S2 E5 - Digging for the Yes, but Why with Ed Southall

In our final episode of Season 2 of ‘Digging For The Why’ we talk to Curriculum Lead for Oak National Academy, Ed Southall.

In this week’s episode, Ed emphasises the need to nurture curiosity from an early age to encourage participation in the classroom.

We delve into the challenges of moving away from traditional teaching models and the benefits that conceptual insight can bring to enrich students’ learning experiences.

Additionally, we explore how to create a classroom culture in which students feel safe to make mistakes, share ideas and engage in discussion to enhance their understanding and shift traditional teaching practices.

Meet our Guest:
Author of ‘Yes But Why? Teaching for Understanding in Mathematics, Curriculum Lead for Oak National Academy and editor-in-chief of the Mathematical Association, Ed Southall, is the perfect guest for our podcast.

Ed specialises in speaking about conceptual teaching in maths and making maths make sense for children of all ages. He has an array of experience in teaching and senior leadership, as well as experience teaching in the Middle East.
@edsouthall

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You can find us on X
Andy - @desire2undrstnd/Bluesky
Alison - @AlisonHopperMEI

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

Chapters

• 0:00 Welcome and Introduction to Ed Southall
• 4:57 Ed Personal Journey with Maths and The Genesis of 'Yes, But Why? Teaching for Understanding’
• 15:53 Challenges and Strategies in Teaching Maths Conceptually
• 22:20 The Impact of 'Why' for Students and Teachers
• 26:27 Exploring the Complexity of Teaching Maths and Mathematical Concepts
• 28:06 The Dangers of Prioritizing 'Why' Over 'How': Cognitive Load and Conceptual Understanding
• 31:14 Curriculum Design: Making Sense vs. Depth of Understanding
• 33:47 The Journey from Primary to Secondary Education and Building a Supportive Classroom Culture
• 41:07 Encouraging Deep Thinking and Understanding in Maths
• 43:00 The Importance of Classroom Culture in Learning Effectively
• 47:42 Concluding Thoughts and Future Directions

Transcript

Andy: 0:16

Hello and welcome to this episode of season two of Digging for the Y, the podcast for math teachers, where we explore thoughts behind asking why I am Andy, one of your hosts. And I'm joined in the fellow hosting seat by Alison. How are you today, Alison?

Alison: 0:29

I'm very well, thank you very much, Andy.

Andy: 0:31

Very, very good. Enjoying a bit of sunshine down there.

Alison: 0:34

No, cloudy today.

Andy: 0:36

We've got sunshine up north. So we went one for the north. It doesn't often happen. So I'm going to claim it whenever I can claim it. Now, when we were thinking about season two and who we would want to talk to about Digging for the Why, it was pretty easy to come up with today's guest. He is the author of Yes, But Why? Teaching for Understanding in Mathematics, which basically would have been our alternative title for this podcast, but that had already been taken. So we reached out to him and thankfully, or maybe foolishly, he said yes. He is currently, now there's a list here coming, this is ripped straight out, don't, don't give yourself away, shh, this is ripped straight out of his LinkedIn profile, so you know, this is pretty good. He is currently the Mathematics Curriculum Lead for Oak National Academy, an author of many maths books, a conference speaker specializing in conceptual teaching of maths, and making sense, no, and making maths make sense to children of all ages. If you go on his Twitter, he often talks about talking to a bot as well, which is quite entertaining at the moment. He is editor in chief of the Mathematical Association, a former school teacher, and member of senior leadership, and also worked in the Middle East for four years. He is, of course, Ed Southall. Welcome to Digging for the Y, Ed. How are you?

Ed: 1:48

I'm very well, thank you. I'm a little bit flustered after that intro, even though I wrote half of it. I particularly like that you threw in that my best friend's a bot at the moment, which is brilliant. Pretty accurate.

Andy: 1:59

I do enjoy your Twitter when you're talking about the stuff that you're doing at the moment. That was quite good. Okay. So we're trying to start the season off with a standard question to see what people are thinking about at the moment and what's going on in their lives. So in the last couple of weeks, what has happened to make you ask why?

Ed: 2:18

Well, I was thinking about this, like, I was thinking, oh, they'll want a clever mathsy thing that makes them go, Oh, I've not thought about the Y for that, but I don't have one of those. But I do have an eight year old and, and he comes to me quite regularly with like amazing, bizarre questions that are actually really good questions, but just, you wouldn't think them as adults because we've, we've, Lived a whole different set of experiences, but he came to me Last week basically and he said And I love this Why is it that the sky is blue when you look up? But if you were at the top of the sky looking down you can't see the blue I thought that's pretty good. I'm not quite sure how it's got to the top of the sky, but What's your answer? Because it just is shut up.

Andy: 3:11

No, don't, don't give the teacher answer when you don't know the answer.

Ed: 3:14

Well, what was good actually was, was his brother who's 15 chipped in with the classic misconception of, oh, it's because it's reflecting the color of the sea, which doesn't really

Andy: 3:27

Yorkshire.

