S2 E3 - Creating Safe and Encouraging Learning Environments with Alex Bellos

In this captivating episode, we invite Alex Bellos, renowned author, mathematician, and puzzle-maker, to join the discussion on why we dig for the why.  

Alex is an expert on the narrative approach to making maths engaging.

We explore the similarities in teaching methods between maths and computer science. As well as the significance of generating curiosity and the role teachers play in encouraging an open and safe environment that prompts students to question ‘Why?’.

Meet out Guest:
Alex Bellos studied Mathematics and Philosophy at Cambridge before going into Journalism. For over 5 years, he lived in Brazil, working for The Guardian as their South American correspondent. In 2010, when he returned to the UK, Alex published ‘Alex’s Adventures in Numberland’, followed shortly by ‘Alex Through the Looking Glass’ in 2014. Alex is also an experienced public speaker and gives talks to a whole range of students, profesionals and the general public.

@alexbellos

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Andy - @desire2undrstnd/Bluesky
Alison - @AlisonHopperMEI

A talented young creative iingledew produced our intro/outro – check out his Soundcloud.

Transcript

Andy: 0:20

Hello and welcome to this episode of season two of Digging for the Why, the podcast for maths teachers, where we explore thoughts behind asking why. I'm Andy, one of your hosts, and I'm joined in the virtual pod studio by my co host Alison. Hello, Alison. How are you?

Alison: 0:34

I'm extremely well, Andy. Thank you.

Andy: 0:35

Very, very good. Now, I am. In all honesty, a little star struck today as we're joined by someone who helped me with probably the last decade of my teaching of statistics Alex Bellos. Now, that's a name that I know, you know, if you are coming to this as a math teacher, you'll be familiar with that name, and you may sit there and go, why do Why am I familiar with that name? So I did my digging and I've done my little bit of background research. And the reason Alex is here is because of, of, of a couple of books that he's written, but to go further back, Alex actually studied maths at Oxford and then went into journalism, working for the Guardian in London and became their South America, South America correspondent, excuse me, living in Brazil for five years. He then returned to the UK and published Alex's adventures in number land in 2010 and the followup Alex through the looking glass in 2014. So why did I ask Alex? Who's not been a teacher, as you can see there from that kind of bio to come onto this podcast. Well, it basically goes back to a chapter about baguettes in the first book. I was teaching statistics and. Reading this book and, and kind of, you know, just enjoying it as a math teacher, as a math person. And then this intrigue as to the lies that, you know, bakers might give you about the weight of their bread led to this whole thing about the normal distribution. And then that came into my teaching and it became the introduction to, to that for the rest of my teaching career, essentially. And the whole book, if you've not read it or the whole book, the whole idea of if you've not read them is there's A question of why about something or a wondering about something. And then this adventure happens where Alex goes into some real depth about the math behind things. But actually, as I used to say to my A level students, the first half of these chapters is accessible to absolutely everybody. The second half delves into some deep math at times, and it can be difficult to read and difficult to comprehend. But the first part is just a joy to read. So anyway. There I am. I'm a little bit starstruck, but it's a good job. You know, we're on virtually doing this. Otherwise I'd probably just sit there going, Oh but anyway, Alex, welcome to this big intro. Welcome to digging for the Y. Thank you so much for agreeing to come on. How are you doing today?

Alex: 2:41

Yeah, I'm doing good. I mean, I've not thought about those baguettes. In a long time and it was giving me, you know, I know not my Madeleine. I know that's another kind of French reference about a food that makes you think nostalgically about the past, but I bought these baguettes. So to explain what I did is that I went to my local branch of Greg's every day for a hundred days and bought exactly the same baguette. And because I didn't know why I didn't throw them away. It was so slowly and this is a picture in my book of that of my kitchen with this about 100 bags there to the big pile. I remember as I was just, you know, the idea was I'd measure them every day and then you'd see there is normal distribution, but actually because I'm more of a pure mathematician than I am an arrived mathematician, of course, it's not perfectly. normal because I was doing things like not accounting for the temperature, for the time of the day that I bought them, all things like that. So it was a bit skewed, but they got the point across and it was a really, really fun. It's a really fun thing to do. And whenever I would invite people into my flat, They were just horrified. Horrified. And I was, I was lucky that I didn't have any rodent friends also visiting . Yeah. Yeah. I can really liked it.

