that visualization of something, like almost seeing those numbers come to life. Again, excellent topic for a podcast. but we do have photos as well, which you can find on the TMiP website.
Yeah, so this is a project, so the MEGA Grant is administered by Talking Maths in Public, which is of course the organization of this podcast. It's all very in house, this one. But I guess, yeah, we, we kind of, the decisions about the MEGA Grant and the support of the projects that go ahead are all kind of coordinated and administered through TMiP. So yeah, we've got a page on the website, which we could put a link to in the, in the show notes for the podcast, but it basically describes this and there's some nice photos, obviously Ben Sparks has made a GeoGebra because you can't stop him from doing that. And, yeah, you can really kind of see this as a, partly as a 3D model, but just the idea of what it's going to be like standing in the place and looking at the thing. Yeah. I suspect the fact that you've built your own model of this at home does mean that you are a mathematician. I don't think you can really deny that.
I've done, it's applied mathematics, right?
Yeah, fantastic. So, so you're the project manager for this, like what does that involve?
So I guess the sort of short answer is overseeing all the logistics of the project. So that has from the beginning sort of involved talking with the team about what size space we needed, like that was sort of a really key thing. Um, and then going out and trying to hunt down a space that would work for this. which proved even- I think we knew it was going to be tricky, but it was even more difficult, than we expected it to be. So now we have a venue. It's, you know, liaising with the science festival, with the venue itself, that we're using at the science festival; keeping an eye on the budget, making sure that everyone who needs to get there actually gets there; and because we're doing it at Orkney International Science Festival, those logistics have been slightly more complicated than originally anticipated. So keeping an eye on budgets, and then also, as you know, we get closer to the project, it'll be smaller things as well: so, making sure we've got the boxes, making sure we have art materials, making sure we have matching t-shirts to wear on the day, creating ourselves a rota for the event. So it really does sort of range from the big picture, how is this going to work, where are we going, to those little details that, mean that we, you know, can run the event and the project on the day itself. And with all project management, one of the most important things as well will be sort of the wrap up afterwards. So again, tying up, budgets, reports, feeding back to the, TMiP committee and the MEGA Grant.
Yeah. Because I guess, you know, it's, it's nice to be able to look at how the, how well this has gone and how things from this can feed into future projects like this as well. So in terms of like the actual number city itself, what's the experience going to be if someone's coming to Orkney Science Festival and wants to experience this, what will their kind of path through this be?
In some ways their path is going to vary depending on what point they arrive. So if they join us fairly early in the day, you know, they're going to see a maybe a small cluster of boxes in one corner of these two lines, and their experience may be more of a discussion with us about how this is going to build and, you know, they can put in some of the boxes, perhaps come back later to see, you know, the build grow. As we get sort of further along the day and further along the build, people will be able to see this city taking shape and they will be able to walk through the boxes, and we were talking about some of the patterns and the visualizations that people begin to see, you know, it would be things like being able to stand at a number and look down and see whether it's empty or whether there's just one box or how many stacks of boxes there are. And, you know, starting to see those patterns through that.
Yeah, I mean, it's, I'm very excited. It sounds like it's going to be absolutely fantastic. And I guess like we've also got some like little- cause the science festival is putting on like a, in the adjacent building. So we're like on, we're on like a sports pitch, right?
We are, yes. It's like a huge bit of grass.
And then in the building next to that, I guess they've got like a little science festival. Drop in thing. Will there be anything in there for people?
So we are also, there'll be lots of things going on in there, but we will also have our own stand in there. And we're still figuring out exactly what that will look like. But for example, it could include like a mini version of the city and some other things to sort of explain what we're doing. And the idea is that we would then direct people to go out to the pitch that we are using for the main build.
Yeah, I'm imagining multilink cubes. I think we're all imagining multilink cubes.
I mean, like, I now own 400 multilink cubes because of, like, wanting to build my own. So, yeah.
I mean, that sounds like a plan, doesn't it?
