Episode 187: Bad maths attitudes, correcting the curriculum, and looking at the current state of primary maths education

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

Welcome back to another episode of The School of School podcast. We've got the two regulars, Andy and Robin. How are you both today?

Andy Psarianos

Hi.

Robin Potter

Hi, we're-

Andy Psarianos

Doing well.

Robin Potter

I am feeling good, thank you.

Andy Psarianos

Were you going to answer for me?

Adam Gifford

Excellent, excellent.

Andy Psarianos

When you say, Andy's doing well.

Robin Potter

It was tempting Andy, but then I didn't know if you were really doing well or not, so I left it. I left it.

Adam Gifford

Well alongside these two. It's with great pleasure that we have also got a specialty guest, Dr. Alison Borthwick. Alison, what a pleasure. The last time I saw you, I was very fortunate. I was in a panel discussion with you and Lynn McClure, and it was fantastic, and so it's a real treat having you back. How are you?

Alison Borthwick

Oh, well first of all, thank you very much for asking. And yeah, I'm very, very well, thank you. And I absolutely enjoyed attending and being part of the panel discussion with you and Lynn, who's a really lovely, very close colleague. So yeah, it's lovely to do this podcast with you all.

Adam Gifford

It's lovely having you back. And the last time that I introduced you, not on a podcast, but elsewhere, I had an incredibly long list of things that you are involved in. You are a lecturer and advisor, you conduct research, you've taught across, I think all phases of schooling, you chair associations you work with. Is there anything, can you introduce yourself better than I have, and just give us a little sense of you and how you manage all of these things?

Alison Borthwick

Well, yep, that's a very, very kind list and a very kind welcome. So, thank you.

Yeah, I think you're probably realising that my Achilles heel is that I haven't yet learnt to say no. I have to say I love life, I love work, I love everything that I do. So you're absolutely right. I started off as a teacher and I think I always, I still class myself as a teacher today. So when people say to me, "Oh, what do you do?" I say, "Oh, I'm a teacher." And they say, "Well, which school?" And then I have to backtrack and say, "Oh, well yeah, actually I started teaching in London, had an amazing school there. Then I moved to Norfolk, both in the UK, again, another amazing school."

But I have since become a mathematics advisor. So I've been a mathematics advisor for... I've now just learnt to say over 25 years. I've stopped counting. So I just say 25 plus years. And for 18 of those years, I was lucky enough to be a mathematics advisor with Norfolk local authority, predominantly earlier than primary, but did actually at one point kind of was with a colleague. There was two of us in the end looking after all 450 primary and secondary schools in Norfolk. But around about 2018, I decided to go freelance. That's quite a big step, but I've never looked back.

And so since then, yeah, my work portfolio, it's very international. So to date, I have worked in 26 countries, which I can give you some of the highlights about. That's a real privilege. I'm still a governor, so I've been a governor of the same infant school for 24 years. So I'm actually in there tomorrow doing a bit of teaching, supporting the head teacher, and probably doing a little bit of handing out of the coffee and the tea and the biscuits for parents workshop as well.

I am also an author, so I've authored quite a few books and I love research. I do still kind of, I love that reading. I love reflecting on things and thinking, well, I thought this five years ago or 10 years ago, but what do I think now? And I love the fact that education is such a fast moving commodity. Things are changing, they change with the times. That's why I love the international work because you go so and you think you know what you think it is that you know, or you think you've kind of got your beliefs and your values set, and then something comes along that makes you just think, oh, that has ambushed me. And I just love that. So I have worked with lots of organisations like Cambridge University Press and Assessment, and I've actually just written their earlier scheme of work, their math scheme of work with a lovely co-author.

I also work for companies like the Education Development Trust, and I did a really exciting piece of work for them, but actually for the UNICEF team in Jordan, that was brilliant. But I'm also, and this is the one that people always go, "Wow, amazing." I'm also the maths consultant for Peppa Pig. So people are like, "Whoa, Peppa Pig has a maths consultant?" Yes, she does. So I have been supporting the Penguin Team with their Learn with Peppa series. So that's me in a nutshell. But yes, basically teacher, advisor, lecturer, governor, probably should say parent of a 20-year-old... So that's me.

Robin Potter

Wow.

Adam Gifford

So you've got loads of time on your hands.

Robin Potter

That's a big nutshell for a nutshell. So I'm really curious.

Alison Borthwick

Not really, not really.

Robin Potter

I mean, obviously you have a hand in all kinds of places. It's so impressive and again, we're so excited to have you here. I don't know where you even want to begin because there's so many different avenues we could take with you. But one thing I just have to ask because I know a little bit about your background is, have you always been a maths expert?