Ed: 3:27

This doesn't work and also doesn't really address the whole from the top down work. I don't know. But I just, what I liked about it was it just demonstrated that weird curiosity that you tend to get mostly with like primary school kids, I suppose, because they're figuring out the world.

Andy: 3:48

Yeah. I love that kind of thing. That's something we've spoken about before Alison, isn't it? Because I've got a 5 year old, no she's 6 on my word. A 6 year old and a 3 year old and they're constantly just questioning everything. And then Alison's got, what's yours,

Alison: 4:02

17?

Andy: 4:03

Yeah, so like that kind of, that, what happens between You know, five years old and 17. And, and where does that curiosity go? And, you know, one of our, one of our episodes on the first season was about curiosity in that classroom. And like, what happens to it? Do we knock it out of the kids? You know, so I, I mean, that kind of leads into a question then, which, you know, believe it or not listeners, we do have a set of questions, which we send to our guests ahead of time. However, I'm straight away going to go off topic, just ask you a question, which has nothing to do with what we sent you. I'm interested in, in the book, obviously. So yes, but why? It's the reason that we first wanted to get you on here. Because obviously you must share something along the same lines as what we think about in terms of education, in terms of teaching, what led you to want to write that book? What, what was that about? What was that, what was driving you to do that?

Ed: 4:55

This could be long. I'll try and keep it brief. I, I have been through a journey with like my relationship with maths and I think it's quite a common journey up to a point. And when I came through at the end, I thought actually this, like where I've come to with this journey would benefit a lot of other people, I assumed. And so that journey was like being at primary school and being good at, I remember being good at maths. I remember getting the answers right. I don't really remember how it was taught when I was that young, but, but I did well in it and I went to a secondary school and I was doing great at maths then as well. And gosh, I got to sort my GCSEs and, and didn't really work very hard for them, but got good grades. And then I got to a level. I was like, Oh, this is. Quite a challenging subject now. And I really struggled at a level managed to get good enough grades to get through to university where I still studied maths Almost accidentally, really. I went to Keele university and you've got to do a joint honors there. And I wanted to do programming. But they, I had, you literally have to take a second subject or you did back then. So I took maths cause, cause I was doing all right at it. And I really started to fall out with maths as it were, because it was just really hard. And I don't, I don't think I really understood at the time why I wasn't enjoying that difficulty. And it's only as an adult really, that I can see that a big part of it was that Pretty much the entire time, none of it made any sense to me at all, ever. It was just, I was good at following the rules and the number that popped out at the end was the same one that the teacher was expecting. And I think I was just fortunate because that, that in retrospect, that just feels lucky, really. I don't think I had a good conceptual grasp of most of what was going on. And at university, I think I can hand on heart. I should be ashamed, but I'm not. Like, I don't think I understood anything that I studied at university in maths. I just followed the rules. And that gets you so far, but you really struggle with creative questions and questions that require you to apply stuff to unfamiliar situations and so on. And I always did. Anyway, so I come through all of that. I get my degree and I wasn't sure what I wanted to do. I wanted to be a programmer, but it was at the point of the sort of millennium bug thing. And so there were loads of jobs going into it when I was studying and then nothing happened. And you came out and the graduate market for computing just kind of drop off. So my mom was a teacher and she was like, why don't you just, while you're sitting around, you know, taking up space in my home come with me to my school and do two weeks and see what you think, because at the time there was a good graduate scheme. For teaching, they paid off your student loans for you. I was like, that sounds pretty good. And I was just really into it. I connect, like my mom worked at a really tough school and I connected with the kids there and she saw that and she was saying, you know, you've got this, you do great at teaching because you can, you can relate to these. You know, these kids who a lot of people can't and they responded to you really well. And I enjoyed it. So, so I did teach training. I trained to be a computing teacher, but at interview at my first job, as, as is always the case I've now found they went, Oh, you've got a degree in maths. Guess what? You're gonna be a maths teacher. So I had no formal training of being a maths teacher, but I ended up teaching maths 50 percent of my timetable for the first three or four years. And it just. Kept, you know, increasing because the demand for that subject is so much bigger or was then and the career opportunities were so much so much more prominent for for maths than they were for computing So anyway, i'm sorry. This is such a long story. I ended up becoming a head of maths, right? And at that point I must have been I don't know like 25 26 or something like that. Just pretty young for a head of math and and I kind of It, it, it I had this realization that up to that point, my teaching of maths had been fairly crappy and had been very similar to how I'd been taught maths, where I was just focusing on, you know, you need to know this rule to solve this problem. You need to know this rule to solve this problem. And so, and I thought, I don't want to be that. And now that I've got this kind of responsibility within this subject, I need to be better at teaching maths. So I just went away and, and. I just started researching all the things that bugged me about the stuff that I'd worked on my whole life in, in maths education. Like, why, why is it that this thing works and what, you know, there must be reasons. And I'd never really thought about the reasons until the point where I thought I need the kids to know some of these reasons so that they don't have this journey that I had of like being all right, but not enjoying it. And it just became incredibly addictive. As soon as you start getting those realizations of Oh my God, this makes sense. And oh my God, that makes, that makes sense. And oh, so I wonder if there's an answer to this thing. And, and you find that pretty much everything has a really sensible reason behind it or purpose behind it or structure behind it, even down to like the etymology of words in math, like words are so foreign, they, you know, we don't use them outside of maths ever really in, in a lot of, in but when you start figuring out why that word is structured as it is and how it relates to other words and you go, Oh, okay, it makes sense to use this stupid term. It's not stupid, but it was for 20 years. And I just kept going down more and more rabbit holes and feeling euphoric at every discovery that I made. And I thought I need, I need to spread the word, so I just, it became the book and I feel like, I mean, I'm sure other people should tell me this rather than me assuming it, but I think one of the reasons people find me reasonably interesting is because I'm, I am the same person as them on that journey of not being seen as a gifted mathematician. I struggled with it, I didn't really understand it, but I could get through it, you know. And I've come through the other side, so I can, I feel like I'm in a decent position to tell people you can too. It's not, it's not magic and it's not about having some crazy gift or, or like sense around numbers that other people don't have. It's just about being informed and being able to access that information and wanting to know it. There you go.