Yeah. Although, I was caught out by the scale of even, like, 2cm multilink cubes. It turns out that when you need 128, that is suddenly, like, 2.6 meters. and I ran out of space on my living room floor, and we will probably run out of space on a stand, but yeah. Yeah. We'll see what, how many tables we can get.
Yeah. Fantastic. Well, yeah, it's, that's good to hear about. So if, if people want to find out more, so we'll put a link in the notes to the MEGA Grant website and any other related information, but yeah, hopefully that will be a good project and we can find out how it went afterwards.
---
Section 2: Top Three - Popular Maths Books (11:20)
Popular maths books are a form of maths communication which allows mathematical ideas to be brought to a wider audience. We asked Ashleigh Wilcox and Calum Ross, who both write for Chalkdust magazine, to share their top three pop maths books from the last 12 months, and to talk about why they're great examples of how to share maths in written form.
Um, so my name is Ashleigh Wilcox. I'm a PhD student in mathematics at the University of Leicester.
And I'm, I'm Calum Ross. I'm a, I'm a lecturer in physics at Edge Hill University. And both of us are part of the, the Chalkdust editorial team. So for anyone that doesn't know, Chalkdust Magazine is a magazine for the mathematically curious. And every year we have a top 10 books that we review from that year. Well, a- a short list of the top books. The length fluctuates, so I think there were nine this year. So we're going to discuss a few of those that were on the short list today.
So if we start with the... the editor's choice? Yeah, we can start with the editor's choice, which was Once Upon a Prime by Sarah Hart.
So I really liked this book as both a, both a book with lots of interesting mathematics, but also talking about that where maths shows up in a mostly unexpected place in terms of appearing in literature. So I don't know about you, Ashleigh, but I tend to think of maths and literature as being quite separate.
Yeah, that was, that was the main thing I got from this book because one of my friends is like a literature student and we never really have much in common in terms of maths and English because it has- I feel like it always is very separate, like you either do English or you do maths, you can't- you never sort of do both. Apart from topology and philosophy, is the only sort of in between we've found, but yeah, so I thought it was nice to- because reading is one of my hobbies, so to sort of see where maths comes up in literature is quite nice to, well, it really added to my reading list.
Yes, yeah, you're right, there are lots of wonderful suggestions for further reading at the back, in this.
Yeah, and every book that's mentioned is listed at the back as well, I think.
Yes, yeah, and a rarity, or at least for the sort of maths books or popular science books I tend to read, was that not every book that's mentioned is a maths or popular science book. There are lots of literature books that are examples of some of the techniques they talk about, and not just, nonsense books, like the book that doesn't involve the letter E, right? Which is the, I think, to me, that was the- one of the well known ones.
We're like, oh yeah, there's some interesting maths here about, that permutations and, how many possible books can you write with a- from a set of letters and symbols. But, yeah, yeah, no, I, I really liked it. And I think particularly the, choose your own adventure. Yeah, yeah, that was really quite interesting, I think, to sort of, because there was an interview, wasn't it, that they had, between how to, like, the process of I guess I never really thought about it, or I thought about it to the extent that it would be, oh yes, you have a choice, that's a split, some sort of tree, and then each choice there's a split.
But I hadn't really thought about sort of the, the scale of, if each of those is independent, right, if you only ever have to, there's only ever one way to get somewhere, it's like, how big a book would you need, right? Not many choices already gets to a gigantic book, and it's a real challenge then to sort of tie it together to have, okay, actually, it's much more railroad-y than you realize.
There are, there's only a small number of, of ways to, there are lots of ways to get to the same place in it. But it seems fresh and different to this. Yeah. That was really cool. Yeah. No, I really, I really liked it. I mean, so all the books on the, on the shortlist, all nine of them were really good. It was a really strong shortlist.
But I think this one, in a way, it was a relatively easy choice for the, like, the editor's pick, that just, this book was so unique, I think, that it really stood out as that, not just a good popular science or popular maths book, but I felt like it was just a really fun read anyway. And you could give this to someone who doesn't do maths or is not so interested in maths. And they'd be able to appreciate a lot of it as well.
