Less is more: reducing maths in schools

I think our education system is fundamentally flawed. I think it’s flawed in lots of ways and for lots of reasons, but today I am going to focus on how we teach maths in schools.

We make maths compulsory from ages 5 to 16 and spend more time on it than any other subject bar English. Despite this we fail at the most basic goal of giving everyone the basic mathematical literacy needed to engage with the modern world, and instead waste countless hours forcing them to learn maths that they do not need or want to learn.

The general response to this state of affairs is to call for yet more maths education. I propose a radically different approach: dramatically reducing the amount of maths in schools. I argue that by focusing on teaching just the maths that is actually required we will improve the level of mathematical literacy in our country, and give teachers the freedom to teach maths in a way that will better achieve the goals of maths advocates.

Why maths?

I’ve chosen maths as my focus for two reasons. One is that, while I am by no means an expert, it is the area I know the most about. I studied maths and maths-related subjects a lot at school, I’ve taught both maths and programming, I studied engineering at university, and I work as both a software developer and an economist studying the skills needs of the highly-mathematical UK space sector. Some of my arguments may also apply to a greater or lesser extent to other subjects, but I leave that task to people more familiar with those disciplines.

The other reason is that maths and ‘STEM’ (Science, Technology, Engineering, and Maths) subjects more generally seem to be very much in the limelight at the moment. It is widely accepted that there is a STEM skills crisis and the government is increasingly focusing on STEM to the exclusion of all else, exemplified by funding cuts to arts subjects and a much condemned publicity campaign telling people in the arts that their next job could be in cyber and they ‘just doesn’t know it yet’.

How much maths do we teach?

Given this shortage of people with mathematical skills, my proposal probably sounds quite counterintuitive. Surely the solution to not having enough people with maths skills is to teach more people more maths?

Let’s start by looking at how much time we currently spend on maths. In the UK, maths education is mandatory for all children from age 5 to age 16. We teach them about 4 hours of maths a week, a minimum of 38 weeks a year. That means that each child is taught somewhere in the region of 4 * 38 * 11 = 1700 hours of maths up to age 16 (though this doesn’t count nursery or homework or maths work in science and other lessons). To put that into context, that’s more than double the contact time of a four year engineering degree of the kind I did.

Why are we teaching maths?

Before we look at the impact of all that maths, it is worth asking what it is that we are trying to achieve. Why do we teach maths in the first place? The International Mathematical Union offers four key reasons which are echoed in most other literature:

  1. Mathematics has a transversal nature … [it] has provided the mental discipline required for other disciplines
  2. Mathematical literacy is a crucial attribute of individuals living more effective lives as constructive, concerned and reflective citizens
  3. Mathematics is applied in various fields and disciplines, i.e., mathematical concepts and procedures are used to solve problems in science, engineering, economics
  4. Mathematics is a part of our human cultural heritage, and we have a responsibility to develop that heritage

These are very similar to my three purposes for education (work, citizenship, and transcendence), so it will come as no surprise that I agree with them. I think they are all good reasons for teaching maths, but I don’t think that they are all good reasons for making maths compulsory or dedicating more time to it than to any other subject.

Let’s address them one at a time:

1. Maths provides mental discipline

The argument here is that maths is not just about numbers, it’s about general analytical, problem-solving, and logical thinking skills for life. This is absolutely true. Maths is highly logical, it involves analysis and problem-solving, and these are extremely important and valuable thinking skills that we should be teaching.

But these noble ends do not justify the means. The implicit assumption is that maths is the best (or only) way to teach these skills, and this is almost certainly not the case. Logical thinking is applicable to many more fields than maths – its origins are in philosophy. Sherlock Holmes is a champion of logical thinking who uses deductive reasoning to solve mysteries, but does very little maths (indeed his nemesis is maths professor James Moriarty!).

If teaching it is our ultimate aim then there are surely better ways to do so than through quadratic equations and angle bisectors. Teaching children maths in order to improve their logical thinking feels to me a lot like teaching them to swim in order to have them learn tennis. Will improving their general fitness help? Absolutely, but they’d be a lot better off if they just played tennis!