Alison: 11:59

Yeah, no, it's brilliant. So when you said you down rabbit holes, I'm intrigued as to sort of where you, where you started looking for the why, if you see what I mean, and where you ended up finding the beginning of that why, because obviously I'm, I'm listening to this with a primary hat on and had perhaps a similar, not, not so similar, but similar journey, but not at the same bits of math. My math ran out at a level. I got through a level by learning how to do stuff and I can still remember the feeling of getting to the end of a problem and proving that the coefficient of restitution lambda equal to third and the Hallelujah chorus played in my head. I was very happy. If asked me to do something about coefficient of restitution now, and other than telling you about snooker balls, perhaps, or billiard balls I would never be able to prove that lambda equal to third. And so my Y ran out at that point, and it was only when I did my PGCE in primary, that little bits of the Y started appearing to me as I pulled apart bits of maths. And having had the luxury of being able to live a life of thinking about maths quite a lot over the last 20 years, in and out of school as well So I'm intrigued as to where you started looking for the Y in terms of the maths and where you ended up.

Ed: 13:13

I think probably trigonometry was my starting point. Like, as soon as you, I've seen this, part of my background is teacher training and I've seen So many trainees get nervy around, this isn't the right terminology, but like the top end of the curriculum, you know, the, the, the, the stuff people used to label as the A star topics, which is ludicrous in some ways. But those, those elements that, that start bleeding into a level where without any conceptual understanding of what's going on. It becomes like farcically abstract and, and you just feel so inept doing anything with it and so lost and you've got no sort of compass bearing around whether the hideous decimal that comes out on your calculator at the end has anything to do with the question that was asked. And you're just hoping and praying it is and you see it. Like with, with an expert hat on, you see it in classrooms all the time. Teacher explains stuff, everyone's nodding. And then even the most high achieving students in the class are putting the hands up after every answer they write down because they just have no bearing of whether it's right. It was that and but I was in the role of the teacher. I just thought I cannot begin to teach these topics without having a really good foundation of, you know, what the hell's actually going on here. It's not just. Pressing numbers on calculators and, and to my shame, I taught this stuff before. Right. And I taught it in that way, just, just like plow through these instructions. It gets you there. And maybe that's because I wasn't trained in it to some extent. I don't know what, why I didn't take that more seriously at the time, probably because I was, I saw myself as a computing teacher and this was like the aside that was put upon me. I don't know. But it was definitely Trigonometry where I started thinking, I need to sort of deep dive I hate that. I hate that that's become part of our lexicon. This, before I go in teaching these, the, these, these pupils with it. And I had a blog at the time where I used to just post maths problems. And I started to, to write instead of just post problems on it. And, and I was writing my findings on this stuff. Not from a perspective of, Oh, look, I found this stuff out. Cause I was kind of embarrassed about that. It was more, it was more, if you don't know this stuff, isn't this interesting? And, and it was those that became.

Andy: 15:53

Okay, I'm going to kind of expand on that slightly, put yourself in a position of, you know, there's a teacher now listening to this podcast and thinking, you know, this is what I think as well. And I, you know, and in my teaching career, I worked in seven different schools and every single school had people that think like this, that you're talking about now and want to dig into it and want to deep dive, as you say. into the why and the understanding of it, but there's also the people who want to know that they can get results. And for want of a better phrase, don't mind if they don't, if the students don't understand because they're going to get it right. And actually that's okay because we're time pressured where everything else that we know we've got in teaching and we've got to get through this curriculum, we've got to do this exam in GCSE and. So put yourself in the position now of the teacher who's there. And then maybe a couple of years in, and they're thinking, I'm not, I'm not, I don't feel like I'm teaching this topic properly. I don't think I'm teaching this topic. I feel like I'm algorithmically preparing these students to answer a question. And when that question is different, they're going to get stuck because they're not got any kind of conceptual understanding. How did you go about. Working with your heads of department, if you like, to allow you to take that time to introduce topics in a different way, knowing that if you're like, let's say we've got three weeks on a topic while I'm going to spend the first week playing around with stuff here, looking into it, diving into it, because I know that then the following two weeks, I'm going to get to the point you need me to get to, how'd you have that discussion with the head of my head of department?