Andy: 4:05

I just, you know, it, I, I liked to engage my A level students in conversation to try and get them asking questions to try and get them curious about things. And it was, it was things like that. And I'd put that on the board and they'd be like, why did he do that? I'm, well, why do you think he did that? You know, he's a mathematician at heart. What's he trying to find out about this? What's he trying to look for? And they guide themselves through this idea of getting towards a normal distribution. And then we talk about, you know, imagine you're the person that makes these baguettes. You're in charge of Greggs. What's your limits on either side? You know, how far below 150 grams, whatever it was that it measured. Are you going to allow it to go and get away with it? Or how far above are you going to allow it to go and get away with it? And then you got to confidence intervals. We got to all sorts of other things. And it was just. It was such a nice narrative to have, to bring into a lesson, to kind of take you through and get the kids to, to understand that, you know what, it's not just us boring maths teachers that ask these questions, why?

Alex: 4:59

Yeah, I mean, I think it's totally right that I'm not a teacher, and it's good that you pointed that out, and I wouldn't ever say that I have advice for teachers for doing teaching. Well what I am, my experience is of kind of telling stories, and I think that what The stories that I write, try and do is, as you say, I try and engage people straight away. I don't really say it's about math. I just try and tell a fun story. I think the minute that you say, Hey guys, this is math. So you're going to lose some people. You just want to tell a fun story. And so I'm happy that you sort of recognize that it's exactly what I'm trying to do. I'm okay. You know, some math, but because it's got kind of massive things on the front, that's how it's marketed, but anyone can read any of those chapters and start reading it. And I always made an effort that anyone even without a professed disinterest in maths could read it. And once you start reading it, you realize you know, why is he doing that? What's going on there? And so telling stories is, is about questioning what's going to happen. And the way I try and do it is that to understand what's going on, you need to unpeel the layers of what's kind of explaining it. So I'm kind of doing this exploration in a sort of narrative way to try and, you know, just, just, just telling a story. And in the stories I tell, I always thought there were the kind of three things that I was trying to do. One was tell sort of possibly the history of the maths. One is the. explaining the actual concept. And then I realized that that doesn't make a book, that might make a few good articles. The extra element that all brings it in is my own experience. So I could have, with the baguettes for example, I could have told the story of Poincaré, because Poincaré did something a little bit similar to sort of make sure he wasn't being ripped off when 150 years ago. But it would have been a bit drier. So it's my take on me having those experiences so that when things, just the, the, the personal story that almost like a kind of memoir is quite a good glue that glues it all together. And it might sound Alex's Adventures in Numberland, maybe that's kind of narcissistic putting my name there. I mean, it's there because it's a good pun with Alice's Adventures in Wonderland, which is a great kind of mathsy book. But really it's because it only holds together as a book rather than a kind of series of articles with some unifying factor. And that unifying factor is, Sort of my presence as the guide. And before I wrote that book, it was my second book. My first one was a book called Futebol, the Brazilian way of life, which was from five years living in Brazil. And I kind of recognized that when I was in Brazil and I started writing that book I was, my profession was a foreign correspondent and I went around Brazil, finding out these stories and kind of translating them from Portuguese from where I found them into English. And I did exactly the same thing with the maths book, which is, I feel that I'm the foreign correspondent in the world of maths. And I'm kind of trying to explain it to a non maths audience.

Andy: 8:28

How, so how, that's an interesting process then in my head. So obviously I read that as, as a mathematician, as a mathematics background, as a teacher, and I'm reading your books and I enjoyed the depth of that second half. So when you're thinking about the different chapters that you're going to put together, how do you kind of figure out the level that you want Get up mathematically versus pros. If you're like, you know, how, how are you planning who you aiming at? Who are you thinking is reading the book kind of thing? And how do you address those different levels that you need?