Most children use logical thinking to come to the conclusion that learning maths they have no need of is a waste of their time.

2. Mathematical literacy makes for constructive, concerned and reflective citizens

Maths is a fact of life. We need everyone to understand the interest rate on their credit card, the COVID statistics that determine the fate of the country, and how to measure furniture.

But mathematical literacy is not quite the same thing as maths. This may seem like splitting hairs, but it is a useful distinction to draw, and it’s for this reason that the term numeracy (‘numerical literacy’) has been coined. Numeracy is the subset of maths used in an everyday context - being able to count, understand what a percentage is, read a graph etc. Maths proper is whatever is left over, from basic algebra up through to calculus and beyond.

Here the IMU has my full-throated support. Numeracy is vitally important and should be compulsory.

3. Maths is needed in STEM work

This argument is becoming increasingly popular as skills shortages in STEM sectors grow. Again, I don’t disagree with the goal. I think we should encourage STEM careers for lots of different reasons, and much of my work for the Space Skills Alliance looks specifically at how we can address the skills shortages that are constraining the growth of the space sector. I do however disagree once again with compulsory maths education as the method of achieving that goal.

I have pursued what would reasonably be described as a STEM career. I can tell you that not once in all my university education or career have I needed to be able to construct a triangle using a pair of compasses.

There was a fair amount of maths that I learned at school – particularly algebra and calculus – that I did make use of during my degree, and so there is a case for teaching this in schools. This however is not a good argument for having everyone learn it regardless of their higher education choices. We already recognise this by making maths optional after age 16, and I think that we should make it optional even earlier.

The variable quality of school-level education and the wide range of education systems that international students have studied under mean that many universities already offer a foundation course in maths in order to bring all the students up to the same level.

4. Mathematics is a part of our human cultural heritage

At risk of becoming a broken record, I once again agree with the goal and disagree with the method. Maths is an important part of our culture, but so are history and art and philosophy, and yet we do not make these subjects compulsory or focus our curricula on them to anything like the same degree as we do maths.

Maths is a hated subject for many precisely because we focus on it to the exclusion of all else. By making maths (or anything else) compulsory and saddling it with a set curriculum and learning goals and exam questions we rob it and those studying it of joy and the value of learning for the sake of simply expanding our understanding of our world.

We are not achieving our goals

With these goals in mind, let’s look at how well we achieve them. Having put every single child in the country through two degrees worth of maths, what is the outcome? Pretty poor.

About a third of GCSE students (~16 year olds) do not get at least a grade 4 (a C pre-2017) in maths, which is generally the minimum entry requirement for A levels as well as many apprenticeships. Less than half get a grade 5 (somewhere between a B and a C).

Some 20% of the UK adult population, or 17 million people, have only primary school level mathematical ability. 60% of MPs couldn’t answer a basic probability question about flipping a coin.

Not a resounding success then. We put every child in the country through two degrees worth of teaching and the result is that a fifth come out having barely improved and a third can’t progress to most of further education. That’s at least 20 million people who are functionally innumerate and will struggle to meaningfully participate in the modern world. The system is not fit for purpose.

The government has noticed, and it has a plan, and the plan is more maths.

The 2015 GCSE reforms introduced ‘new, more demanding content’, the national shortage of maths teachers is being addressed with an offer of a £5,000 bonus for new starters, and a new £560 million programme is designed to help half a million adults (3% of those 17 million) improve their numeracy.

I propose instead that we significantly reduce the amount of maths. Why would that help? Well let’s take a closer look at the curriculum and what those 1700 hours are spent on.

The maths curriculum is bloated

Primary school (ages 5 to 11) accounts for about half of that time, and the primary curriculum is pretty reasonable. You must be able to do basic things like count, identify shapes, tell the time, and understand the basics of fractions, decimals, and percentages. There are a couple of bizarre inclusion like a requirement to be able to read Roman numerals up to 1000 and to construct pie charts by hand, but these are relatively few, the main focus in on valuable numeracy skills. 50% of the way though and so far so good.