Alison Borthwick

You've read a bio somewhere definitely. No, absolutely not. I was actually, I'm definitely that maths-phobic. So in primary school, I mean I have to say, I absolutely loved my primary school teacher. I was actually something called a jinfant, which was I attended a very, very small primary school and there was one infant class and one junior class. And I was six years old so I should have gone into the infant class but there were not enough chairs, there were not enough spaces. So I was actually an infant, but in the junior class, and I have the badge of being a jinfant, and I love that. I think one day I'll get a badge made saying jinfant right here.

However, my primary school experience was, it was a math scheme called SMP. Now it's kind of a love or a hate thing. For me it was, fill in the cards, get 25 answers correct, go and get them marked at the teacher's desk. If you get them right, you get onto the next card, the next colour. And I don't know whether I've made this up in my head, but I never reached the pink cards. And anybody that knows me, that knows I kind of, my training rooms are always, I've got lots of glitter and it's really colourful because I'm trying to promote maths. But I never made it into, whether it's the pink card, the blue card, the green card. But for me, I was already starting to learn that maths was not my friend.

And kind of that journey carried on at secondary school. Again, great teachers, but they just weren't doing it for me. So I was the type of child who would say, "Look, we've got a bunch of calculations and you're saying to multiply these numbers, whether they're integers or decimal, fractions, you're saying multiply them by 10, but you're saying quite often, particularly the integers, at a zero." And I'm like, what? That doesn't seem right. Why? And they were like, "No, no, no, no, just do it. You don't need to understand. You just need to do the calculations. And if you don't understand them, just do 20 a bit louder, a bit slower, etc, and you'll get there." And that didn't work for me.

So I built the maths wall, I realised, I believed that I was not good at maths, built the wall, and every year I believed it even more. So it was a bit of a shock when I became a teacher, everybody in my life said, "You're going to be a teacher." So I said, "No, I'm not. No, no, I'm not going to be a teacher. I'm going to be something else. I don't know what, but," just because I don't like conforming and being told what to do, and but I became a teacher. I did two degrees, I did a philosophy degree and also a teaching degree at Roehampton. Brilliant, brilliant degrees, got a great school, taught maths really badly. Well, I taught, my first class was year threes, so they are seven and eight year olds. And I spent a long time teaching them how to use a ruler because that's what I believed. That's what I thought was really important. Now I realise it was not.

But no, a couple of things happened. I went on an amazing CPD event, and so that's why I'm so passionate about teachers having training and getting out and talking to people and networking and just having that access to training, and that training event kind of basically turned my life around because I was there terrified, can I say? Absolutely terrified, worried that somebody would ask me the answer to a question. Like they would, we were adults in a room, and it was there that I learnt that actually, being good at maths is not about being quick. It's not about knowing your multiplication tables. It's not about being able to do simultaneous or quadratic equations. It's about resilience and it's about perseverance and it's about understanding. And it just changed my life. And so that moment on, I became a maths advocate.

So what drives me? Why don't I say no? It's because I'm so passionate about children and adults understanding and having a love of maths. That's what I really want.

Andy Psarianos

Also, it is a really interesting story. I don't think it's that uncommon. I don't think it's that uncommon to find out that people who end up in mathematics had kind of a troublesome beginning with it. At what point, was that one training session, was that really the catalyst for you? Was that really when you discovered that, hey, maths is not, it's not this sort of, all about remembering procedural things and stuff but it was actually about a lot more? Maybe we could even go as far as describing it as something creative. Was that one event the catalyst for you or was it a gradual thing that built up?

Alison Borthwick

No, it was really, that really was a catalyst. There is another one, which I'll mention in a second, but that absolutely was the catalyst, that training event. It was a two-day training event. I was really lucky to be able to go. The school funded it back in the day when schools had money and two-day training events existed. And I think it was that kind of parachuting into two days of immersive mathematics training with very lovely colleagues who actually, the people who are leading some of the workshops that I attended are now some of my closest work colleagues, and I've actually authored books with them. But it was just that revelation because nobody had actually ever told me that I wasn't good at maths, but nobody had told me either that I was. And I think that kind of understanding that if nobody actually takes you to one side and says, "You're doing really well here," or, "Well done," or, "I love how you were thinking about the maths," or just all of that. I had built up this belief that I just do maths.