Alex: 8:59

So that's a brilliant question. When I wrote the book, I was aiming for the non math audience. I was saying, this is going to be the book that people who said they don't like math are going to read it and find it interesting. And the way that I was going to. And I didn't make that happen because there are lots of great math books, but often math books are written by mathematicians, and I felt I've got to write the book that only I can write, and what is it, what am I bringing to the table? And that's the fact that I've been a foreign correspondent. So, essentially, I mean, I had the idea in my head of two readers. I had a reader who was a kind of someone who I knew who liked maths, and I had a reader who's a friend who I know who's never studied maths and not interested, and I needed to at all times sort of read through each sentence and think, If I sold that to Bridget, would she, would I keep her interest? If I said it to like my maths friend, would he keep his interest? And you, you know, it's hard writing maths because you've got this whole idea of level. Is it too difficult for the people that don't understand it or are afraid of it, or is it too simple for the people who get it instantly? And so it took many times to write it and then rewrite it and then rewrite it. And I realized that what you do is you take it slowly. But the way you make it interesting for the people who get it fast is that you fill it with anecdote. So even though I had written it for non mathematicians what was amazingly gratifying and initially quite surprising then I realized, okay, now I get it, is that the math community really loved it. The math community really loved it because all these anecdotes which I'm putting in they don't know. Because when you study math, you don't learn the history and the anecdotes and often the applications. You know, so lots of teachers, math teachers were saying, oh my god, there's all this kind of fun stuff that I can put in my lesson. And I didn't know that makes it a bit more interesting. So yeah, for example, there was one of the chapters is about zero and zero have only been invented in India relatively recently. So, you know, 3000 years of math before zero. And I thought you could say zero was invented in India, which is what, you know, what they all do. And this is the reasons why. But then I thought, okay, I'm going to go to India and I'm going to speak to it was an Indian kind of priest, a Shankaracharya, which is a kind of priest level in a certain Hindu, I don't even, I don't even know how to explain Hinduism, but there's part of India, the Shankaracharya is like the top guy. And it's much better me saying, I'm in a temple in India, bit of description this guy and he described the Shankaracharya who is a kind of embodiment of zero himself because he is wearing a simple robe and he has no possessions so all of a sudden you're thinking why am i talking about that and as a reader i think this is kind of interesting and then he you say i'm in a temple in india the guy is wearing virtually nothing he eats virtually nothing he's got no possessions he turns around and he looks to me and he says Zero was invented in India and all of a sudden you're thinking, this is interesting. I knew that fact, but it's kind of curious. Why, why we, why is this guy saying it? And then the punchline, you know, many pages later is that actually one of the reasons that zero was developed first in India is because of this whole kind of spiritual approach that nothingness is something that nothing that you can have. Nothing is the nothingness is. is not self contradiction. And you then bring that right back to the whole nature of the priest, who is kind of nothing, the embodiment of nothingness. He's obviously someone, but he's nothing. And so you have all these sort of fun little games all these kind of circular kind of narrative arcs, you might call them. And it's got to be really well crafted because write about math. It can get pretty boring pretty quickly because the way to, you know, the way to sort of ingest maths is kind of by doing it, not really by reading about it. So you've got to twist, you can have a great maths book that has great maths, but you don't read it like you might read a great novel. So to give someone that reading experience, you need to use all these other kind of literary tricks, so to speak, to really make people interested in the reading of it. And the other thing in which is really true is the way the brain reads numbers. The digits is very different from the way the brain reads words. So when you're writing, you've got to have as few digits as possible because subconsciously the reader will just start to think in a different way and maybe lose their track or kind of get bored. So you've got this other thing, which is how to try and write about numbers without writing about numbers. The person who has done that best actually is. It's a young American author who wrote a book about a year ago called Maths Without Numbers, which really has no numbers. I mean, that was brilliant. But what, you know, I love puzzles, and maybe we're going to talk about puzzles and why I kind of like puzzles and do a lot of puzzles. But to me, The fun thing about writing about math is that it is a puzzle that you have all these really quite tough constraints that you know, can't write too many digits in it can't get too hard too fast, but you can't get too slow without putting it enough color. So yeah, that's what goes on in my brain when I try and write these books.

Alison: 14:42

I think I've found this really easy. There's a few things, there's a, I've just been jotting down some things because there's so many, so I can't hold, couldn't hold it all in my head, but there's a, there's a few things that you said that really resonate with a lot of the work that we do. With teachers, and I know you've, you've, you've said, you know, you're, you're not, not a teaching background and you wouldn't hold yourself up as a, as a guide to teachers, but there's some things that really, um, that really, really sort of struck me that I was doing some reading the other day and it was talking about, you know, engagement in itself, students being engaged in lessons isn't enough. And I'm still trying to process that because I think there's an element of where they need to be engaged. So it was interesting. So that you're kind of hooking, hooking readers in with something interesting. And you also talked about starting slowly or two different readers in mind. And, you know, one of the things that we, we talk about a lot with the teaching for mastery stuff at the moment is go slower to go faster. And that if you can secure that basic underlying concept, your understanding of what's going on, you can then build on it and take that idea and develop it. And, and you also use two words, which I, I always listen out for when I hear teachers talking about children and their learning, and you use understand and get it. And sometimes we sort of, we get the know it and do it, but the understand it and the get it, I think is, is it's a deeper level. It is that. It's the why bit, it's, it's the understanding the why and the teachers asking it and so I just, yeah, I just found that really interesting that sort of taking it into, into the, the world that I live in where I work with professional development for teachers that there were lots of, lots of things that you said there that really echo the way that we, I hope we at MEI and NCTM try to engage with teachers and get them to think about maths.