Ed: 17:22

Yeah, it's tricky. Right. And, and it, it almost comes from a few. Steps before that, I think, I think focusing on what the practice is turns into more in depth conversations about how the modeling looks and how we're testing different elements of how, how much children understand the topic. So I think it's easier to get people enthused about. Practice first and, and start thinking about, well, what's a good question look like on this topic and how much do I actually know that they know when they can answer this question correctly and, and like, what level of understanding do I need them to have to be able to tackle this style of question where, where, Like the purpose is hidden or the maths is hidden and so on. And so from there you start thinking, well, why is this a smart question? And how is this question better than that question? And so on. And to me, then you start kind of working backwards and going, well, to be able to tackle. These more in depth questions, they need to have this understanding. Well, how can I get them to get that understanding? How am I introducing this topic? What does my modeling look like? What does my questioning look like? How can I improve that? And it, it. An easy way to do it really is like a comparison of like the before and after. So, so something, I mean, everyone always falls back on something like Pythagoras or the area of a triangle and so on, but I think one of the reasons for that is that both of those lend themselves really strongly towards being able to teach it procedurally quickly, but not very well, and teaching it slowly and, and really going to town on, on, on. What's actually happening with structures and with, with the maths behind, you know, where do those formulae come from? And I think if you can get people on board with, with this kind of excitement of revisiting stuff and improving it it kind of naturally generates from there. And in my, certainly in my experience, I found that, I mean, I mentioned that I did a blog about writing puzzles. The reason I used to do that. Was because I was working in a maths maths department as a kind of lead practitioner type thing. And, and no one was talking about maths at all. And everybody was, you know, the being a maths staff room together, the, Talk about their days and so on. And then they'd go off and teach in silos and then come back again. And the departmental meetings were all about the bulletins from senior leadership or from wherever. And there was nowhere in the cycle of a week where people were talking about what they taught or how they taught it. Or there was just no sense of enjoyment about the subject. So I just started posting these maths puzzles on the board in the staff room, the maths staff room, just to see what would happen and over the course of like a month or two people just everyone started talking about them and and people would share their different ways of solving stuff and and it just nudged me. People to reflect on why they love maths and why they love their subject and made them realize, and this wasn't my intent particularly, but it made them realize that they haven't done any challenging maths for years because the only maths the teachers are doing is the stuff that's pre prepared or the stuff that's been on the curriculum for 20 years or whatever, and so putting them in a place where they actually had to solve something that they weren't that familiar with, kind of. Fired up their love of, of the subject. And I think if you can get people to be fired up about what they're teaching, then they're going to naturally want to talk about, you know, what's the best way to teach this? What's the best way to draw, you know, this student asked this great question yesterday. How did that question come about? What did I facilitate to get to that point? And how, how would you respond to it? And that to me is one of the most. exciting things about teaching. And you know, you, you look at some other cultures about their perception of teaching and how you can never be perfect at it. And you can never, it's just this never ending journey. That's what they find exciting. They don't find that daunting. They find that exciting. And, and that's the thrill of it, that it, that it's, you know, there's this intellectual side to it where you go, how do I constantly do better? And, and I don't think we have that. enough here but if you can latch onto it or nurture that, then, then you're going to fall into those rich discussions about, you know, how do I get people to understand this really clearly to a level where they're not just. regurgitating that they're thinking hard about stuff.

Alison: 22:20

How did the, how did the pupils react? Cause I think that's, that's something that's quite interesting. You, you've found a way to get through to the teachers, getting them excited about the maths again, but then changing that way of presenting maths in the classroom is a real difference in the way that the pupils engage. So did you, what, what did you sort of, what, what happened? Yeah, I mean, I'm, I'm,

Ed: 22:41

I'm. I'm going to be brutally honest, because I want people to understand that this is normal, or it is from my perspective, like my biggest battle in the classroom was getting top set year 11 to want to know why anything they could not care less. And it's understandable when you take a step back, right? They, they are in their last year. Most of them of maths education, they have had 11 years of being taught in a certain way or being familiar with. Certain styles of teaching and they have been extremely successful in that arena. And so to change it at the end is uncomfortable at least and, and threatening, you know, it's like, I'm really good at this and I'm holding onto that and now you're, You're, you're putting me in a place where I have to do things differently, where, where perhaps I'm not going to feel as successful or, or even just at a base level, like I'm near my exams. I've got this don't mess with the system. And to be honest. I say this in some of the talks I do about, I think it's really complicated about how you put why into lessons, which I think we'll probably get onto, but I think it's, it's not going to be appropriate all the time and I think with year 11, depending on their prior experience, you know, your priority really. is get them through their exams, that's why they're there, right? And, and as a principal that I struggle with that because that's not why I'm there or it's not why I want to be there. But really that is what you're employed to do, right? Like get them through school, you could argue. And particularly at that point. You know, I don't have time to, to go, right. I'm going to explain prime factors in way more depth for you so that you're, you're really satisfied with understanding it because that comes at a cost of, Oh, by the way, you're not going to know three topics in your exams in a few months. So it's definitely complicated, but I think at year seven and eight, you can nurture it really quickly. Genuinely. I think, I think the message that I give is that your default. At key stage three really should be, this needs to make sense rather than you need to get the answer right.

