Episode 89: The pros and cons of developing mathematical understanding in mixed age settings

Andy Psarianos

Hi, I'm Andy Psarianos.

Robin Potter

Hi, I'm Robin Potter.

Adam Gifford

Hi, I'm Adam Gifford.

Andy Psarianos

This is the School of School podcast. Welcome to the School of School podcast.

Adam Gifford

Are you an early years teacher struggling with lack of support for lesson planning? Foundations can help. Foundations is the new reception programme from Maths — No Problem! It's a complete reception package with workbook journals, picture books and online teacher guides all in one place. Visit mathsnoproblem.com today to learn more. Welcome back to another episode of the School of School podcast and once again it's welcome to the regular team and welcome to Jo Sawyer. Jo, it is such a pleasure having you back. Can you just remind the listeners of all the wonderful stuff that you do please?

Jo Sawyer

Yeah, of course. Thanks Adam. So I'm Jo Sawyer and I'm just absolutely in love with primary maths and I spend most of my time focusing on that. Two days a week. I'm a teacher, I've got a lovely year three class in a two form elementary primary school in North Yorkshire. And the other three days I'm a consultant for primary mathematics and I work with ITT trainees right the way up to experience teachers and leaders looking at how we can develop systems of mathematics and pedagogy of mathematics, particularly teaching for mastery within primary schools.

Andy Psarianos

Wow, you said that really quickly. That was pretty impressive.

Adam Gifford

Jo, one of the things that I've had the pleasure of visiting these schools and I know get asked it quite a bit, schools that have gotten mixed age classes, how do you deal with that? Often quite small schools with multiple year groups in a single class and a single teacher. Any top tips? It's tough, hey.

Jo Sawyer

it's really tough. I mean, I Think that there are some aspects of education that makes mixed age classes absolutely amazing, like relationships with teachers and things like that. I think you get to know the children inside out and back to front. I've worked in a mixed age class where I had year four, five, six for three years and I know the names of their goldfish and I knew when their granddad's birthday was. And so you do get relationships with children that are absolutely unique and built up over time and that is just such a privilege as a teacher to have impact on a child's learning for three years or two years or four years. In North Yorkshire and around the country there are hundreds of schools that have got mixed age classes, in some instances four year groups within one class. So there quite clearly are some challenges to overcome within that.

And there are some hurdles, things like if we take the maths curriculum where in United Kingdom the objectives are aimed at individual year groups, how do you teach a maths lesson or a morning or however it is you are going to do that so that every child accesses the education or the learning that pushes them forward without maths becoming the only thing you teach that day because you've also got the same challenges in English and how are you going to manage the curriculum in the foundation subjects, et cetera, et cetera. So there are some really unique selling points I think with mixed age classes, but there's definitely some challenges that need to be considered and I've worked with a range of schools with maths on how to look at this. And is it that you try and split the children into individual year groups? Certainly that is a strategy that will work but less so if you've got four year groups in your class.

So do you then split them into, for example, year three, four and year five, six And if you do that, do you over teach? Do you teach to the year four and the year six curriculum? And is that putting the younger children at a disadvantage or is it giving them aspirational targets? Are there elements of the maths that you then miss out? Do you look at time tabling in the day? There's some really interesting questions around what works well. I'd love to say I had an answer, if I did I would maybe be moving down that line and publishing some materials. I don't know that there is an answer and I don't know that there's an answer in one school that lasts over a period of time because the children in every cohort are different. And I think with a mixed age school you need to take each year and reflect each year on the structure of your classes and what the best approach to learning is for them. But that's my initial thoughts. I mean I don't know what your experience is of mixed age and what were your thoughts?

Adam Gifford

It was actually my very first year of teacher training I think or maybe second year, I went to probably one of the most gorgeous schools in the entire world in the province of Otago in New Zealand down the south island and it overlooked this beach down a long track. It was stunning, beautiful. And I reckon there must have been 20 children tops and I taught in this school and it was a real steep learning curve for me because it was hard because you're teaching across the year groups, I endorse what you're saying about the relationship, Jo and that people like the granddad would come down and do the gardening and someone else would pop in and drop off the cakes to the... It was a real community, there's no two ways about that. I think that one of the skills that I realised really quickly that I had to develop probably a lot faster than if I was teaching a single age group was understanding the journey of learning and the subjects that you're teaching.

So if I first started teaching addition to a year one child, I also needed to know how that was going to help a year four child and everything in between for that lesson because there were elements of the lesson that other children were listening to and we were trying to juggle in between. So I think that whilst it was very good for my teaching practise and understanding a subject because the scope of what you are teaching, I think the preparation time for it initially was far greater and you had to really concentrate on fewer number of lessons to look at what is that scope straight away. And that takes quite a bit of doing.

Jo Sawyer

And do you think as well, it's a different way of teaching? So I'm just thinking of some of my experience with mathematics, do you look more for an inquiry based approach where you are looking more at what the context of the maths and then you are providing different questions at different levels but you are teaching the same mathematical idea to all learners, which is perhaps very different to the way you would approach planning and teaching and delivery in a single age group class.

