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Here’s a puzzle for you. The UK’s capital city is one of the world’s most important financial hubs, and yet many Britons find their own money matters are blighted by poor maths.

I can’t tell you the amount of times I get the, well, I couldn’t do maths at school.

What’s gone wrong with maths in our education system?

Sometimes a bad experience in secondary school, or sometimes just a fear of maths.

We are teaching mathematics at the moment as though everything outside the classroom walls is the same as it ever was.

Who is this affecting?

If you don’t get level 4 in maths and English, you’re written off.

And what can be done about it?

The UK population has shockingly bad number skills, compared to other countries. And there are two sides to this equation. A significant proportion of kids leave school each year without a good maths qualification. And more than half of working-age adults are estimated to have low basic numeracy.

5 is going to be B. Good.

Huge efforts have gone into improving state schools in England since the 1990s, with massive progress in primary schools. But an OECD report showed that in 2011 young people in the UK had even worse numeracy than older generations. Maths skills are patchy and unequal, and with an exam system that creates hidden losers. A third of our 15- and 16-year-olds are destined to miss out on a pass grade at GCSE maths, locking them out of later opportunities at college and at work.

So I won’t sit back and allow this cultural sense that it’s OK to be bad at maths, to put our children at a disadvantage.

And the prime minister wants everyone to learn some maths up to the new school leaving age of 18.

So put simply, without a solid foundation in maths our children risk being left behind.

So it turns out that there’s actually already a debate raging about whether the way that maths is taught and examined in schools is actually hindering gaining competent number skills. This really concerns me. I’ve written about education policy for a number of years. I now have my own kids in the state school system. I really want to get out and find out what creative ideas are bubbling away as to how we can tackle the nation’s lack of number skills.

Hello, everyone. Welcome to the community garden here at Stockwell Centre at Morley College…

Let’s start off. – bear with us – at a gardening class on a sunny weekday morning at Morley College in south London.

And in particular, this is our 1-foot garden. So you can see every square has been divided up. And we’re going to be thinking about how we can really get the most out of the garden. So it’s a really exciting way of putting maths into practise.

We’re talking about spacing out onion seedlings. But it’s a course funded by the government to tackle the adult part of the numeracy crisis. In this case, we could call it maths by stealth.

If each of these is a ruler apart, and then you have a right angle, you know that that’s a straight line, then you can map out your garden.

Those who didn’t master maths or even basic numeracy skills at school come to community colleges like this to try again and see if they can get over the vital hurdle of a maths qualification. But first, these cunning lecturers, like Gerald Jones and Sola Sobowale, are tempting them in and hoping to build up an appetite to get back into formal learning.

So you’ve found a way of hiding the maths, effectively.

People say, I hate maths. So the government Multiply programme – this is a national multi-million-pound programme – is designed to try to help people overcome that fear. And we’ve taken that to mean teaching maths so that it doesn’t feel like you’re back in school. It doesn’t trigger those big strong emotions that people have around maths.

So you can, in fact, embed some maths in almost anything.

Yeah, yeah, yeah. We’ve got Spanish with maths. If you’re learning art or jewellery or ceramics, every course that we could think of, because it’s very hard to live your life from morning to dusk without using maths – time, money, travel. Everything is maths.

You, presumably, would want to tempt people to actually getting a maths qualification of some sort.

Definitely. The maths that can be weaved in can go from really very basic, where you’re just counting and looking at squares and measuring, and you could go up to really complex, like doing trigonometry. When you look at the big vegetable patch, you can actually look at angles. You can look at hypotenuse. Those concepts that you would think are abstract, you can actually help students to see how all those things relate to one another, which aids understanding.

The gardening group offered a taste of how lack of functional maths can be imaginatively remedied for those adults stuck with a numeracy deficit. But our second stop is a school where the pupils mostly sail through. There’s no hiding the math lessons here at Shoreditch Park Academy, where the GCSE pass rate was 80 per cent this year…

10 questions…

…way above the average for England and Wales.

This is an angle, this is an angle…

It’s a much more traditional set-up for learning trigonometry… and with no lettuces in sight.

Two sides and two angles, sine rule; three sides and one angle, cosine rule.