Yeah, I think it's a sort of good book for maybe literature enthusiasts that don't like maths, so that they can read it and be like, 'oh, I didn't realise that was part of maths' or something like that, that maybe we can convert people into like maths.
Yeah, I think this is a good thing. Whenever someone says, 'Oh, I don't like maths', or 'I don't see why maths is relevant to me'. And you could point them to something in it, this book, and you could say, 'Oh, well, do you like poetry?' And they go, 'Yes'. 'Do you like the different structures that different sorts of poems have?'
And they say 'yes', you go, 'well, that's maths, how you choose which structure is there, how you decide how it should rhyme'. Yeah. Yeah, there's lots of ammo here to sort of convince people that mathematics is more than just multiplying numbers. Yeah.
So then the next book, I think we wanted to talk about, was the reader's choice.
So not only did we, as Chalkdust editors, decide on ours, we also polled Chalkdust readers. And the reader's choice was That's Mathematics, by Chris Smith, who's a Scottish maths teacher, illustrated by Elīna Brasliņa, and based on the fabulous, or at least I think fabulous, Tom Lehrer song, That's Mathematics.
So this is a book aimed at, well, I think they say aimed at young children, but I think it should be aimed at everyone. It's another of these books that I think is wonderful for the breadth of maths it talks about and the way it really brings it to life.
Yeah, and there's so many images in there, and 'Try this' sections. So I think that, that really helps, regardless of your audience, like, people sometimes don't think about how long it takes to count to a certain number and, like, what numbers you can count to, and sort of the concept of infinity.
Yes. Yeah, and there's lots of great, like, right at the end, the last bit is, it's talking about maths and music, right, that this concept of beats in a song, and part of it is, it has the major advantage that, so, Tom Lehrer, who wrote the song, was a mathematician, but he- a lot of the time, he wasn't teaching maths students. He worked at universities teaching, like, liberal arts students, or social science students, and that's, so he was- I get the impression, and you see this I think through a lot of his other songs, they're not all maths related, they're a lot of political satire. But there, a lot of it is about, like, bringing sort of concepts to the masses, expressing things in very accessible ways, is wonderful terms of phrase, and it really lends itself, I think, to a children's book, and can really be brought to life.
And also, there's lots of wonderful resources online that, you can get extra things about. So, the website for the book has, I think bonus information for parents and teachers that you could help, go further with what's in the book.
So shall we discuss the final book that we selected, which was also one of the shortlisted books for Chalkdust?
So we selected The Truth Detective by Tim Harford. So this book, I think if this book was around when I was a child, then I might like stats more. Because when I was reading this book, like I really did think, maybe statistics is a lot more- maybe there is a lot more to it than... because in my head, like, a lot of the time, the main reason I don't like statistics is that you can essentially say whatever you want, and you can get statistics to- you can portray them in such a way that they support you, and you see that a lot in the news. So, I think, because it seems like it's aimed at a younger audience as well, that to get people from a young age to think about the validity of statistics and what, sort of, because there is the, people are relatively afraid of maths, that if they see, a graph or a figure or some numbers that say, for example, 70%.
So they think, 'Oh, that's a high number'. So, and that's as far as it goes. So they think, 'Oh, 70%', whatever they're talking about, 'that must be bad'. And that's all the convincing that they need is just, a number, whereas if you think it's actually, what the percentage is or where the data has come from or what is being portrayed, then it's a lot- yeah, you, I think you get a lot better information. It's giving really good skills.
Yeah, I particularly like the concept it introduces of a, like a mind bouncer, that you almost think of, you have this protective layer, almost like another- a person that stands outside your mind. And you see these potentially dubious statistics, and it's just somebody who queries them, and it's about habit building. It also, similar to the last book we talked about, it also has some wonderful illustrations. And there are some brilliant pictures in there. But yeah, it's- I think it's a great, it's a great way of getting you to- not quite second guess, but to think about things when you see them and go, should I believe that? And I think it does a great job of doing that.