Andy Psarianos

The challenge here is really understanding that the issue lies in the fact that the system isn't developed for multi-level class teaching in the sense that the structure is made in a way that there's expected outcomes at each group. That it separates the content in such a way that is really challenging to say, well in year one they're at this level, year two they're at this level, year three they're at this level and especially in the young ages because the gaps between year one and year two and year three are massive really. It's more of a problem there, I think it is than it is later on. Although people intuitively might think the other way around. The flip side of that is that there is some consistency from year group to year group. So it is possible to line the curriculum up and say, okay, well we're teaching, I don't know, whatever it is, multiplication, let's say, small children, these guys are operating at this level, these guys are operating at this level, these guys are operating at that level.

But we can modify the content in such a way that we're going to use what Jo Bowler would call a high ceiling, low floor, low floor, high ceiling activity, however she says it, and introduce that concept and say well I'm going to teach a concept but I'll vary the complexity of the numbers let's say for the appropriate age group. And you can apply that in calculation lessons, you can apply it in measurement lessons, if you're doing mass, these guys are measuring in increments of 10, these guys are measuring in millimetres. You could see how you could orchestrate that in a classroom. But the problem is, what Adam said, it's a tremendous amount of lesson planning that's involved in doing that successfully, it's really hard. You need experience really highly proficient, efficient and effective professionals doing that kind of stuff. It's not easy. Throwing a newly qualified teacher in that situation is like, you want to get somebody to quit the career.

That's a perfect way to leave the profession. That's a perfect way to do it because its really hard to do well but it is possible. But we face this problem largely because of the way the education system is structured. That's how the curriculum works and that's what everybody goes back to the curriculum Ofqual, Ofsted, whoever, they all refer back to their curriculum and the expectations of the curriculum and therefore that's why we have this problem. Because if you think about it from the education of that child and what their experience is, you could make an argument and some people already have that, that's a better environment to learn in, that mixed age group than it is to just bunch everyone up conveniently by the same age because you open up all kinds of experiences and situations that actually are quite useful skills because it is more reflective of real life.

Not everybody's at the same... How often in any stage in your career or life have you been grouped with people who are of equal attainment as you? It never happens. Think of your work life, Jo you're a teacher, you've been teaching for some time, you're an expert in what you do, you're renowned, people know you and it's taking you a long time to get to where you are. Same with you Adam. You guys are at the pinnacle of your careers. People look up to people like you and think, "Wow, they're so wise and know so much." And you're working with people who are just coming out of university who may or may not have had a good experience learning what they need and they're certainly not anywhere near as prepared as you guys are to be left alone in an environment like that.

But if you look at the school that you work at, you work with people at all different kinds of levels and you got to make that work somehow. And that's a reality of life. And if your classroom is set up that, that will give you skills. How do I negotiate this situation where some people know a lot more than me and maybe some people know a lot less than me or one year I know more and the next year I jump into this class and then all of a sudden I'm the one who knows the least amount. That's quite a shocking thing. It's like moving from primary to secondary for example, you're the expert, you're at the pinnacle of school and now all of a sudden you're a junior again. And those kinds of things, they're important life skills. So I don't know. But I will say one thing.

First of all, I know nothing about this, I am not in any way should anybody listen to anything that I say and use it as advice because that would be the wrong thing to do. But what I would say is I spent two years in a mixed age classroom as a student and when we said we're going to talk about this, I said, "Well what's my experience with this?" And I said, "That's the only experience I had." You know what? I mean I knew that I was in a mixed age classroom, but it never ever was in any kind of way an obstacle to my classroom experience or I was aware of it but I never thought about it. It was never in any kind... So clearly I had great teachers. So do we make too much of a thing out of it? Have we just set up the system so that it's just too difficult for it to succeed, is that really the problem? Maybe the problem isn't mixed classrooms but the fact that the system that we set up doesn't accommodate for mixed classrooms very well.

Jo Sawyer

Yeah, I think you make a really good point there Andy. Depending on what aspect of the curriculum you looking at. If say we were looking at history and you are talking about teaching history in a chronological order and you've got year three, four, five, six in your class, how would you go about that? I mean that is a challenge, isn't it? Potentially an impossible one. And yeah, that is based on the curriculum that creates that challenge. If you've got flexibility to be looking at you can do it in an appropriate order for your learners, then that opens up opportunities to make the curriculum your own. And I do know that these challenges exist in the schools and there are elements going back to the maths curriculum where things are very specific to a year group or an order of teaching. If you are learning multiplication tables for example, there tends to be a set order in which you would teach that and on a rolling programme that might not work.

So yeah, I think it possibly does come back to the curriculum, but what I do think it does for teachers, if they've got a mixed sage class, I think it gives them a phenomenal knowledge of the national curriculum because in order for them to adapt to teach a mixed age class well and teachers do an incredible job of doing this, I mean honestly I've seen the most phenomenal lessons. But for them to do this well they have to know the national curriculum, they have to know the expectations and how looking at individual children they can stretch and support for their individual age even within that mixed age class. And for me, when teachers have got that understanding and the idea of that progression of learning, it works at its absolute best.

