Episode 155: Incredible textbook impact - Louise's Masters thesis

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.

Adam Gifford

Welcome to the School of School podcast.

Welcome back. It's another School of School podcast episode. I've got Robin and Andy. This is quite unique. You're in the same room. It doesn't happen off very often. Welcome both. How are you doing?

Andy Psarianos

We're very excited. We're like little school children here on the school trip. It's fun because we're in the same room. Never happens.

Adam Gifford

Yeah, so this is great stuff. Part of the excitement is probably proximity. Also, the fact that we've got Louise Hoskyns-Staples here. Louise, what an absolute pleasure it is to have you on the podcast. I've known you for a while now and you work as an independent maths consultant, but the list of what you've done, and you've worked, you've done a fair bit of work with Maths — No Problem!. You've evaluated things at a national level. I mean, I'm going to let you talk a little bit about some of the things that you've done. And so for listeners that haven't met you or haven't had the pleasure of meeting you, I wonder if you can just tell us a little bit about yourself and what you do.

Louise Hoskyns-Staples:

Hi. I began life as a teacher. Started off in primary and ended up moving into secondary by mistake. I did a little bit of supply and stayed. Ended up running the maths department, because I was the only one with any form of maths background in a secondary school. Everyone else was a non-specialist, and I was the primary teacher, so we were a great crew together.

After that, I headed off to the Department for Education and worked as a test researcher, so looking at assessment and came out from there and was working in Hackney and in schools that were starting to implement Maths — No Problem!. I went on a Maths — No Problem! five-day training course and met Ban Har who were running it, and Andy. And Andy and I started talking and that's when I ended up in my long involvement with Maths — No Problem!, because I think that was January 2014, so 10 years ago now.

Andy Psarianos

Yeah, mid-January 2014 in Merton. I remember it. I remember meeting you there, yeah.

Louise Hoskyns-Staples:

It was a great week actually. I think I'm often asked what's impacted my teaching and my thoughts about teaching most, and that week probably was it. Sitting down and just going, I've just been researching the mastery approach for two years in the Department for Education. I've looked at textbooks for ages, but sitting down, doing it, it being real, had more impact on me those five days than the last two years probably. And I was able to put that into practise across the three schools I was working in at the time, and then in my own school as a head. And since headship, I've worked as a teacher educator, both with pre-service teachers, trainees, and now I mostly work with teachers who are working in school who are qualified.

Adam Gifford

I could pick from a list of things, a lot of which you've not even mentioned yet, but I hope will unfold as we keep talking. One of the things that I'm really interested in is your master's thesis. There's a bit of a Maths — No Problem! overlap. There's your input with teachers that are training and the subject of a fraction. So I just wonder, perhaps you could start us off by just a brief summary of what your thesis was about.

Louise Hoskyns-Staples:

Having used Maths — No Problem!, having used it in my own school as head and worked with my math lead to implement it, I watched the impact it had on my own staff. And we had the full day's training, and then I worked very closely with my teachers. But what I was noticing is the more they read the textbooks, the better they understood maths. And so I was really interested in the impact of Maths — No Problem! as a teacher education tool, as opposed to just a pupil education tool. So when working in the university, they don't get enough maths. They really don't, primary generalist course, there's not enough maths.

And so I spoke to Andy at one point and said, I'd really like to do this as my MSC dissertation. So I had to do a big piece of research for that, and I worked with my, they were second year trainees. They were very, very generalist. They weren't necessarily fond of maths beforehand, but they'd got a good relationship with me from their first year. But my motivation was to see how much it would develop them as very, very beginning teachers.

The impact of the project was enormous on them, but we can come to that later. I wanted to know, I'd seen it in practising teachers and I was frustrated with how little we could do at the university, and I just wanted to know what working with the textbooks and essentially without me, me there in the background, but leaving them to it. So yeah, that's where it came from. That was the beginning. That was my real motivation and rationale.

Andy Psarianos

I'd like to jump in if that's okay, Adam. I mean, I'd just like to get right to the meat of it. I mean, what did you find?