That was insane. It was like being 15 again. Clearly, for some people it’s conceptual, and there’s a real dopamine hit from getting the right answer. But for everyone else, you know, that world of equations is a sort of rite of passage when you’re 15, 16. You never come back to it again.

The GCSE trigonometry class was taken by head of maths, Sam Mitchell, who we managed to catch as he dashed in and out of class.

So in the past, when I’ve interviewed educationalists about the UK and our maths problem, they’ve said the really verbal culture – parents play word games with their kids. You go to Asia, everybody’s playing numbers games.

I can’t tell you the amount of times I get the, well, I couldn’t do maths at school, or maths was never for me, when I’m on the phone to a parent. And that’s a really, kind of, painful phrase to hear. They think that now, jobs require Excel or a calculator or those things, so therefore, they don’t think that numeracy is important beneath that. But obviously, it is.

With over 50 per cent of the pupils on free school meals, which means they’re in the most low-income households, the staff here know they are giving these kids a leg up, a passport onto better things, even though the maths exams have become tougher in recent years.

Sam, do you think that maths at school has become too abstract?

I definitely think, for your typical students the abstract concepts that they’re learning about is quite difficult to put into real-life contexts for us to get the engagement that we would want from students, whether that’s talking about your classic trigonometry, as you saw me teach earlier, or whether that is even, kind of, a graph itself. We don’t see enough of those in context.

When you look at the idea of risk and reward, it doesn’t always work. I’m sure that we’ve all seen that in the news – Bitcoin, NFTs.

To get that real-world relevance, Sam was also giving his GCSE group a financial literacy lesson. It’s a pilot scheme with materials designed by the charity Flic, and being used in PSHE classes – that’s Personal Social Health and Economic Education.

It’s a national curriculum requirement, though not tested and often neglected. And full disclosure, this project is backed by the FT. I found the class pretty switched-on, interested in the idea of risk and return, and even in crypto.

Post-pandemic, and look what that did to the stock market.

It was a very vocal group, I thought. Are they that vocal in their maths classes, I wonder?

It depends on the time of day sometimes. Um, no, probably not. It’s that real-life context, isn’t it?

Yeah.

That is particularly for students in year 11 now, on the verge of going out into the real world. They have this idea that financial literacy is a really important part of being independent, and they all quite want to make money.

So teachers are under pressure to cram in this real-world maths, alongside the more traditional topics in the GCSE maths exam, and with overloaded timetables. This school is unusual in getting so many to respond to both. Since the pandemic the UK’s achievement gap in maths between deprived kids and their well-off peers has become even wider. A decade’s progress in narrowing it has been lost, according to the Education Policy Institute.

If we’re not careful that’s going to make the national problem of lack of numeracy even tougher to tackle in the years to come. Maybe one of the ways of doing that, as they’ve suggested here, is to change this GCSE curriculum, which is very academic and is, essentially, a straight line from Pythagoras through me sitting my O-Levels decades ago, to these kids here sitting GCSEs.

You’re all familiar with the three…

The way our exam system is structured means around third of every year group sitting the maths GCSE is destined to fail. Since 2015, if they don’t get that vital grade 4, as a pass is now known, they have worse options for advanced courses, both academic and vocational. Enrolled at FE colleges, they have to resit the maths exam again and again and again.

Headteachers’ organisations, unhappy about all this demoralisation, have called these kids ‘the forgotten third.’ They want a different set of basic maths and English qualifications that would give many more a passport into more learning or a good job. At Morley, meanwhile, they are busy picking up the pieces.

We have students who have failed at maths in secondary school, or because of, sometimes, bad experience, and also because, yes, the fear of maths. And sometimes concepts need to be broken down into little, little steps just to overcome those barriers.

This may seem strange, but those barriers are now blocking so many young people, that even the man who introduced the GCSE exams…

Circle the solid that has seven vertices.

…looks at those endless resits and wants a radical overhaul.

What’s the game? What are you learning here? You tell me…

As education secretary in the late 1980s, it was Conservative politician Kenneth Baker who designed the current system.

The reforms which I’ll be introducing over the next 12 months will improve the quality of education for all our children throughout the country.