Alex: 16:20

Yeah, I think sometimes it's quite nice reading something that you already know, because it reforces those kind of deep, that deep understanding that you have. It shouldn't always be about the new, sometimes just going over in a kind of methodical way. In terms of the conceptually it's really good because people, people like to feel intelligent and if they read something that they already know, they've got that kind of pleasure of, I know that, but it kind of, it reinforces it and that's quite a pleasurable thing, thing to do. And no one minds having that stuff reinforced. And, you know, you put a little bit of humor, a little bit of anecdote, a little bit of history. It makes it really, it makes it really enjoyable. And I think that's the. Another thing about maths, which, so moving on to one that I wrote about, about puzzles, is that maths is very satisfying when you get it. And puzzles is the kind of the epitome of that. It's a pure bit that you don't get and then all of a sudden you get it and you get that real aha. But even in books in a much slower sense, you're always getting that feeling of, Oh, I get how it works. Oh, it fits in. Oh, that kind of makes sense. The sort of underlying. The kind of foundations of all mathematical knowledge, and it really is pleasurable. I'm not going to ask a psychologist why, but it really is pleasurable to have that, that, that reinforced. I mean, what is not pleasurable is reading something you don't understand. So you'd never want to do that. You never want to put someone off because that is, you're in kind of crisis mode. So I feel that you can know it, and it's quite nice to have, have it repeated. I mean, This is maybe slightly similar, but for example, I like to read the New Yorker and the New Yorker magazine quite often has pieces on England, about England or Britain. And I know absolutely everything that is in that piece, but it's just really refreshing reading someone else writing about it. So everything that I know, it's just like a slightly different take. And so I think that maybe that's what I do with math is that lots of people, they know everything, every math thing that I'm writing in my books, but just because it's a slightly different take. It's actually really, it sort of encapsulates it in a way, which feels, there's something very, just very satisfying about reading about what you already know.

Andy: 18:45

I mean, that's, it's interesting that it comes back. One of the reasons we set this podcast up in the first place is that idea of asking why, and we want to ask it of our students. Well, they're learning their maths, you know, so, so, Why did you get that answer? How did it work? Can you explain it more just to try and get them to think of the understanding behind it and the meaning behind it, rather than just regurgitate. Oh yeah, I can learn that. Repeat, learn, repeat, because you end up hitting that brick wall in maths around about year nine, 10, when it starts to get a little bit more interesting. And you go, Oh, I'm going to have any ever just learn and repeat this. So what am I going to do? So we're trying to encourage that, that asking of why, and you can almost reverse it around a little bit. And. When you're a teacher, you want a student to say to you, you know, but why does that work? And yes, you can say the same thing, but it's challenging the teacher to say it in a slightly different way, maybe, or to try and put themselves in their shoes. And I guess that's something you've already alluded to that really, in your writing, that you've got to put yourself into the shoes of the non mathematician. You've got to put yourself into the shoes of the mathematician to get something engaging. So I'm interested in what. When you, I know you do presentations, you do talks. If you were to talk to a group of students, let's say, and you're talking about maths, cause I'm, I'm going to assume most of the things you do, I've seen your number file, et cetera, you're going to be there to talk about maths. How are you going to plan to enthuse those kids about maths and get them to. Go away thinking, not, you know, Oh, thank God that's over. You know, we had to talk about maths, but actually to walk away from it, going, but that was amazing. Like, Oh, I wonder about this. I wonder this, you know, how can you design what you do to give them that feeling? I'm

Alex: 20:23

giving away my trade secrets. Just give us a, give us a little,

Andy: 20:27

a little sneaky peek. Go on.