And to be fair, I was always a writer. So my mum was a writer, so she wrote a diary every day, she wrote a book. I was always the kind of, you mentioned creative. I would always associate that creativity and innovation that I had coming out through the power of the pen, if you like. I did the philosophy degree. So I'd love just to be able to say, "Do you know what? Give me a side, give me an argument. It doesn't matter which one, I love talking about it and that kind of thing." So for me, the maths and the sciences, kind of the whole STEM area that I'm now so passionate about, just wasn't really on my radar. So I was definitely, I was an avid reader. I would write, and I was massively into sports as well. So I think it, you naturally go down one way, but the problem is that you then think that you're not kind of good at... Just because you don't pursue something, you then start to think and believe that you're no good at it.

And you mentioned that this idea that actually quite a lot of adults have this perception. You're absolutely. We actually have a bit of a national crisis, and it's been going on for about 20 years, where adults will very openly say, "I'm no good at maths." So I'll go out for a social event and people will say, "What do you do?" And by the time I've said, "Oh, teacher. Oh, not quite a teacher, but an advisor. Oh, a maths advisor," people will often just back away and then hands will go up in the air and they'll say, "Oh, you're not going to give me a test, are you?" I'm like, "Well, I wasn't planning to." Whereas you don't get that for English. You don't get that for people saying, "I can't read," but you openly get it for people saying, "I can't do maths."

And the problem is the politicians say it, the celebrities say it, the parents say it. And we have some really interesting research done by Joe Bowler, who's over in Stanford University in the US, the YouCubed website. And Joe has some amazing research that says that if parents and in particular mothers, but it doesn't have to be mothers, but if the mothers say to their children and in particular their daughters that they can't do maths or they don't like it, we've now got research that shows that those children go back a whole term. Not a week, not a month, a whole term, because that self-belief is self-fulfilling.

Adam Gifford

I suspect that the UK was no different to New Zealand when I was growing up, and that the world seemed to be divided into mathematicians and non mathematicians. Right? So it was genetics, it was just simply, you identify with this and it sticks. And even semi suggested there that parents can decide also that, no, no, it's okay. He's not a mathematician or she's not a mathematician or whatever. You are in a pretty, I consider, because I consider this true for me too, a very fortunate and almost privileged position to go into lots of schools, talk to lots of educators, be in education circles. Do you think that that attitude of that sort of really binary mathematician, non mathematician, do you think that that's changing from what you see in sort of education settings? And if so, how much has it changed? Because it was absolutely the societal norm when I was growing up that you just fell into one of those two camps into story.

Alison Borthwick

I think unfortunately it isn't changing. I think it's still a very binary, which, are you an arts person? Are you an English person? Are you good at languages? Are you good at maths? I think we are very good, particularly in this country but internationally as well, but we're very good at silo-ing the subjects. So we kind of have all of these different kind of buckets, whether it's primary or secondary. And we actually say to children, "What are you good at?" So we're almost kind of forcing them to choose a subject or a discipline or a skill. What we don't say is, "Tell me something that you're good at in every single subject." So I think unfortunately, I don't see the attitudinal position changing. I definitely don't see it changing at the moment with the adults.

I mean, back in the year 2000, we had a national campaign in the UK called Maths Counts or Every Child Count. I can't... It was a big kind of national campaign to really, really promote how important it is to be good at maths, and it didn't actually make a huge amount of difference because it's often a money thing. But people would say, "Oh, yeah, yeah, yeah, but I'm not. I mean, I know everybody else is, but I'm not good at maths." And then they go to prove it. The problem is that we are still attaching the wrong elements of what we believe it is, what it is to be good at maths. We're still attaching the wrong things to them.

So for example, you stop anybody in the street and you say, "What do you need to be good at to be good at maths?" And they'll say, "Well, you need to know your times tables." And I will say, "No, you don't." And they'll say, "Yes, you do," and then we'll have this backwards and forwards about would whether you need to be good at your times tables. Now there's a difference in knowing some of your, I would actually call them multiplication tables. There's a difference in knowing more multiplication tables than not, because it helps with that cognitive conflict when you're doing that cognitive overload when you're doing a problem. And you might just need to know seven multiplied by eight in order to do another step in order to do another step. Yes, of course it helps. So I don't think anybody is saying you shouldn't know them, but what we're saying is you don't need to know all of them really, really quickly, and we definitely don't need to test them. And that's kind of one of the things that we do in this country that's a fairly recent test.

So we are now damaging even more, I would say the attitudinal aspect because we've introduced another test for our year four children, which is eight to nine year olds. So now the year four curriculum is skewed, lots of teachers are worried about having their children to sit the test. Lots of parents are worried and children are into the rote learn. Can I pass? And the test is 25 questions, by the way, 25 questions. Anybody want to guess what the pass mark is? What do you need to pass to pass the multiplication tables check as it's called?