Andy Psarianos

So just like if you look at multiplication as an example, one could envision how you could turn a lesson, like a lesson on sharing for example, grouping, but let's just use sharing as an example because it's conceptually easier to understand. You could say, "Okay children today we're going to share, I don't know, whatever it is, apples." And then you've got, okay, and then you say in this year group here there's three children, I'm going to give them 12 apples that's going to have one outcome. This table, there's three children, I'm going to give them 21 apples. There's a different outcome. So the lesson is the same, but you're just slightly modifying that lesson for an age appropriateness kind of thing. That that's possible for a teacher to do. But just think of an amount of planning that has half of them in order to orchestrate this on a day to day basis is just phenomenal.

Adam Gifford

But I think that's the thing that way you have to spend your time, Andy, is that because the curriculum will tell us do this times table at this year group, but what it doesn't tell us is remind us what the key idea of multiplication is, equal size groups and the key idea around these things. And that's what the challenge is, is that when we're working that the reason why you've been able to give that example is because you understand the idea of multiplication, you're not just teaching the seven times tables, you understand the idea that underpins it and so then you can vary it to give it that breadth. And I think that, that's something that if people, you'd like to think if you go into a school that has mixed ages is that, that's something that's really highlighted those early concepts, they don't change, it's just the content within them or the context within them. And that I think is, it's not that surface level on the curriculum and I think that's something they need to-

Andy Psarianos

But the point, I think the important thing though is that the skill of the teacher is so critical. So I can easily come up with that construct in my mind. But you got to remember, I've been now for decades been doing absolutely nothing else but working with the best people in the world to create mathematical content and train, I don't know, how many teachers have we trained? Tens of thousands of teachers and yada yada and worked with curriculums from around the... I've done nothing but this for decades now. This is all that I do.

Now go back to 1996 when I was teaching and I was teaching at a different level, at different topics, so on and so forth. And I knew how to read a curriculum then, if you gave me the curriculum and said this is the outcome and here's your next age class, would I be able to construct anything at that stage that would resemble? No, I wouldn't, there's no way. I would be totally clueless. I wouldn't know what to do. I'd be scrambling around the classroom, running around like a chicken with my head cut off trying to accommodate the specific needs of every particular individual student and probably have a nervous breakdown. It's really hard.

Adam Gifford

On the plus side, I know we have to wrap it up, but on the plus side is this, often in those classrooms there are fewer children at each year group, so you are able to attend more to them. I think the other thing is, is that you get a chance to help children out. They don't move on in the same way and usually just in a physical space you are able to support children at different moments, whereas you may not have that same opportunity to do that where you haven't once your children have left. So I think it's understanding it. Don't be put off going into them. You learn a whole lot and it's a totally different experience. But yeah, I think it's just being prepared to keep on working at those concepts that underpin it and you've got that time to work with those children.

Jo Sawyer

I think there's a gap in the market there as well really because if we're looking at conceptual understanding of a mathematical concept, Andy, which is what you were using as your sharing example. If there isn't that bank of what are the concepts and where are the low floor, high ceiling activities within that to explore within CPD for teachers in mixed age classes. I don't know that, that exists at the moment. So that would be an interesting PhD for somebody maybe, not me, but somebody in how to go about that inquiry based learning with mixed age and to get the best out of children and to give the best support for the teachers.

Adam Gifford

Hey, I'll tell you, just get some Maths — No Problem! books. And the other thing you can do, I know it's a shameless plug, but it's true because those problems, if you start with a good problem, one of the easiest things that you can do in that context is as long as it contextually works, take the numbers out, take some numbers out and see what happens. Let the children replace them and all that sort of stuff. Just make sure if you're doing additional something, don't use people on a bus if you're adding like 8,000 and lots and lots of people cause they don't fit on a bus. But in all seriousness, if you've got a well written problem and you have a look at the numbers, it doesn't work all the time. But it's amazing. I've seen a lot of people write loads of different problems when actually the numbers within the problems might be something that you can just have a look at. But it have a wee look at it.

Andy Psarianos

Adam, we should look into this. We have loads of schools, we should know more about this, really. We have loads of schools who are using Maths — No Problem! in multi-age classes. We should go find out and talk to some of those really super experienced people and ask them how they're making it work. And we should come back and talk about this some more. Yeah.

Adam Gifford

Yep.

Andy Psarianos

Joe. Thanks so much for joining us again. You bring all these really amazing things for us to talk about and these are some of my favourite podcasts recording for sure is when you're here. So thanks for joining us, yeah.

Jo Sawyer

A pleasure. I've enjoyed it.

Adam Gifford

Come back soon, Jo.

Jo Sawyer

Thank you.

Andy Psarianos

Thank you for joining us on the School of School podcast.