Alex: 20:29

I did, I did several different ways, depending on what the audience is and what I'm there to do, but what I never do. I did it first. I realized it just doesn't work because is to try and actually explain and get some math because that's what teachers do. That's what's there. And I'm there to try and do something a bit different. So the very At one end, what I try and do is no math at all, but just let's talk about numbers, which is a bit about math, but just about numbers in a really fun way, in a way that you maybe had never even thought about before. So, for example, just really basic stuff like Like what, what is it to count? And like, what can human counts and can chimpanzees count? I have these videos of chimpanzees counting and the, the parrots have learned how to count. Well, like what, what, what does all that mean? And I, I think that young children particularly, I mean, we all are, but talking about animals is really interesting and really grabs their attention. And there are these some like kind of amazing videos that you show of these chimpanzees doing things with numbers that you can't quite imagine, can't quite believe. And that just, it just grabs them and it's a kind of wow. And then you use that to just sort of often through them asking you questions and then you take it whichever way they want to go. And I have some other videos when I went to Japan researching Numberland and I've been back back since actually I got interested in the abacus and kids roundabout. Key stage two and three in Japan, like a million of them every year. I learned through the abacus and afterschool clubs was just saying that the kids go, really, I'm going to not go to football and go to abacus club. And so I show them little videos and it's just kind of amazing. And they go. Cause they're seeing people of their own age doing these amazing things with abacuses. And then when you get good at the abacus, you can do this thing called Anzan, which is an abacus without the abacus. Basically you're imagining the beads in your head, but because you've been doing for so long, you don't actually need to have the real beads. So they can do these like amazing kind of mental math tricks. And that always gets a wow. And it's interesting. And I think that I would have mentioned little bits about numbers, where they come from, and how it, you say maths is a universal language, but actually the approach to maths and numbers varies around the world. I find that that's a talk about kind of the culture of maths, that what I hope that I've done is firstly I've shown, here's a guy who obviously is really into maths, and isn't particularly nerdy, and says funny jokes, and talks about all these things, so it's getting an idea that mathematicians aren't maybe a traditional, traditionally what kind of maths. person might be. And they've shown how math links to all these different things. So what, what that is doing is just countering this idea that math is not useful or not interesting without actually trying to, it's just that message. That's what you want them to go away from feeling. So there may be the next time they do some math homework and think, do you know what, this is, I kind of get it why we may be doing this. Another talk that I do, which I find surprisingly successful, it was unexpectedly how successful it was going to be, is that about 10 years ago, I did this online survey to try and find the world's favorite number. And I only did it because I don't have a favorite number. And it was kind of, It was to try and prove myself that it was interesting. Anyway, I did this survey and 44, 000 people joined it. Easily the largest survey of its kind. And the thing with favourite numbers, I don't really have a favourite number, is that I didn't realise, is that everyone has an opinion. And it's irrespective of whether you're good at math, the people who are really good at math might say, Oh, my favorite number is pi or something like that, or my some complicated, fancy reason. But the people who hate math might just say my favorite number is seven, because it's Cristiano Ronaldo, you know, they've all got a reason. Yeah. Everyone wants to take part. And so you can start by talking about favorite numbers, which originally I would have thought, my God, that's anti maths. That is just, you're kind of having, you're sort of, it's trivializing the entire thing, but actually now I realize it's completely not what you're doing. It's like open access. You know, I've spoken to PhDs you know, in Google about favorite numbers. I've talked to primary school kids about private numbers and everyone is as interested because they've all, it's all about their personal interaction. But once you start doing that, and obviously the results of this favorite number survey we tend to like prime numbers more than non prime numbers, and then quite quickly, like how deep do you want to go? You can go to. Primary level deep, which is just, isn't interesting that you can divide some numbers and you can't divide these others. And we like the ones that divide, but isn't that weird? Because they're harder to do sums with. So all of a sudden you're kind of engaging with it, or you can take it. Prime numbers. You can go all the way to almost degree level when you can talk about, you know, the goldback conjecture or you know, your Ulam spirals and all this, you know, where you can talk about. You know, public key cryptography or whatever you want to do. But you've started that talk, getting everyone involved. And I think that, so that, that, that's another way that I try and get kids involved. I feel like I'm ham, I'm pitching for all your listeners to put me into your skills. Now, I don't know what I'm doing, but the other thing that in terms of big audiences. And often you might be holding and, you know, there's 400 kids, it's the entire key stage group or something like that. What I sort of learned this almost by accident because I did a talk that was maybe not so well prepared. And I realized, oh my God, this works really well, is to do puzzles that every, that the entire group solves together. And essentially what you become, you become like a stand up comedian who has a set, which is basically divided up. Into, you know, they've maybe got 20 gags and they tell whichever guy's going well. And if it's not going, they just stop and they go to the next one. Puzzles are like that. So you can have a short puzzle. You can have a long puzzle. You can have the puzzle can go to whichever depth you want to do. But what you have with the puzzle is that you have this amazing interaction. So you can say, do it an odd one out puzzle. There's a great odd one out puzzle that's on the cover of one of my puzzle books, which is a kind of. It's not a trick problem, but it's the one where basically anything can be the right answer for a different reason. So you put it up and then you say, okay, who here thinks the answer is A? And then you get a few people that are looking around because, and then you say, who thinks B? And there's slightly more people because people aren't so sure because actually everything can be the right answer. And so you've already got people taking an interest, sort of voting, you know, they've got everyone, everyone has skin in the game. And obviously it's a puzzle. What you try to do. He's trying to get that aha moment where they don't know what it is. It's like the shaggy doll story. Then they get the aha. It's fun. And then you quickly change it and then you're on to the next one. It means that someone was daydreaming and didn't get it. They don't need to have be concentrated for 90 minutes or 60 minutes. You just keep on going. Bang, bang, bang. And so I use puzzles to try and get that sense of release or kind of aha the ones that tend to work the best are geometrical or visual puzzles, just because you're looking at a screen and it's easier to sort of, it just, it just, it just works better. So that's.