Andy Psarianos

I don't know. What is it, Alison?

Alison Borthwick

It's pass or fail, it's 25 out of 25. 6 seconds, you have to answer a question.

Adam Gifford

I mean, we talk about attitudes and we think, there's the public face of success as times tables. And that's the sort of summary document of six success of mathematics up to year four, considering you've been doing maths in a school setting for at that stage close to six years, and there's your signpost of, this is the public face of success.

Andy Psarianos

Yeah, it's just complete nonsense. We know that. I mean, this be, just as stupid of an idea to say, "Hey, you've got to spell 25 words correctly in six minutes in order to be good at reading, right? This is dumb. You don't need to convince us, Alison, that's for sure.

Alison Borthwick

I know. I know.

Andy Psarianos

And the amount of time that we spend talking about it, parents, educators, children worrying about it, kids coming home crying because they can't remember what seven times eight is, which was the case of my daughter, which is why I started Maths — No Problem!, by the way. It's just a ludicrous thing and there's so many more important things to try to get through.

But this whole mindset about mathematics, you had a catalyst moment when you went to a training session. I had a catalyst moment when I was doing a training session. It was a training session for Maths — No Problem!s, this was going back quite a number of years. It would've been probably about 2000, maybe 2013. It was before the new national curriculum came out in the UK anyway, and I had a very big-time mathematician come to one of my seminars, which is kind of intimidating because I didn't study mathematics at university. So I don't consider myself a "mathematician," as far as labels go, although I consider myself a mathematician. I think everybody's a mathematician, but anyway, that's another conversation. You could be quite intimidated when you have these people. So is the dean of a faculty of sciences at a major university in Canada comes to one of my seminars. I'm thinking, oh my goodness, I'm going to be put the shame here.

Now, what the interesting thing was, I had this revelation. First of all, this person didn't naturally know all the answers as I sort of expected he would, which was kind of, I don't know why I thought that I should have known better by then. But what was interesting about this character was that he was the most awkward one in the classroom because he wouldn't stop when you gave him a puzzle. So I remember giving him a puzzle with tangrams, and it was just an activity. It was a tangrams, it was really an introduction to area and a conservation of area using tangrams. He wouldn't stop. He just kept finding other things and he wanted to talk about them. And it's like, "Okay, yeah, well, we're done here. We've got to move on because we only got a whole day and we've got to finish all these things." And that was interesting.

And it's effectively the conclusion I came to is, is that really science, mathematics in particular, mathematics being the language of science, it's really about curiosity. It's about like, when you see something, how many questions can you ask and how many different ways can you solve a problem? And those are the types of things that mathematicians tend to gravitate towards. And it's not about tedious calculations and procedures and all. Yeah, those things are just conveniences, a column addition or place value, all those things. They make mathematics a lot simpler and they're great conventions and thank God we have them, but realistically, that's not what mathematics is, right? It's just about problem solving in the end.

Alison Borthwick

Oh, absolutely, absolutely. And I think kind of circling back to, have attitudes got any better or any worse? I think they've stayed the same and I think it's because there's just such a misunderstanding between what mathematics is. And quite rightly, as you say, if we kind of had that problem solving approach, that reasoning, that curiosity, that I have a few little mantras that I kind of, the one question, but five different ways, that type of thing. That's much better than five completely random questions. It's about pattern spotting, it's about kind of being excited about a problem, not knowing how to start a problem and thinking, well, I could do it like this, or I could do it like that. And actually I've got a whole bunch of equipment that I could be using. So do I need to use my bead string or should I look at some cuisenaire rods or what about double-sided counters? Or just that whole approach about, it's not just procedural. There's a real conceptual understanding there.

And also, it's okay to talk to your partner as well. In fact, I really want you to talk to somebody else. I want you to collaborate and I want you to communicate. And then it gets exciting. And if you can't do a problem, brilliant. I always say to teachers, "If your children can't do a problem, fantastic. It's a good job you came to school today," because if they can do them, a little bit redundant in the classroom. So there's a lot, I think, in terms of the mindset to change.

Andy Psarianos

So I suppose the danger is, if we fixate too much on things like this timetable test, is that not everyone will have the opportunity to have that catalyst at some stage in their life like you did. Where okay, you recognised, hey, you know what? Actually, all this, ideas, this mindset that I had about mathematics and what it was and my ability to do it successfully was all nonsense. And I'm actually very capable and this is actually a very interesting subject. Not everyone will have that opportunity to have those catalysts and just their mindset and their idea about mathematics and their ability to be good at it will be formed by these high pressure tests that we put in front of them where they fail because they can't remember seven times eight or whatever. And then that's like, okay, now you're a failure.