Yeah, I think as well, there was the Florence Nightingale pie charts in there, like information about that. And I thought that was brilliant. It was super, super interesting to know because if you think of Florence Nightingale, like, all you think is nurse.
Whereas if you think mathematician or inventor of the pie charts, I think that's a very nice thing for people to know. Yes. Yeah, it's packed full of interesting stories like that because I think it's also this book, one of the other ones, is about, Arthur Conan Doyle as well, who people will know as the author of Sherlock Holmes, but talking about him being fooled by, by the Victorian equivalent of a photoshopped image.
Right? And it's, it's, by going through that, so talking in the context of someone who's famous for writing probably the ultimate detective in fiction, or the ultimate logical fictional character, to see how easily he was fooled. By this, it's something that, yeah, it's a great example of why you should, you should think about, like, you shouldn't always jump to the conclusion that the person that's showing you the number or showing you this fact says it's true.
Yeah, and there was other real life examples in the book as well. One of them was about inflation. And sort of what inflation means to the items that you compare it to, and I think that's quite relevant, the, the life at the moment. Yeah, I'm particularly making clear this, this concept that what actually is inflation, because of course it's something we see all the time, but it's not- you see it referred to all the time, but it's not, it's never really explained. And it's laid out clearly in the book about how, okay, this is the rate prices are increasing at. And it makes clear that the, the fiction and statements about, 'Oh, inflation is reducing, so things are getting cheaper.'
And it's like, no, no, no. Inflation is reducing. So things are getting more expensive, slower. Yeah. Yeah. And it was great examples like that. Yeah. It's a brilliant book to, like you were saying, get somebody who is, you maybe a bit, a bit, a bit negative on statistics or that side of maths or graphical representations that show up in the news, and sort of get them to have confidence in themselves that they, they can understand it.
Yeah, definitely. Yeah. I think, yeah, all three books have, in their own ways that were really unique and wonderful pieces of maths communication, I think. Yeah. And I definitely, I definitely really enjoyed all three of them. Yeah. I don't know if I could pick a favorite. So, I mean, I could, but that's because I'm biased towards Tom Lehrer, right?
I'm not saying it's, it's the best book of the three, but anything with Tom's, Tom Lehrer's name on it gets my vote.
---
To read issues of Chalkdust Magazine and see their previous Book of the Year lists, visit chalkdustmagazine. com or follow the links in the show notes.
---
Section 3: Obtuse Angles - How Much Do You Explain? (25:20)
Up next on the Talking Maths in Public podcast, in a segment we're calling Obtuse Angles, I chatted with maths education expert Peter Rowlett about our opinions on mathematical explanations, and how we decide how far to go with them.
So I was listening to an episode of In Our Time about Emmy Noether, and something came up. So Colva Roney-Dougal was one of the guests, and she was explaining some concept. And it doesn't really matter what she was explaining, but she kind of got through the technical bit, a little bit of the technical bit of the explanation, and then she said, 'Once you've got all those things together, subject to certain rules about things making sense, you can then do...', and went on to explain the implications of this topic.
And I just thought that was really nice, because as a, as a mathematician, I'm recognising that what she's done there is fudged over a bunch of detail. And then because she doesn't feel quite comfortable omitting that detail, she throws in, 'subject to certain things making sense', just as a sort of cover for that, so that she can get away with not going into the technical detail that the audience wouldn't follow or tolerate, I suppose.
Yeah, I mean, this is the big challenge, I guess, if you're trying to communicate some kind of mathematical concept, because aside from the sort of fairly straightforward concepts, which people will probably know anyway because it's covered in maths at school, like, almost everything at university level requires some kind of foundation layers, like you can't just go in and start explaining, you know, abstract group theory without first saying, 'okay, well, this is the definition of a group and this is et cetera.' And I find it a really interesting thing because yeah, you, you want to be accurate - like, precision in maths is, is a really key feature of it, that you can't say something that's technically wrong. And this is really nice dance that you can do sort of around saying things which are technically correct. And some of it is just like, 'yeah, in certain circumstances you can do this'. And when you say 'in certain circumstances', you mean four pages of, like, working out and technical doodads. But it's sort of, you know, you understand what the motivation is for those circumstances and that allows you to do this interesting thing that you want to tell people about.