Alison: 24:58

Yeah.

Ed: 24:58

And that kind of shifts as you move towards exam periods. But if you assume that, that that why has been integrated from year seven, then then you shouldn't have to be a hundred percent focused on the answer must always be right by the end.'cause that comes with it. Yeah. But it does take time.

Alison: 25:18

Yeah, no, I think that Andy, Andy mentioned his, you know, we seem to have our offspring are all at sort of span the for span preschool to what, well, I think, I think with both of them up in, up at the, the top end and I must admit, it's possibly because he grew up with a, a maths teacher and an engineer that my 17 year old, We got over the initial early in year seven. Just tell me the, just tell me what to do. It was it was fractions and it was depending on whether you knew the value of a part or the value of a whole. Did you divide by the denominator and multiply by the numerator or divide by the numerator and multiply by the denominator? Just tell me how to do it. And I. didn't because I'm cruel and mean and horrible. But the upshot of that is that now we're in first year of A level and further maths and his biggest bugbear is when he comes home and he doesn't understand why this works and he gets really, really frustrated. When the understanding why it works doesn't matter. So you said the tricky bit is how you get the why into the lesson, into the lessons. So go on, tell us. I think, well,

Ed: 26:28

I just think it's really nuanced and complicated. And I think people want an easy answer where there isn't an easy answer at all. So for example again, forgive me for going back to the same blooming examples each time, but area of a triangle, right? It's one that everyone can imagine in their heads. I think, I think, I think a poor way to teach that would be, here's the formula, practice, practice, practice, move on. Right. But I don't think there's a right answer. way necessarily with, with, with the next two examples, like model and explain and, and get to the core concept of this is why this is the formula and then practice and then move on or introduce the algorithm practice, practice, practice, and then introduce like, this is why this formula is right. And I think some, I was really, really like consciously careful when I wrote the book to not promote a sequence of how to introduce stuff. I saw it as, this is the explainers that you are probably going to want to use sometimes, Probably not going to want to use over time. Some of these you probably will never use, but I think it's important that you know them. And I think we've, we've, I don't really have much evidence for this. It's just my gut feeling is that there's a default position of I've got to explain the why first. And I think that's really dangerous because you take that trigonometry example, or the example I usually cite is like the volume or surface area of a sphere, right? You've got really neat. beautiful tiny little formulae for those things. And to understand where that formula came from is way, way more complicated than the maths they have to ever do in that year group for that unit. And so if you go down the y route, it just feels like a a, a poorly idealized ego trip of, I, I know how this works and let's all study it cause it's brilliant. And it's like, well, actually what you're doing is completely derailing any sense of what the purpose of the unit is about and what they need to focus on as important. And, you know, any confidence built up and being able to use that formula is going to get smashed when you start trying to derive it. And, you know, there's a very strong argument for some sequences to be front loaded with procedure because you want to reduce the cognitive load associated with what they're doing and what they're thinking about. And so you get that automaticity in place. Then you introduce this complexity of where does this stuff come from? And it feels more focused, right? Like you want them to, you want the intent to be, you have to be fluent in this stuff. Not, you know, the purpose of this unit is for you to understand where this came from. Because that's, that's not really the purpose a lot of the time. It helps in the bigger picture. And, and as I've alluded to, you know, like we take students or students, you know, students are all on different journeys and at different points. You can't just go into their environment and ignore their prior experience and go, right, let's go in with the why. So it, it. It's really complex about where you, where you decide to do it and where you decide to not do it at all and where you decide to strip it back to like a rough explanation that helps them understand that this comes from somewhere without going into like grassroots deriving stuff from first principles. And that comes from just, just teacher agency, right? Like you have to make those decisions yourself based on the class that's in front of you. I can't tell you what to do. What all I can tell you to do is justify your own decisions. I think the default, as I said, should be try and make things make sense. Particularly if it's. Year seven onwards if you're picking up a year seven or eight group secondary or, or, or similar but don't be a, don't, don't feel guilty if there's certain units where you do have to just go procedure and, and, and kind of fall back on this does make sense, but we're, we're short of time or, or the explanation for this is really complicated. So I'm going to give you this kind of simple overview. I think people need to be comfortable with that but you know the flip side is don't go all in with we're going to ignore all explanations of understanding and sense making because it's just easier this way around.

Alison: 31:14

So you gave a couple of examples just then about times when it's, it's not appropriate to look at the why first is that I'm just thinking about reflecting on curriculum design and wondering, you know, how that how those sorts of issues relate to the way we design a curriculum for maths right from primary onwards. I'm thinking of some examples in primary that would that same category.