She finds a letter…

At the time, most 15- or 16-year-olds took O-Levels, with the less able pupils entered for CSEs. But the all-ability GCSE maths Lord Baker introduced should now, he argues, be retired. When I arrived, he was deep in a quadratic equation. As someone with the mind of a puzzler, he finds it diverting, but not necessarily useful.

I have to say that having left school when I was 18, I have never used a quadratic equation in my life, nor have I used trigonometry.

What do you think about this idea that the UK has, as Rishi Sunak put it, an anti-maths mindset?

Reading is the important quality that must come first before everything. And that has dominated the whole of the Department of Education since 1870. And the curriculum that we’re now following in schools, in GCSE, was announced in 1904 – one English, one maths, three sciences, foreign language, and history or geography. And numeracy does not materialise so importantly in that, quite frankly.

Now that the age for leaving education or training has been raised to 18, Baker is worried that pushing everyone through the same old academic hoops at GCSE condemns too many to downgrade their ambitions.

There’s been a very strong emphasis, in recent secretaries of state, on this idea of reintroducing rigour and making the maths GCSE very much more an academic GCSE.

There should be much more functional maths from 11 to 16. You don’t have to worry about the master mathematicians. They are some of the brightest kids in the country. You have to worry about the kids below them.

Why not shake up the exams? He says. Maybe with two subjects – academic and core or functional maths, a bit like English language and literature, which separate the real-life and basic skills from the other knowledge.

In the GCSE exams each year if you don’t get level 4 in maths and English, you’re written off. So something has gone wrong at a very early stage. People have been turned to be turned against figures and maths, because it’s all a bit too complicated for them.

He wants core maths taught in all schools.

Core maths must deal with basic calculations – addition, multiplication, and division, fractions and decimals, and percentages and margins. Because it doesn’t matter whether you sell buns or whether you sell British planes. You’ve got to understand the difference between the gross profit percentage and the net profit. Otherwise, you won’t be in business.

Talking to Lord Baker, who’s really the main architect of the assessment exam system that we’ve inherited in English schools, and to hear the extent of his doubts as to whether GCSEs are really fit for purpose, whether maths GCSE, or indeed, maths A-Level, can help tackle the numeracy crisis in the UK – that’s quite a wake-up call.

So how much damage does poor numeracy do to people once they are out in the adult world of jobs and household budgets? I caught up with Sacha Romanovitch at the House of Commons as she petitioned those with the power to change the system. Sasha heads up Fair4All Finance, a UK charity helping the financially vulnerable and excluded. A former accountant, she once ran Grant Thornton and studied maths all the way to 18, as Rishi Sunak wants everyone to do in some form.

I still, every now and then, do use solving a quadratic equation to work something out. But actually, I think this is where it comes to the sort of numeracy versus maths. The comfort of being able to scan a list of numbers and without actually adding them up, knowing broadly, yeah, that adds up, that makes sense.

She agrees numeracy and financial education are important, but says it’s of limited help lecturing people already failed by the system that maths, however it’s taught, might save them.

There are about seventeen and half million people in the UK who are in financially vulnerable circumstances. When you look at the root causes behind that, numeracy is only one part of the problem. If someone’s in a deficit-income situation, learning to budget better isn’t going to magic up that they’re going to be able to have more money. So financial capability and numeracy – absolutely important, but one of a multitude of causes of low financial resilience.

We know that a lot of kids already fall by the wayside with maths as it’s taught in schools. Is this the right approach?

So some people say they’re frightened of numbers and scared of maths. But I think that if we can approach it from, how do we make numbers meaningful to people and you maybe present things in a pie chart, anyone can make sense of that. Because most people have argued at some point with someone around whether they’re getting the fair share of the pie.

Once we have that money into our account, what are we going to do with it?

What does someone who knows classroom maths, inside out, make of this debate? Rebecca Roden tutors GCSE maths candidates and taught the subject at an all-ability secondary school. She now also works for the FT-backed charity, Flic, improving financial literacy for all age groups.

There’s a lot to navigate, even with a payslip, isn’t there? And I think you’ll find lots of young people get the shock of their lives when the payslip comes through.