Yeah, because often you get results that are sort of okay 99 percent of the time, and then there's a few weird edge cases. And just by saying, 'for sensibly behaved situations' or something like that, you just kind of protect yourself from somebody coming- another mathematician coming at you and saying, 'well, excuse me, but you haven't thought about...'.
Yeah, I think that the mixture of, like, for me, the mixture of mathematicians and YouTube has been a real education in how you can't say anything that's not quite completely technically accurate because people will pick up on things that are, 'actually, I think you'll find', and you're kind of like, 'Well, I actually do know that because I've been doing this for a very long time. And I know that you know that I know that, but you're just making a point anyway'. And I guess, as much as it's not worth trying to pander to the whims of YouTube commenters in general, I think it is a valid point, though, that if you are saying something, you need to be technically right.
So I wrote a thing recently for a magazine, and, it took me a while to get down to the word limit because I had this slightly knotty concept to explain. And there were a lot of aspects of it that were only technically true in certain circumstances. And I had to make sure that without making it sound horrific, I had to make sure that I was being accurate.
And once I'd edited it down, I sent it through and they sent me back a copyedited version. And they changed the wording in so many places where they'd just made it, you know, inaccurate again, because it was like a thing where, you could in theory carry on forever, but that didn't mean that you could do it infinitely long. Like, it meant you could do it as long as you wanted to, but it still had to be a finite number. But that finite number could in theory be any number. And there's this really subtle distinction between that and something that carries on forever. And they just sort of destroyed that distinction in this- in the text.
And I was kind of like, 'no, because I know that, you know, that's, I think, that's not what it means, and I don't want to say that, even though that kind of feels like it reads more nicely, it's not actually explaining the maths'. But do people need that? Do people need that level of accuracy or precision?
Well, probably not is the answer, isn't it? You sort of feel like you don't want to send someone away with the wrong information. That then will trip them up later down the line if they then come across the weird edge case that you weren't quite thinking of at the time. There's sort of two ways to go about this, right? So one is the sort of slightly arm wavy, let's just pretend that we're dealing with something very well behaved. And then the other is not really addressing the mathematics but doing it via analogy. Mm. And you often get this with, I'm thinking of, Russell's Paradox and the Barber Paradox, which I probably won't explain, but you could Google, and you always have this thing that the, the Barber analogy is not quite Russell's paradox, but they're more or less the same. They give you the core of the idea, but kind of because it's an analogy, people sort of like that because there's a little story to it.
Yeah, well, it definitely makes things more concrete if you've got, like a real world thing you can imagine, but I think, yeah, the danger is that if you explain something by an analogy that's quite nice, but not quite exactly the thing, then you risk losing the subtlety of the thing. Yes, and as an educator, I would say you're risking to sort of breed misconceptions.
Because if you, if you take the analogy too far, you'll get quite far from the- yeah, you then find yourself having to explain why it isn't quite like that and in the certain cases and things. I think also, you know, the like, sometimes if you have a really good analogy, the temptation is to use that and you'll explain the bit that you have a really good analogy for more than you need to necessarily.