Ed: 31:36

Yeah, I. I struggled with this and as per usual, I've changed my opinion over time. But I when I wrote the book, I was thinking you shouldn't have anything in the curriculum that you can't explain. In terms of making it make sense and therefore. Something like a surface area of a cone or a sphere or so on would probably have to go and go somewhere else. But I think the, the, the difficulty with that is even if they were at a point where that maths was really accessible, it's not going to be accessible to everyone. And so you're still going to have that conundrum of. Some students are not likely to be able to understand this to the level of depth that I want them to and so a compromise is going to have to be made somewhere. So, in a perfect world, yes, the curriculum would just, just be a sequence of, of nicely tied up things that are easy to make sense of. In the moment and the next thing you teach relied on the thing that was taught before and so on but we know that it's not as neat and tidy as that and learning never is anyway, so I think we have to just kind of accept that there's going to be points in the curriculum where you aren't going to be able to go into that level of depth and, and You're going to have to be comfortable with that. And, and there's ways around that. I think there's ways to make things make some sense without having to go into too much depth. But I also think there's, you almost take away those nice moments at a level where you go, remember that thing that we learned? Like let's, let's figure out more about it and revisit it. And then you get those great moments in teaching as well. And let's be honest, when you, when you're a, when you're an employed mathematician further down the line, you don't have all the answers to stuff, and you don't, you know, you're, you're frequently in areas of, of, of the great unknown and discovery and dead ends and confusion and so forth. So maybe there's, there's an argument there that, that, that's just part of this journey of, of, of thinking. of what it's like to be a mathematician anyway.

Alison: 33:47

It it's interesting with that because I mean at primary school we touch on circles, we do a little bit about circles, we don't really look at the formulae around areas and perimeters of circles but I used to in the, back in the old days I had a, I had my level six group in year six and they did. And I thought to myself, goodness me, how do I, I can't remember, what do I do with these kids about the area of a circle? How do I make it make sense? And I didn't, I didn't want them I realized I wasn't going to be able to teach them the full why this works, but I wanted them to have a sense of why it roughly worked. And so we did things like put circles into squares and think about what the area of the square would have been related to the radius of the circle, and realized that we had that idea of it would have been four, four r squared, for the area of the square around it. And so therefore we knew the value of pi and that was less than four. So three and a bit times made, made some sense. And so there was a sense, I don't really know exactly why this works, but if I'm ever really stuck, I can sort of rationalize why that's going to be the case. So, so that was, that was quite That was quite a nice way of looking at it. I was going to go there and think, did you work with other departments across the school? Because asking children to, or pupils to work or to, I kind of, I'm thinking this is leaning into the sort of the metacognition work about, you know, do I really get what's going on here? Can I make this make sense with what I know already? And, and I mean in primary we have the luxury of the one teacher teaching across the curriculum but so when when when the kids you taught for for maths went off to science or you know history and geography was there did you have any cross department discussions across the whole school around digging for the why

Ed: 35:45

No i think it's it's what You know, in a perfect world, I think every maths department wants to work closely with the science department to, to, you know, they have the most explicit links with maths. And there's, there's a lot to be said for the benefits of, of getting stuff tied together there. But in terms of the, the, the kind of general pedagogical approach, no, it's not something that I got into. The one thing that did resonate around that though, is when I used to. I used to have this like standard speech when I picked up a new class, particularly at Key Stage 4, which would be around expectations, but not, not my expectations in terms of behavior, but in terms of what they want to get out of the lessons and what they want to get out of maths and what I want to get out of teaching them. And I would always start with just asking them, like, put your hand up if you hate maths. And, and, you know, the few sort of cocky ones would put their hand up almost straight away. And, and then I would say, well, I used to hate it. And then more hands would start going up and so on. And I would just say, right, I don't want to teach you anything yet. I want to just talk about that. And let's get to the bottom of why some of you don't want to be here and how I can work with that. And. It's all a bit Dawson's Creek, I suppose, but basically. Hey, come on.

Andy: 37:12

It's 2023. I'm not sure Dawson's

Ed: 37:15

Creek

Andy: 37:15

is a relevant reference.

Ed: 37:17

I don't watch TV. You

Andy: 37:19

don't

Ed: 37:20

watch TV since the late nineties.

Alison: 37:25

We'll put a link in the notes to anyone who's never heard of Dawson's Creek. It's

Andy: 37:28

a wonderful show, everybody.

Ed: 37:31

But you just kind of, where we would get to is, you know, this isn't actually about maths. It's not, it's not. That that you hate it's that you don't feel confident here or, or that you don't or that you feel more threatened here than, than you might in other subjects and, and you start developing, you know, this realization that some students feel the same way in art because they're going to an art lesson and they're sat next to someone who's brilliant and they're going, I can't do this, I hate it and you get people in PE. Who just fill with dread at PE because the person next to them is really athletic and does loads of stuff and just seems to get it and I don't. And it's, that's the feeling. It's not really about maths. It's about confidence and uncertainty and this kind of mental barrier of, I can't do this and therefore I will never be able to do this. And so we kind of get to this, this point where I say, well, I can work with that. And I will help you. Make this make sense and get through those barriers of, of fear of this subject, but I can only do that if you're coming to me with, you know, this is how I have felt about it, but I'm going to, I'm going to work with you to, to, to see what you can do with us. Because I don't think you can get anywhere with most students and this isn't just a maths thing, but, but without a good culture and without a culture that where it's safe to make a mistake and it's safe to not know what you're doing. And it's safe to have an idea that. 10 seconds later, you think it was a stupid one. And until you get to that point, you're going to have a good proportion of your class who, who are anxious about it, who are never going to get to a place where they're confident to just, to just try stuff and to try and understand stuff. Because there's just this huge barrier of, I can't do it. And as soon as I pop my head up. It's going to be wrong and I'm going to get shut down. I'm going to feel like crap. And, and the one thing I used to be really strict on was student responses to other student responses. So if a child or if a pupil said, You know Oh, I think the answer is three. If another student came in with, Oh, that's stupid. I would just hammer that child because they are destroying the, like that one offhanded comment they think is funny in the moment sets that child back a long way in terms of their confidence to share an idea or a thought or, or a reason for, or a justification. And without that culture. I just think you're up against far too many barriers to get to a point where you can explore why and explore concepts and explore a way to make something make sense as a group, rather than as just me telling you what stuff does.