Robin Potter

I'm really curious then, when we're talking about the classroom and the emphasis on possibly the wrong things. If you were to give one tip and say, we need to make sure all teachers are doing this in the classroom to help their students, what would it be, as it pertains to maths?

Alison Borthwick

Yeah, I mean, the one tip is easy. I mean, it's problem solving. All roads lead to problem solving, and within that I would include reasoning, thinking and reasoning, and collaborating, and communicating. So for me, problem solving, it's quite a big kind of thing, it's not just solving a problem. But I think if we can get away from a lot of abstract calculations, whether it's number or geometry or statistics or whatever, and we can get excited. And for me, that excitement often comes through a problem solving question. That excitement and that love and that belief that we can do maths will come through.

But I have to say, it's not a quick fix because while we might, we can say over and over and over, "Don't worry about the multiplication tables check," we're not in school. And those teachers have a certain level of accountability. So I totally understand why the year four curriculum is now skewed to including much more focus on, do you know your multiplication tables up to 12 times 12? I understand that. We have Ofsted coming in and checking on schools. We have lots and lots and lots of tests.

I read something recently, so I can't qualify whether this is true or not, but I think we are. We have the most tests across the world than any other country. When you kind of think about our baseline and then you think about our phonics test, and then when you... I mean, we have just removed the test at year two, but people are worried about, well, what do we now do? We've now got our multiplication tables check, we've got our year six and so on and so on and so on. So you can't just change attitudes without changing curriculum, without changing assessment, without then changing the pedagogy. So I would love everybody to have a catalyst moment. And for me, that does start with beliefs, that even when I talk to teachers and educators about, what do you believe, they often believe some of the things that we're talking about, but they are not in a position to action them.

So I think part of our job is to help them to understand how they can action, how they can make the curriculum work for them, how they can make the assessments that they are accountable for work for them in a way. And I think that's part of my job, and that's what I do as a maths educator. I say, "Okay, well just, we won't think about the stats for now, but let's have a look at doing X, Y, and Z," and then, oh, actually you will get those results but it does take a leap of faith, and it does take a little bit of a risk. But then those schools do, they get there, they don't just get the results they want, they get better results. But it is a journey

Andy Psarianos

Also, it's so interesting to hear your story and your journey and the things that brought you to where you are now. We're going to wrap this episode up. I'm going to ask you one question. So through some tremendous turn of events, you find yourself in the position of being the Minister of Education.

Alison Borthwick

Oh, I call it Maths Prime Minister, but I'll go with that. Yeah. What would I do? Oh, gosh, that's... Well, I would definitely review assessment because we over assess. So I don't think we shouldn't assess. I'm not saying assessments are all bad, but I think we have too many. So let's strip out the ones that don't work, and actually, let's assess qualities that we've been talking about, like problem solving and reasoning. But you might have to get back to me on that one because tricky to do, but not impossible.

I think we definitely need, we're in need of a new curriculum in England. The curriculum, as you've already mentioned, was kind of born and published 2013, 2014. We need a new one. We are kind of now playing catch-up with the international market. We know that spatial reasoning, we know that data science is the future. So our curriculum early as primary and secondary needs to reflect that. So I would definitely be looking at the international research and kind of thinking about the skills that are needed for the next 20 years.

I would want to inject somehow, that level of enthusiasm and opportunity. And I do think that that training and CPD is one way to get there. And I know that school budgets are so tight at the moment. So the first thing that goes is the training opportunities. We've definitely seen a decline in the opportunities for training. And I don't necessarily mean just everybody coming out on a training course, there is multiple ways of accessing CPD. But I just think, getting people to think about that.

And I'm a great believer in, in order to be kind of that maths advocate, you also need to do maths. So we can talk about problems and we can talk about calculations and we can talk about whatever it is. But actually sitting next to a colleague and just having half an hour to actually do some maths and then to review, well, what did you do? And did you know where to start? No, I didn't, and I was a little bit worried to begin with. So I did a little doodle, and then I played around with some of the equipment and that made me feel a bit better. And then I tried this and that worked, and then... That kind of actually doing maths is a... How do we learn to ride a bike? We ride a bike. How do we learn to drive a car? We drive a car. How do we learn to be better at maths? Do we do maths? So in a nutshell, that's what I would do with my maths prime minister magic wand, but there we go. I can yet dream.

Andy Psarianos

Alison, thanks so much for joining us today.

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