So, like, in the In Our Time that you mentioned earlier, there was this really nice bit where someone explained how topology works. So like the idea of, the, the way of differentiating between different shapes in terms of kind of paths on the surface, and they had this really nice analogy that if you take a surface of a torus or a surface of a sphere and you cut along it with a pair of scissors. the, how many ways are there to cut along it and cut all the way around to where you started such that the whole thing stays in one piece, that you end up with one object at the end of it. And you can imagine this sort of, rubber sheet or something, you know - topology is also called rubber sheet geometry sometimes. And that's such a nice analogy. But because they had this really nice analogy, they just explained in complete detail how like fundamental groups and topology work, just as part of a little anecdote about Emmy Noether and about her contributions to algebraic topology. And I was like, well, I love that because it's one of my favorite things, but no one listening to that will ever need to know about how algebraic topology works, but, you know, it was a nice illustration of Emmy's genius, and it was perfectly acceptable to have it in there, but the explanation was in far more detail than it actually needed to be, potentially because of this nice analogy. So, you know, it may be that there's a danger that you over emphasize the things that you can explain better, even if they're not necessarily the most crucial aspect.
Yes, and I was thinking about, there are, there are some mathematicians who, their work is very important, but they aren't very well known, and it's often because they're not at the right level. Like if they're, if you don't come across them until undergraduate, or if their work is quite advanced, but there's a nice analogy for it, it might be more commonly known through popular science books and things like that.
So there, there are some very sort of worthwhile humans out there who've done fantastic things for mathematics that are not very well known, because their work is quite abstract and hard to analogize.
Yeah, I mean, I wonder if it also favours applied maths over pure maths as well, because You know, people who've done maths research that's led to medical breakthroughs, or whatever, might get a bit more notoriety for that.
Because, you know, things like, with apologies to science and medicine and so on, you know, if it's a physical thing you can hold in your hand or point out, or that everyone's got one attached to themselves of, you can probably explain it to more people in a more accessible way. Yeah, or more relatable. Yeah.
---
If you have your own 'obtuse angle' on an aspect of mathematical communication and would like to share it with us for potential inclusion in a future podcast, you'll find a submission form at talkingmathsinpublic.uk/podcast.
---
Section 4: Research into Practice - A Sense of Belonging (33:40)
For our final segment today, we'll be looking into some of the research behind so we can learn from it and improve our practice. I asked maths communication researcher Anna Maria Hartkopf to choose a research paper and share her thoughts on it with us.
Hello, so this is Anna Maria Hartkopf, and I have been asked by Katie if I would like to provide a little insight into a paper that I find interesting that's related to mathematical science communication, which is the subject of my research.
And I have I've chosen a paper. It was not easy to choose one, of course. but I've chosen one that is not very new. It's from 2016, and it's by researcher from the Department of Mathematics in California State University. The researcher's name is Alison Marzocchi, and the title of the paper is The Development of Underrepresented Students' Sense of Belonging in the Mathematics Community Through Participation in College Outreach.
And when I read the title of this paper, I was intrigued because, here we can see a lot of things that are very interesting to our math/science communicators community, because here we find, a conceptualisation of something, I guess that is at the heart and motivation of many of the projects - that is, the sense of belonging to the mathematics community.
And then we can see that the researcher aims to measure the results and the outcome of an outreach project. So at the heart of this project is the Upward Bound Math and Science. programme, which is run in America since 1965, and I think this special branch of the project that is described in this paper has been done in 1990, and it aims at encouraging students from underrepresented populations to encourage a STEM degree.
'Underrepresented population' here means that it's students coming from a low income background and that they are the first generation college students. And the study has two main research questions that I will read out from the paper. The first is, 'After participating in a college outreach program during grades 10 to 11, including three years of summer program participation, how do underrepresented students in grade 12 describe their sense of belonging in the mathematics community?'
Second, 'In what ways, if any, do students report that features of the college outreach program contribute to their sense of belonging in the mathematics community?' So we see that this the Upward Bound program is aiming at college students and gives them extra support in their mathematics education, especially.
And after the participation in this, there has been a study which was qualitative interviews with some participants. And then we see how their sense of belonging is affected. This leads us to a lot of questions. The first is, 'how do you conceptualize a sense of belonging?' and this, has been done by the author.
Sense of belonging is conceptualized as 'the subjective evaluation of the quality of the relationships with others on campus'. So it's a very subjective thing about the, like very felt reality of a relationship with others that are in the course. So it's conceptualized that the sense of belonging in the mathematics community for a high school student who participates in the project can be described as the the sense of belonging in this Upward Bound course.