Andy: 28:34

Take that, what the more abstract maths rather than what kids think is just numbers and sums and stuff like that. No

Alex: 28:40

equations, like totally no equation. And also what works. There are so many fun different things you can, you can do if you've got a smaller group. You've got these ones where you can bring two kids onto the stage and they can hold, you can interlock them because they're holding a rope, but the rope is connected. How they kind of untangle themselves and that can sometimes, if you do it wrong, it's complete chaos, but you do it right, it's like really, it's really good. And you get kind of basics, the basics of topology because you think it's two interlocked circles, but it's not two interlocked circles because it's, it's a loop around the wrist, which is another circle. And it's basically, you sort of go into the loop around the wrist and then it just makes you think, oh, I get it. That's interesting. And you might think, well, what does that got to do with math? It's nothing to do with algebra. or adding. And so I quite like just sort of the key, it's got to be either fun. Well, there's the element of surprise and fun and learning. And it's the, it's the aha, the aha. Also, the nice thing about puzzles is that they all have an answer and you want to set a puzzle that is, they might not get in the time they're set as an audience, but they would ultimately, if it was just themselves, be would probably be able to get even if it took a bit longer because you know life is full of so many Problems that don't have answers that you can't do, it's really nice thinking, okay, there are these little baby problems that you can solve and you can do, and that's really nice. And actually, if you learn how to solve these little baby problems, which is kind of what maths is, you know, someone I can't remember, Jordan Ellenberg or Eugenia Chang was one of these maths writers. So the whole thing about maths is that maths is there to make things easy. You think that math is there to make things hard, but actually math is there to make things easy. So you just gotta take one step back. Yeah, yeah, yeah. Reframe that initial sort of judgment.

Andy: 30:46

I used to have, I've said this before on the podcast, but I used to have in my classroom, I had two things. I haven't said the other one, which, which also I think I basically stole from your book. But the first one used to always say, you know, math is problem solving. Problem solving is thinking. Have you thought question mark, because you'd get kids in that their first thing in class is just go, don't get it. And be like, okay, well, don't you get, you know, what are you talking to me about that explains me where you're up to. This is about problem solving. Have you tried to solve the problem? Have you broken it down? Have you done this? We've done this. And that's kind of what you're saying there about that's the beauty of math, right? It's, it's Yes, it is a universal language if you like, but it's done in so many different ways. But at the core of all of it is maths is about breaking things down into a smaller chunk that you can figure out and then expand and learn and build those foundations and build those big blocks up. The other thing I used to have on my wall, which I think came from your zero chapter basically, was that zero is nothing and everything. Yes. And the kids used to read it and be like, what does that mean? I'd be like, well, what do you think it means? You know, how many elephants are in this room? And they'd be like, what? Like, well, there's zero elephants in this room. And they'd write, you would do some measurement work and I'd set it up. So the answer was zero for a length of something. And they'd write zero centimeters. I was like, is it zero centimeters? And they're like, what do you mean, Mr. Lumley? Well, if there's no, if there's nothing there, there's no measurement. Does it need centimeters? And just, just to try and do something to get them thinking that's different. We used to do a carousel in one of my schools where the whole aim was to take year seven and do something that was nothing to do with the curriculum at all. I used to do combinatorics stuff and take them, imagine them going to the cinema and they're going to sit in a line and how many different ways can you sit? And, you know, you've got 20 kids in the classroom. That was a private school. So 20 kids in the class and you're getting into the, you know, the Billions of different combinations that they can sit in and the kids sit there going like, what, and it's that little level of engagement. It's exactly what you're saying about your talks. Just. Something to interest them, you know, math can become this monotonous thing of, here's some questions, do some questions, here's some questions, do some questions. And obviously what we're about here is saying, we don't do that. We don't need to do that. You know, we can do a lot more than that. You know, Alison is our primary expert and it's, It's been really interesting hearing the things that you've said, Alex, knowing Alison as I do now and having done first season of the podcast together. And so such similarities between what you're saying, work, writing for everybody, producing, you know presentations for different levels of kids. I know Alison's been doing exact, does exactly the same things, the same mentalities with her teachers. And then when she's working with. You know, five year olds, six year olds. What, what, what can you apply from what Alex has said, Alison, for that primary school teacher?