Andy: 40:34

It has to be a two way thing. You know, it's like talking to a kindred spirit and maybe that's why we share a birthday. Who knows? But it's like, you know. You can't, you can do everything you want as a teacher, you can do all of the reading, the planning, the preparing, the thinking, the predicting of what the students are going to say. But actually, unless you've embedded that culture into your classroom from the start as a two way thing, you're not going to get it. You know, I was so similar to what you've just described there, and we've talked about that in season one. And, you know, I would start when a brand new year seven class, who hates maths? Why? You know, let's talk about it. Let's discuss it. My Twitter handle is desire to understand because that's what I wanted the kids to try and do and like you've both alluded to you Can't always do that Like it's an impossible task to think you can get every single student in every single year group to understand everything that's going on But you have to kind of embed that culture that is Reason it, you know, ask me about it so when you know, like you say when kids are given answers and you'd have this the The silly student who would say something daft about it or take the mick out of someone's answer. I always used to try and make, and this is the whole digging for the why thing that Alice and I have talked about before, if a student would say an answer, they'd have to justify it in some way. I don't want guesses and in fact if they just said I'm just guessing well fine you've justified why you've just said your answer But actually if you can get that embedded into them that if they give an answer of three Well, where did you get three from? Because actually the misconceptions that come out of that answer if they can justify how they got there is a brilliant teaching point It's a brilliant discussion to have and even if somebody then in the classroom goes what and you go, okay So let's listen to what they've said Well, why do you think they got the answer three? You know, what could they have done? What, where maybe they've gone wrong? If you're so clever and you're, you know, you understand it. Well, what have they done wrong? Can we teach, can we talk about another example where that might happen? Sequencing is a brilliant topic to get an idea of how your students think. You know, just put random numbers on the board, which in your head are a sequence, and then just get them to guess the next term. Why is that the next term? Justify it to me. And they can come up with the most wild answers. But actually you go okay then let's go with that what would the next one be actually the next one was this so yours wasn't right but it was working for that sequence and it's that cycle that you talked about earlier it's that cycle of discovery of maths that i don't know if we get enough time to do in school

Ed: 43:00

i think i think you're absolutely right i think there's there's work we can do To, to develop cultures and, and for me, it, it, it predominantly resolves revolves around having activities where there's no right answer and what I want is your thoughts and your reasoning. So a really simple one could be, you know, you, you put an array of dots that, that have some kind of patterns in there, but nothing. Too clear. And you could interpret it in lots of different ways and just sort of say, right, count the dots for me. And inevitably they kind of go one by one the first time around. And then you just go, actually, I don't care how many there are. Like, let's forget that answer. Just tell me how you group them. And if they just group them in ones, that's fine. And then go, okay, I group them in this really different way to that and show them. Then you bring out another one so that they're kind of enabled to think about this, not as a linear one by one, but where's a pattern. I don't care what the pattern is, but where is our pattern or where is, you know, how did you see a square in here or see a triangle in here and everyone has a different thought, everyone has a different idea and. You know, you'll get some teachers who say, well, what's the point in that? Like, there's no maths, that's not going to help them with their exam. That's not going to help them develop their understanding of this, that, and the other. And, and you're right in some ways there. But what it is doing is helping to create a safe space where people are willing to share ideas and thoughts. And I think you have to purposefully design some tasks. to facilitate that. Otherwise, when you do get to those more meaty topics, there's just this, this back against the wall fear of I don't want to put myself out there with an idea here because it's going to be wrong. If you've already covered that ground and that work of, I don't care if it's wrong, like I'm wrong all the time. Like this is part of what we are here. You know, we have ideas, we think things through, we get to dead ends. It doesn't matter. That's all part of it. Like a journey I've struggled with on, on the podcast. Teaching PGCE students is you, you can talk to them about great models for explanations. You can talk to them about great questioning. You can talk to them about all these great benefits of some of the stuff that's intertwined with mastery and so forth. It's so easy for them to kill off those ideas because they try it in a class without the culture and nothing works. And they just go, Well, that was stupid. And then they just roll back to the way that they were taught or the way that they've got it embedded in the head of what a traditional teacher looks like, where if I just tell you stuff and you don't have to talk back to me, I can get through this lesson really easily. We've got to work on the culture thing.