And then the conjecture behind this is that if there is a very subjective sense of belonging, that this helps to encourage the students to choose a STEM degree. So this is the background of the study. Before we look into the study, I want to talk a little bit more about the outreach program. The goal is to increase the graduation rates for low-income first-generation college students and predominantly ethnic minority students, and it has a special focus on- it's on preparing for success in a college level math class, and this is done by curriculum, so there are courses, but also role models, for the students that the students can get in contact to and an environment that supports academic advancement.
It offers a welcoming environment by, and I quote, 'offer youth a place of hope, a safe place to express themselves and to explore new ideas that make it possible for them to be in charge again of their future'. So that's very high aim for this project. the role models are, I guess, another very important part of it.
Um, and there are two kinds of role models. One is professionals that work in math-heavy fields or in mathematics academia itself. And the other group of role models is graduate and undergraduate students that the participants of the college outreach program are in contact with. So the method of the study is that nine students that have been participating in the project for at least two years are then interviewed qualitatively.
Each participant is interviewed twice in a one-on-one setting, face-to-face, and there are audio recordings and then these are transcribed and each participant also gets a pseudonym and then we can, in the paper read some examples of what they say about the project. All nine participants of the interviews reported feeling a sense of belonging.
And what's really striking, because it wasn't even asked in the interviews, is that all participants also compared their sense of belonging during the college outreach course to the sense of belonging in the school mathematics course. And, what might not be very surprising that their sense of belonging in the outreach course was much higher than what they experience in the school mathematics course.
When the participants were asked what were the factors that contributed to their sense of belonging in the mathematics community, they believed that it was the learning in the collaborative environment, and that it was also the environment in which they were surrounded by other peers who were also motivated to do mathematics, and that they felt it was a warm and welcoming environment, and they could receive some help. Those answers are like in descending number of mentions.
Some students also reported that they felt that it was acceptable to be good in mathematics and, that they felt that in the school environment - even though they were in the advanced class of mathematics - they felt like, it was- they could not, like, show their enthusiasm for mathematics, the same way they could in the special outreach project.
Another point that was very important was that the participants felt that their teachers and tutors in the project cared a lot about them and their academic success, and compared it also to the school environment where they reported that they felt that the people cared less. And as the sense of belonging is measured by the quality of the relationships, then, of course, we see that the sense of being cared for is very important here.
Looking at the limitations of the study, we see that the project like Upward Bound is aiming at students who are interested in mathematics and science, so the responses are not- the responses do not reflect all underrepresented students, but of a pre-selected group that has already self-identified as interested. And, I guess there's also some sort of, application process to even get into the project.
Also interesting is that the author has conducted a follow up study where she followed the same participants into their first year of college and then interviewed them again about their current experiences with college mathematics and then reflects upon if the preparation for college math courses that is the main goal of the Upward Bound math project has been successful.
So summing up, we see that all nine participants that have been interviewed for the study are pursuing careers - so, first majors, and then later careers - that are math related. And thus we see that the Outreach Project has fostered a sense of belonging in the mathematical community for the participants.
Yeah, so this was a little summary from my side. I'm very excited to be part of this new podcast project. And I guess my wish would be to further discuss all of this and to, yeah, find a little community of people within the mathematical science communication community who are interested in exchanging ideas with me and yeah, to further discuss matters related to the ones that I have just presented to you or anything else. And, yeah, that was it. thank you very much.
---
And if you'd like to get in touch with Anna and have those conversations, check the show notes for links to Anna's website and details of her research.
That's all for this episode of The Talking Maths in Public Podcast! Head to talkingmathsinpublic.uk/podcast for more episodes, to suggest your ideas for future podcast segments, and to find out more about the TMiP Network. Tune into the next episode for more mathematical communication chat.
The Talking Maths in Public Podcast is presented and edited by Katie Steckles and funded by the International Centre for the Mathematical Sciences. The music is For Her by Lidérc on Pixabay.