Alison: 33:38

I mean, there's, there's, there's, there's loads, there's loads in there. I, I think, I think part of it is, is this, the slowing down of, of, of, of the starting of, of the start of things and the finding the, The hook's not, is, is, is too trivial to say, but it's, it's finding that way into something which, which gives a reason for it, which seeds that question of why, because I think we can, you know, we like to ask why that, you know, and there are teachers who will, will question why. But what we really want to do is foster that, that why that comes out of young children all the time. You know, they constantly ask why, trying to make sense of what's going on around them. And at some point we, we lose that. And I think it's, it's that engagement that says, hang on, I want to know why this works. I want to ask why this works. I want to see what's, See what's going on here. Well, hang on. If we move that to there, what, why does that make a difference? And and, and the questions you were, you were talking about with the zeros and, and, and what have you, and, you know, do we need centimeters if there's no measurement there? Or do you know what to, what do we need to talk about? And I think we get, we get very formulaic, very quickly with children too formulaic, too quickly, and we squeeze out that. The questioning and the sense making and what you were saying about those aha moments I've bored Andy with it lots of times before, but that I had a moment of realization with a group of very, very high attaining mathematicians. They were, they were top end junior school, so year sixes, and one of them, we were working on some problems and one of them went. Oh, and then explained what was going on and I said, Oh, you've had that warm fuzzy feeling I heard about on the radio. Someone had put the warm fuzzy feeling in the Museum of Curiosity on radio 4 and and this group of, of children, and it was a mixture of boys and girls, looked at me as if I'd passed out. lost the plot yet again. It was a look that was relatively common when we were working together and I explained the story about it. So there were about 12 of these very high attaining mathematicians and half of them, when I talked about the warm fuzzy feeling, went, oh yeah, I know what you mean. And what scared me rigid and shocked me was that half of them didn't. And I think that, you know, a lot of what we're talking about here is that, that personal engagement with it and those moments that lead to, and we can, you know, we can go into all the cognitive science stuff around it as well. But But I think sometimes that's the bit that's missing and we're not engaging them with it. We're not engaging the teachers perhaps with it in a way that says if you, if you find this way in, if you really expand that early bit of, of the, of the, of the new introduction of a new concept and really secure it and generate those aha moments and those, those, those warm fuzzy feeling moments and support our pupils to recognize that that we could. That this whole digging for the why would become a absolute core and fundamental to to the way we teach maths to children. It was a bit of a ramble, sorry.

Andy: 36:48

It's, it's just interesting isn't it, to talk, you know, we spend. Our daily lives, talking to teachers and working with teachers and we've been teachers and knowing kind of what it's all about in the classroom. And it's just really interesting to hear the similarities really in, in your, when, what you do, Alex, which is completely different to teaching in terms of what you're planning and stuff. Now, I'm going to ask you a question here. We're kind of getting towards the end of our time here, but I'm going to ask you a question, which we normally ask at the very start, which is, you know, In the last couple of weeks, has anything happened that's made you ask why? I

Alex: 37:23

mean, that's such a big question. It depends on what level to take it. The first thing I thought of, which maybe is not entirely relevant, but that was what I thought of, you know, is that I'm getting quite interested in computer science. And I have noticed that there are almost zero books. Aimed at Key Stage 2, 3, well, Alex in Numberland has probably stated 3, 4 and grown ups, but the ideas are definitely, you can explain Key Stage 2. There are no good books on computer science. There just aren't. Computer science is the fastest growing A level computers dominate the world. So I've been going into the British Library and trying to read everything that anyone has ever written on the basic concepts of computer science and trying to find out why This is such a massive area and there's not that much stuff about it. What you have, you have textbooks, you have academic books, but there's no kind of thing that makes it exciting and engaging. And I'm interested for two reasons. One I'm interested in because, you know, I make my living from writing books and if there's a big gap there, then I want to go and fill it. But I'm also just more just fundamentally, well, what is it about the way we teach maths, the way that we teach computer science, the way that we exercise. use computers. The you know, I think that math famously has an image problem. I think a lot, lot less now than when I was, when I was a kid. But still does a little bit. Computer science has a different, but also does have an image problem. And like, what is that? And in the future, I think that computer science is going to become more of a mathsy subject and less of a kind of engineering y. Kind of subject and so that's I mean, maybe that's just too high level for this podcast, but these are the big things that, you know, I'm thinking about at the moment and when I go to bed at night, these are the questions and I don't really have any answers, but that's, that's where I'm going.

Andy: 39:43

But that's the challenge, right? That's the whole point of being a person that wonders why you're not just going to stop. You're going to go on now, hang on, what, what's next? You know, why is, why is there a gap? Where is this, why aren't people writing it in this way? Why aren't there these things for these kids? It's interesting, isn't it? Cause you know, my, my kids play computer games on their little tablets. And essentially everything behind that computer game is decision maths and algorithmic and you know, how it works and it's vectors and it's everything. I could see, I can easily see. Some kind of new a level, which is math and computer science.