Louise Hoskyns-Staples:

So I assumed that looking at the textbooks would help to develop their mathematics knowledge for teaching, and it did. I was hoping it would have some impact on their beliefs about how to teach maths and what maths actually is. What I wasn't expecting was the depth. We had six two-hour sessions together. So the first session was essentially me just going through, doing a bit of baseline with them, establishing what they knew of fractions, discovering that questions such as a third of three fifths were neigh on impossible for Bagwam. In fact, some of the others, two of the girls had written it in really tiny little bit in the corner of their piece of paper, but said they didn't know how to do it. They were very under confident.

And we also, in that baseline, they tried sequencing. So I asked them just to try and sequence where they thought fractions would be taught in the primary school from beginning to end. And although they came with most of the fractions knowledge that would need to be taught roughly, the sequencing was all over the place and there was little understanding.

Andy Psarianos

Now I want to just dig a bit deeper on this one third of three fifths, because-

Louise Hoskyns-Staples:

Oh, here we go.

Andy Psarianos

Here we go. Because Robin and I were talking about this before we started recording. Because look, when I saw that, I knew right away, I knew exactly why you picked one third of three fifths. It's a brilliant... I actually said to Robin, I said, I couldn't think of a more eloquent question to illustrate what I expect you were trying to illustrate, which was how if you actually spent the time to understand what one third of three fifths is actually asking you, how simple and how there is absolutely no calculation that needs to be done, because it's just a simple, logical question. But if you don't have any understanding, it's rather tedious coming to the solution. It is not too difficult, but it's tedious, right? Can you talk a bit about that?

Louise Hoskyns-Staples:

I chose it deliberately. I'd been involved in a session with practising teachers, most of whom were math leads in primary schools and watched them. They were using a perfectly valid method. They were using quite a modern method. They turned it into a nice grid and they'd cut it into fifths, and then they were finding thirds, and then they had fifteenths, and then they were simplifying. And I'm sitting there going, you need a little bar cut into fifths and three of them shaded and you need... And so having seen experienced teachers do that, I thought it was a nice question to use as a baseline. And yes, not a single one of my student... One of them said, oh, is that a multiplier or a divide? Which one do you turn it upside down with? So they were remembering all those bits of their learning, without having a clue what to do.

Andy Psarianos

Well, that's what Robin and I were talking about, and that's exactly what I suggested to Robin would most likely happen, is that you're presented with this problem one third of three fifths. The first thing you need to recognise, I suppose, is that the word of is a clue that it's a multiplication problem. But even that's pretty obscure really. When you're dealing with fractions, that's a multiplication problem because fractions always throws people off, because they think there's some kind of magic that where all the rules change with fractions, right? So they get confused and then they try to remember, okay, I probably did this in year, whatever it was. It depends what country you're in. But I did it in year X and is this the one where you have to flip the say, what's that called, find the reciprocal, or do you do some other kind of fancy trick and you're trying to remember what's the fancy trick to solve this problem that I apply? But you're not really conscious of what you're being asked. You're just trying to remember what the trick was, what's the procedure?

And the beauty of one third of three fifths is that if you just slightly modified the question, and you took the fraction in its essence and you said like, let's forget about fifths for a second and let's call them biscuits. What's one third of three biscuits? Well, you go, that's pretty obvious. That's one biscuit.

Louise Hoskyns-Staples:

That's one biscuit.

Andy Psarianos

Yeah. So what's one third of three fifths? Well, there's three of those things, and one of those things is called the fifth, not a biscuit. So it's one fifth. It's such an easy question to answer if you can just decode the language and find the logic and the understanding. You don't need to do any calculations. It's the simplest question, how many, and I'm sure that's why you chose it, but it's interesting to hear that the teachers were struggling with this. What point were you trying to make, I guess, with that?

Louise Hoskyns-Staples:

I wanted something that I could just establish partially their confidence with fractions, because if they were confident, they would've paused and looked and they wouldn't have lept into trying to dig up all the old procedures. They'd have stopped and thought about what it actually was. For a baseline for me, I was able to see what they could do, where they would go, and it gave me a good position of their own understanding of the subject matter that we were going to look at.