With the rise of gig work, she sees exam candidates scared of numbers, and coming out of school unable to deal with today’s complicated world of navigating irregular income, budgeting for hard times, or handling a pension outside of regular employment.

So if somebody gets that pass in maths GCSE, which is so important for later life, is that a guarantee that they can cope with numbers in everyday life?

I’m not sure it always the case. I think we could have somebody that passes with knowing their indices, like 5 to the power of 3, but not being able to apply a percentage change to a really useful question or being able to sufficiently analyse a core bit of data.

Rebecca worries that maths at GCSE isn’t quite working, whether you’re in the group taking the so-called higher papers, or instead, the foundation papers for the less able, where you can only ever hope for a pass.

I don’t think we’re necessarily meeting the needs of either of those groups. So the foundation… a stretch to have to apply lots and lots of different content, which could be extremely overwhelming, especially if they don’t have their basic number skills. And then, for the higher set, I’m a fan actually, of the inclusion of more problem-solving questions. But we’re still finding students struggling through, and then also not being fully equipped with functional maths.

And if you can’t get over the hurdle, it prolongs the agony.

I think it’s deeply damaging, what we’re doing to some of those students, potentially failing on those papers, and then having to resit and resit and resit. That’s a disaster, really, because some of the biggest decisions we make are around numbers, whether it’s taking out a loan or putting your money to a savings account. So there’s something’s broken in the system that needs to be addressed.

Talking to Rebecca makes me think that if teachers themselves feel they’re not able to prepare young people, maybe the prime minister should actually look at the current compulsory maths curriculum, rather than asking for more maths further on.

I wanted to see what somebody who delights in maths can bring to the discussion. Alf Coles, a professor at Bristol University, is an expert on how maths is taught and recently co-authored, I Can’t Do Maths: Why Children Say It and How to Make a Difference.

He definitely sees the beauty of maths, not just a set of useful skills, and worries about shutting people out, worsening the UK’s educational divide. You might describe his views as a counterpoint to the campaign to strip out or hive off those abstract elements.

If you get into doing mathematics then you read a script. And if imagine it like a music script, you read it, and you can hear the music. But the way it’s often taught and presented, it’s as though all the game is, is just trying to analyse this bit of writing, and there’s no sense that there’s something else it’s pointing to.

So the way you talk about maths is a source of joy.

Yes.

But do you understand why so many people talk about learning maths as something that sort of scarred them slightly?

No, I do. I mean, it’s been talked about as cognitive bullying, what happens in some mathematics classrooms, where children are forced to revisit sites of failure and learn, sort of, fractions again and again and again. And so we end up teaching people the same content for, maybe, five years at secondary school. And then, if they haven’t succeeded, then teach them again in these classes. So I don’t think it’s any surprise that people are then completely turned off.

Alf explains that schools look at the exam requirements, and then work back from them, fitting their classroom teaching to how their pupils and the school will be measured.

So I spent 15 years teaching in secondary schools. And I think teachers… I think they’re an incredible asset in this country. And teachers are incredibly pragmatic. But I think there are these sort of ideas that cross society, really, that influence then the curriculum and influence our assessment, and then lead to things being taught in a way that doesn’t connect with people.

There’s a lot of people who would like to see a separate numeracy qualification. What do you think of that idea?

Well, yeah. I mean, I would be worried that it would divide along class and socio-economic lines. And I think if you look at other countries – China, for example – almost everybody in China achieves a very high level in mathematics. So I just don’t think it’s the case that there’s a proportion of the population who will just never get maths and shouldn’t be taught it. To me, it seems like it’s one of children’s rights to be offered some of these cultural achievements in mathematics.

In the UK, which is plagued with lifelong disadvantage for the education have-nots, he has a warning. There could be unintended consequences of introducing two different pathways for maths.

For me, the danger is that we give up on students early in their school career. We’ve got evidence of children who have not attained very highly in maths, being able to be successful on Pythagoras and trigonometry and things that are way ahead of what would have been expected of them in the curriculum. And I would be really sad if what went along with the sort of more functional qualification was the closing-down of possibilities.