Alex: 40:21

But also before you mentioned, sometimes you teach your kids combinatorics and it blows their mind that, you know, with only five people reorganizing them, you know, I know a hundred combinations or something, but whenever you get to say 20 or 30, it's just like billions and billions and billions. That's the kind of computer science issue, because that's all about how you in the trade offs that you have to make within the computer, how you don't get too much complexity in order to do what you want to do, because it's no longer about Can you do it? Theoretically, that's math. It's, can you do it practically? So to look at those problems in a way, in, in a different way and in a way that I'd never learned when I was doing, doing math. And yeah, I think that's, that's interesting. There's one point that all of a sudden came to me about this asking why, which maybe I can help contribute, is that what a journalist, you know, I'm, I've got a degree in, in math and philosophy. And then I trained as a journalist, I went to kind of journalism college and did all of that. Journalists, my job has been to ask why, always. And the thing that journalism teaches you, probably taught me just the overriding Kind of life skill is not to be afraid to ask a question. If you don't know something, just ask someone. I mean, and this goes from, if you're walking down the street and you can't find a house number, just ask someone. Loads of people won't even do that. But you know, I'm, I'm, I'm different. So I'm yesterday I was in the library and I read this book on computer science. And and it was about written 10 years ago. And as a guy saying, and I believe that this, this is going to happen. And I was just like, do you know what I'm going to literally right now, right to this guy and ask him, so did it happen or not, you know what I mean? And I only get that from the kind of. It's not fearlessness. It's more like a chutzpah or a kind of opportunism that you learn as a journalism. Just like, if he's going to say that in a book, well, I want to know. I just sent him an email. I said, I know this is maybe cheeky of me, but I couldn't resist. I'd literally just put your book down and you say that this is going to happen. And I, you know, it's like this algorithm is going to be a really important algorithm. And I was like, I don't know that because I'm not a computer scientist. I just asked him. And actually, as it was, he wrote straight back and says, Oh, do you know what? Take me too long to write. Why don't you just call me on zoom on Wednesday? He's like some professor in an American university. And so that is journalist. Speaking, but it's so, so useful. It's so useful. Like I'm probably a really annoying person because I just like question people all the time and, you know, a lot of good journalists are quite rude people because they're, you know, it never hurts to ask that question. It never hurts to ask that question and we should not be afraid and we should be trained, that's a good, a journalistic skill that everyone should learn. Don't be afraid to ask the question. Like it doesn't matter. I mean, it's just a question you're just asking

Andy: 43:29

it's, it's, you know, we've, we've talked about it before. What happened? I mean, my three year old boy never, never, literally never stops asking why I can answer it a hundred times, but why daddy, but why? And it's that whole thing. When does that go? And why does that go? And that's what we talked about a little bit in season one, like what happens to that curiosity when the kids just go, Oh, I'll just do with what they say then. You know, it's. It's so true. It's so true, Alex. That, that isn't a, that, that's almost a nice way to finish, to be honest. As the takeaway for the podcast is something I'm always trying to figure out is what is somebody going to take away who listens to it? Ask why it doesn't matter who you are, what walk of life you're in, whether you're a three year old or whether you're a 43 year old ex math teacher like me. It's not

Alex: 44:13

embarrassing to think that you don't know it. It's like, I mean, maybe that it comes, you have to have a certain intellectual confidence to say, think it's fine to not know anything, but everyone should not be afraid of not knowing anything because lots of the people who think they know things don't know anything and you need to be sure you need to be sure. So it's never embarrassing. I mean, sometimes I ask a question, it's like you know, it's so obvious and like, I might say, Oh, how embarrassing, but I'm not actually embarrassed at all because I wanted to know what I asked.

Alison: 44:43

Yeah, and I think as teachers, we need to create the the, the atmosphere in our classrooms, the, the culture in our classrooms, where it, you, you just, you do, you ask and it doesn't, and just as he said, Alex, it doesn't matter about the question whether the question ends up being the question that makes everybody go, Oh, wow, that's really interesting. Let's have a think about that. Or it's a case of, yeah, yeah. Yeah, come on, remember what we did yesterday? Yeah, yeah, all right. Yeah. Okay. And we move on, but I think it's that culture and the culture of asking questions is really important to keep.

Andy: 45:17

Absolutely. Well, Alex, thank you so much for giving up some time for us today. It's been really, really good. It's been amazing to talk to you. I'm already looking forward to Alex's adventures in computer land. Whenever that arrives, I will I will link to, to, to Alex's socials and for all the schools that want to go and book him, I'll, I'll put a link onto his website so you can go and And, and get him in to talk about math and then to use your kids. But yeah, thank you so much for coming on digging for the Y. It's been really, really good. Alison, thanks as ever for your company. Over the last 47 minutes or so. Thank you for listening. I hope you can take something away from this. We just really enjoy talking to people. with a maths interest and, and getting to know about what, what makes them tick and why they ask why. So Alex, thanks again. Thank you very much.

Alex: 46:01

It's been great fun. It's been really, has been really enjoyable. Thank you.

Andy: 46:04

Enjoy the rest of your week. And if you're listening, we will look forward to you listening to us. Hang on. That doesn't sound right. We'll look forward to you. No, wait, again, you can look forward to listening to us. I don't know. It's getting too egotistical. Right. We'll see you again in the future. Take care. Bye bye.