,Fractions have two jobs, they're a number or they operate on another number, and I think that's where people get upset and they get confused. I didn't want to give them anything too simple because I wouldn't have had anything to baseline, and I wanted to know where they were. So that was half my baseline and the other one, well, I suppose to me that was half my baseline. The sequencing of the fractions was another part of that, just their curriculum knowledge, but their raw subject knowledge, what could they do? I just wanted them... And they did what children do, they dive straight in without thinking. There's some maths to do, so I must do some maths. And they ceased to think about what they're being presented with. I have to say by the end of the six sessions, they weren't doing that anymore.

Andy Psarianos

Can you talk a little bit about what the sequencing fractions was?

Louise Hoskyns-Staples:

So I used an S-plan and I just asked them to start, what did they think would come at the beginning of school, and what do they think would come at the end of primary school, and to just put the key points on. And they recognised that they would have to do equivalent fractions somewhere. They'd have to multiply some fractions, add some fractions, divide some fractions, and they fairly haphazardly stuck them over the curriculum with actually some of the things that are easier right towards the end and some quite hard stuff, such as addition of fractions quite early on. I then asked them to think about a year group, and I had our early year students who trained to teach children from age three to seven, and our later year students who trained to teach children from age five to 11. And so the students from five to 11, I gave year four, fairly in the middle and quite a lot of fractions in year four. And the other two looked at years one and two together, because there's only a little bit of fractions in key stage one.

And I then asked them if they could give me a rough guidance on what they thought was in those year groups. And they were interesting, not terribly accurate, but to be fair, they were at the beginning of their second year, so they'd had very little time in school and very little time exploring the maths curriculum, so it was guesswork for them.

Adam Gifford

Louise, I wonder, alongside the subject knowledge, which was what you were looking at, did you get a sense of their attitude towards textbooks as a vehicle of helping them be a better teacher? Did they have an opinion at the beginning?

Louise Hoskyns-Staples:

At the beginning, they'd chosen to join the project. They were interested in working with me, and they were very open. There was no negativity towards textbooks from them. What was interesting is once they started delving into the textbooks, they bought their own copies. So for the time that they were working with me, they had access to the teacher hub through Maths — No Problem!, and they had access to the textbooks. All of them bought their own textbooks. One of them, I could do with finding his quote, it was just lovely. I asked them to rate their confidence, and so they rated how confident they felt at the start, not very. And at the end it was interesting, because this chap said, well, in some ways I'm much more confident, because I know a lot more now, but in some ways I'm much, much less confident, because I now know how much I don't know. And I thought that was really lovely.

But all of them said they wouldn't want to go and teach without the textbooks. They would be really uncomfortable in a school that didn't use them, because they were aware how much it supported their own pedagogic knowledge. And I think that, for me, was really interesting because they were able to recognise the benefit of having that support, and they could also recognise the quality of the support they were given. Their attitude to math teaching changed hugely from maths as being something that you basically took the empty beaker and you just tipped it in, to really thinking about children constructing their own knowledge and providing opportunities to do that. It was lovely. It really does make me smile thinking about how they were exploring stuff.

I was aiming not to teach them at all, because I didn't want to contaminate the study. They also didn't use them in schools, so I didn't want to do this study in their own teaching practise. Because when you're a beginning teacher, you're so busy worrying about how the children behave and all the other things that they've got to think about, I just wanted them to explore for their own subject and pedagogic knowledge. So we were completely in the university.

But I think it's session three or session four, they'd noticed the variation theory in the textbooks. They were seeing, oh, they'd be looking at a group of questions saying, look at this, they're just changing the denominator in these ones, or in this one, they'd just changed the numerator, but in this line, they're doing this. And as they were slowly pouring over each lesson, they were able to pull this out. So I did a quick session bearing in mind, it's quite complex theory, but a quick session on what that was, why it was there, how that if we use variation theory, we can enable the students to understand the mathematics better and to make more connections. I don't think that's something they'd have spotted or understood if they hadn't done the textbook study.

Adam Gifford

Yeah. And am I right in saying too, Louise, that at the time of that study, the landscape generally was one in which certainly in the UK, the idea of using textbooks wasn't a favourable one for a lot of teachers. So they were going into an environment as trainee teachers that effectively said, this richness that you're talking about, that was never part of the discussion. Would that be fair to say at the time that you're doing the study?