Some critics say the UK’s problem is a lack of basic skills in maths, but Alf and other experts say schools should teach better stats literacy. That’s an essential skill in today’s world.

If you look at the skills that we need, it’s things like, how do you look at a graph of Covid infections and make sense of what’s likely to happen? So if we’re thinking about the kind of skills you need to function as an adult, I would see it much more as around data literacy and statistical literacy. Political debate is full, now, of statistics being bombarded at people. So how are you able to make sense of those in a kind of critical way?

It’s been really good to come here to Bristol and talk to Alf, because really he’s buzzing with enthusiasm for the idea that abstract maths, academic maths, actually gives young people an enormous amount of cultural capital as well as intellectual stimulation. That should be for everyone.

Numbers are everywhere. And they’re something all of us use every day, without even thinking about it.

So making this film, we have really uncovered what I would call a degree of panic about the challenge of improving the nation’s numeracy.

We simply cannot allow poor numeracy to cost our economy tens of billions a year.

But there is an emerging consensus, and that’s about overhauling the way that maths and numbers are taught and examined.

It feels that maths is so important, that we can’t let people drift away from it.

But the problem is there is a real divide over whether you should hive off, as a separate set of qualifications, functional numeracy, and also, how do we fit in financial literacy in all these life skills to do with numbers that seem to be lacking in the current examination system?

Core maths, which strips out the more academic and abstract content, is already a growing option at A-Level. It has elements of finance and of the sort of statistical skills that both Alf and Sacha would like to see. But for 16-year-olds, outside Scotland and Wales that is, numeracy at GCSE-equivalent level is not widely available.

Perhaps there does need to be a conversation between people setting the syllabus, the specification, the examination bodies, and people who are very, very distant from understanding maths.

We are teaching mathematics at the moment as though everything outside the classroom walls is the same as it ever was. Floods, fires, you name it, mass migration – and mathematics is hugely implicated in these things – in modelling, in predicting and communicating climate change, and all sorts of things. We are crying out for a new curriculum. We really are.

Education reform needn’t take a long time. Parents want it. Students want it. Teachers want it. So why isn’t it being done?

It’s a huge challenge to bridge that numeracy gap, with people struggling with a cost-of-living crisis and a government wary of spending on extra teachers or resources. Shoreditch head of maths, Sam Mitchell…

Maybe the GCSE becomes more core maths, or we have extra time in our curriculum. That would be great. But I can’t tell you how long we will have maths adverts out for jobs at this school. So the idea of being able to recruit double the amount of maths teachers or have people who can teach those skills and are trained to teach those things is pretty farfetched, looking at teacher recruitment at the moment.

When it comes to Sunak’s promise of a more maths-savvy nation, it’s going to take more teachers and inventive thinking. We need both rigour and real-world relevance. Navigating numbers will always be more of a necessity than a vocation for many of us, especially when numbers on a bill start to get as scary as a maths exam. But the problems are particularly acute for those whose struggles are hidden outside the mainstream.

A lot of financial education is designed by numerate people. And it works really great for numerate people, but it doesn’t work for people who aren’t naturally numerate. And when somebody is in crisis their ability to think and process stuff is about that thin. And so saying to them at that point, oh, right, we’ll learn some maths, is not helpful.

So in a frequency table…

We need a population where far more of us are equipped to cope with everyday calculations, but without shutting out already disadvantaged kids from the riches of the maths so beautiful that it sounds like music to enthusiasts like Alf Coles. It’s a policy puzzle we’re yet to find the solution. In the meantime, at least I can get an answer to my question about soh-cah-toa.

And Sam, can you just remind me that terrifying word that I heard again after so many decades – soh-cah-toa?

Soh-cah-toa.

What does it stand for again? Because it did strike a chill into my heart.

Did it? I mean, not all maths teachers like teaching it like this. But it’s the sine of the angle equals opposite over hypotenuse, cos of the angle equals the adjacent over the hypotenuse, and tan of the angle equals the opposite over the adjacent. That’s for a right angle…

How could I have forgotten that?

No, I know, exactly.

I’ll just stick to soh-cah-toa.

There’s a few giggles the first time you teach it, but yeah, we’ve got there in the end.