Andy: 45:53

Yeah, you know, too often, too often, I've said this one before as well, year seven parents would come to me at parents evening and go, I don't really know what's happened this year. Little so and so was so good at maths last year, and they just seem to be struggling this year. And it's like, I mean, you know, you sit there and you want to say, well, they were probably good at answering 50 questions having just been taught how to answer that exact question. And, and that's great, you know, and, and that is a skill to have and we're going to need that skill. We're going to need that willingness to learn and practice and, and get that fluency. But I don't feel they've ever really been asked why before. And all of a sudden you put, you're turning that pressure on to an 11 year old and saying, well, why? You know, explain that. Tell me how that's going to work. Well, here's a different question. Can you answer that one? Because you've got all the skills that you need, but if it looks different, what are you going to do? You know, and that, again, that has to be part of that culture of students going, and I used to have above my board I used to make them write on their book desire to understand, math is problem solving, problem solving is thinking, have you thought? Because if you're going to put your hand up straight away and go, I'm stuck. I always used to be, you know, Okay, expand, you know, what have you tried? I haven't tried anything, I don't know how to do it. I'll come back to you when you've tried something, when you've thought about it, when you've discussed it with your partner, you know. Let's get that culture going, let's get that conversation going, that I can work with.

Ed: 47:10

Yeah, I would just add for balance there, like the flip side is quite common as well. Like students are used to talking about the maths and exploring ideas at primary, and then they go into secondary and the joy gets sapped out of it because they've got a teacher in year seven who is just like answers, answers, answers, answers. It can be any phase. Oh,

Andy: 47:32

absolutely. Absolutely. That's, that's season one in a, in a, in a nutshell where I played the role of the arrogant secondary school teacher played the role of. Yeah, I wish I'd, I wish I'd had this podcast to listen to when I was starting out teaching, believe me, but Hey, right. I am conscious of time. We've got some very, very busy people on this call. I'd like to just put you on the spot very one, one last time, Ed. So you're a teacher listening to this again. You know, what do you want them to take away? Just one thing you want them to take away from listening to us for this hour or so. And, and try or think about or develop or ponder over with a cup of tea.

Ed: 48:11

I think if you've never done this or never emphasized it much, like for me, the drug that was in teaching was trying to figure out how students were thinking about stuff and that never stops being interesting. So lean into that and think about how you can facilitate opportunities to, to understand how they're thinking about stuff. And one of the richest ways to do that is. Is through discourses through talking to them is through giving them time to think deeply about something and then bringing it back and learning from them about how their understanding is developing on on a concept or an idea. Be persistent with that and, and understand that it takes time to develop. You can't just go, Oh, that sounds like a nice idea. I'm going to try it on, on Tuesday. You're not going to come out of Tuesday going, perfect. I should do that all the time. Now you're going to come out of Tuesday going, that was really hard. And, and. There's things I need to do to make this work better, and the biggest thing you need for it to work well is time. Because new ideas take time to develop, for you to install, and they take time for the students to shift their understanding about what your classroom is about. But if you can get to a point where they're willing to share their thoughts and ideas, it is such an interesting environment for a teacher to be in, compared to like the, the, the old school, you know, who's got the answer, right? Brilliant. Aren't you good in my class? Like that to me is just not interesting. And if you're disinterested or you're getting bored of what you're doing you know, it's not fun anymore. The fun for me. You know, figure out how their brains are ticking.

Andy: 50:02

Sage on the stage versus guide on the side. It always, it always seems to come back to it. You know, teachers love being the person at the front. And you know, there's something in us that likes that, but it's getting yourself out of that mode. Talk to your students, listen to your students, encourage them to talk to each other, because that's where you pick up on little nuggets of all sorts of things that you can run with. Right, Ed, thank you so much for giving up this time for us. We will be recording another episode with Ed at our MEI conference in a little while. So that one will probably come out last in terms of this series. So look around for that. And that's going to talk a little bit more about what Ed's doing now and how that's Working over the next couple of years. So that's why if you're listening to this thinking, well, I haven't, they mentioned anything about Oak stuff. Well, that's coming in a, in a, in a different podcast. So yeah, that's coming soon. Alison, thank you as ever. For that, for those people who didn't realize I disappeared for about 15 minutes. I had complete massive technical issues So I'm looking forward to also hearing what was talked about in the podcast So thanks Alison. It's great to as always to

Alison: 51:08

Just give an update you're sunny the Sun has come out in dorking.

Andy: 51:15

Yeah, you see the South Always gets the sunshine at some point, it's still sunny here. There are clouds which are not just gray, so it's quite good. Ed, thanks. We'll talk to you soon. Alison, talk to you soon as well. Guys at home, thank you for listening. I hope you've learned something from this. It's another brilliantly insightful chat. Good luck. with people who just love maths and want to do the best with everybody with their maths. So enjoy. If you have any questions, please reach out to all three of us. I'm sure I'd be happy to answer any questions on Twitter as well. And I'll link to his wonderful book and his other publications and his website and stuff in the notes. And we will catch you again on the next episode of Digging for the Why. Goodbye.