Louise Hoskyns-Staples:

I think it was mixed by this time. It was 2017, so there'd been some textbook funding. They were in some of our local schools, not many, but they were in schools where we were placing students. What I was noticing was how poorly the textbooks were used in the schools and how little the trainees were told. They had about five minutes with a teacher to say, this is the textbook, this is what you're doing now. The teachers might or might not have had the day's training with Maths — No Problem!, so there was almost nothing for our students. And so some of them were getting through... It was get through the textbook bit quickly, now I need to get stuff in the pupil book, and now I've got half a lesson left with nothing to do. As opposed to taking the time to explore and spending the time on the anchor task and really unpicking with the students.

And I'd observed one particular lesson that sticks in my mind, which was that format. The whole of the textbook was gone through in the first 15 minutes of the lesson. I just said nothing was learned. The children were then doing the practise with the student teacher running around the room trying to help them fill out the textbook, the pupil book. And then he got to the end of half an hour and said, oh, and now you better do this. And I sat down and thought, okay, I've seen this scheme used. That's probably the worst I'll ever see it. I hope that's the worst I'll ever see it. But I'd like our students have a better understanding. And that's part of the curriculum still at the university. They've got some of my old textbooks. Now we've got the updated series, they've got my old ones for the students to go through, which I thought was a nice use of them.

Robin Potter

Well, how fortunate for your group of teachers to be a part of your study and come away with feeling so much more confident knowing that they could use the textbooks?

Louise Hoskyns-Staples:

One of the really lovely stories, she wasn't particularly confident at all, but she went for an interview for her first teaching job a year after we'd done the study. And she sat in the school and they asked her some questions about maths, and she started talking and she talked about this project. She chose to do her own dissertation on maths in her final year, which prior to this she never would've done. And in her interview, they asked her if she'd support the math lead and if she'd consider being maths lead in her second year of teaching, but they realised they couldn't give her such a core subject. She just came back to university she said, "They offered me this." And really, really excited and really excited to be in that position and to have maths as a subject. And she said, one of the comments that came out was, I told my dad that I really like maths at university, and he fell off his chair laughing.

Andy Psarianos

That's funny.

Louise Hoskyns-Staples:

Yeah, there was a lot about this study that was just lovely, watching their attitude to mathematics change through that exploration and understanding.

Andy Psarianos

You said one thing that I thought was really insightful, and I'm paraphrasing here so I might get it wrong, but it was something along the lines that none of them entered into this believing that maths was a creative, that there was any creativity involved in mathematics.

Louise Hoskyns-Staples:

No. It's a bit sad, isn't it? I also did a wider survey as part of my dissertation just to see whether my students are unusual. So I stuck a survey out through some of the Facebook primary maths groups and on Twitter, one of the responses was, no, it's not very creative. There's not much glitter in maths is there? And as we worked through this, I think the main thing they realised was that maths was very few topics, but that they were all really interconnected. And once you understood those connections and how much creativity was needed when you were problem solving and how creative you can be when you're exploring an anchor task, and as a teacher with that. It was lovely. Yeah, really, really lovely.

Andy Psarianos

That's great. That's great to hear. Let me ask you an imaginary question. You decide to leave education and go into politics, Louise, and you're now Minister of Education.

Louise Hoskyns-Staples:

I would fund every single school to have Maths — No Problem!. I'd love to be able to do it. I'm working with some schools in difficulty as a school improvement advisor, and I see their maths and what they've got access to. I've also seen their budgets. There's no way they can afford to spend a lot of money, and yet we have a government that spends an awful lot of money on maths education. And I'd be really happy if that could be funding textbooks, because I think we'd have had massive impact, the impact of Maths — No Problem!, but that's another topic. But yeah, the impact of Maths — No Problem! in schools is huge. And it also has proved to be huge for my trainees. So yeah.

Robin Potter

You heard it here first, folks.

Andy Psarianos

Louise, thank you so much for joining us on this episode of this School of School podcast. So great to hear about your wonderful research.

Louise Hoskyns-Staples:

Thank you.

Adam Gifford

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