The bit where I start to have a real problem is the 850 hours in secondary that culminates in a Maths GCSE certificate at age 16. The GCSE curriculum requires that students be able to:

(Though academies, which make up 37% of primary schools and 78% of secondaries, do not have to follow the national curriculum, in practice most do for many subjects, particularly maths. In 2014, 77% of academies followed it ‘to a great extent’ and 22% ‘to some extent’.)

We’ve left the bounds of numeracy and we’re well into the territory of topics that the overwhelming majority of people will never need in their lives. Indeed, the GCSE curriculum is now so bloated that many schools have changed from teaching it in two years to instead teaching it in three. To compensate, as many as 90% are cutting back on teaching the arts.

But perhaps the fact that the most people will never need this maths is half the problem? Not enough people are working in STEM jobs, but once they do this maths will come in handy. Not so.

Most people don’t need maths

Since this essay is about maths, let’s look at some more numbers. About 18% of the UK workforce (about 7 million people) works in ‘STEM occupations’ including healthcare (the NHS accounts for a little over a million of that).

Let’s go beyond the wildest projections of any economist and say that not only do we need the STEM workforce to grow, we need it to double to a whopping 36% of our national workforce. Does that justify making it compulsory for the other 26 million members of the workforce to spend a combined 22 billion hours learning maths they will never need? What an absolutely gigantic opportunity cost, even for our most generous scenario.

What new worlds would open up to us if we spent that time elsewhere? What new music or art or culinary delights might we invent? What new forms of thought or approaches to problem solving? What new historical discoveries?

Most STEM people don’t need maths

Our little thought experiment contains within it another assumption that I would like to bust, and that’s that the maths curriculum serves the needs of the STEM workforce in the first place. I would argue that it doesn’t. I say this from my own experience of STEM jobs and from my analysis of the skills needed in the space sector, an industry that is perhaps more STEM-focused than any other.

If you also work in a STEM job, ask yourself: When did you last need to construct a perpendicular line using only a ruler and compasses and not CAD software? How often do you calculate the nth term in a sequence without Excel? Do you remember the exact value of Cos60, or is it something you would just Google when needed? These are all things that can be outsourced to the computers that are today so ubiquitous that being under the age of 70 and not having one in your pocket is considered unusual.

While we focus on training people to do calculations that computers do with ease, we place very little emphasis on those areas where computers stumble: determining what numbers to put into a calculation in the first place, knowing what the limitations of a particular algorithm are, and understanding what the end result actually means. A typical maths question will present you with the results of a survey and ask you what percentage of the respondents like the colour red. A spreadsheet will calculate that in an instant, but it will not tell you if your research methodology was correct. Invisible Women by Caroline Criado Perez catalogues countless scientific studies which were mathematically flawless and yet fundamentally flawed because of biases that fail to account for half of our species.

Isn’t it important that we understand how those computers work? Yes, as a species we should make sure that we don’t lose that knowledge, but that doesn’t mean we need to teach it to our entire population. It’s equally if not more important that we don’t forget how to sow crops but we don’t require that every child learn to drive a tractor or a combine harvester. Specialisms exist for a reason, and have for the whole of human civilisation. Even our distant ancestors didn’t teach everyone to both hunt and gather, and they didn’t cut cave painting out of the curriculum to make room.

As society and technology develops, the skills that are required to participate in the new paradigm change. We’ve discarded etiquette and sewing and Latin from our compulsory curriculum without civilization collapsing, and now we need to do the same with maths that virtually no-one has need of. To take full advantage of technological advancement, we have to build on it to reach new heights, not require everyone to retread the same steps from wheel to cart to electric car. Our education system is designed for an age that has passed. It is time we update it.

Less maths means better maths

The alternative I am putting forward is to strip back the amount of compulsory maths very significantly and at the same time to place a much greater focus on ensuring that what remains compulsory really is learned by all. Let us focus on the quality of maths education over the quantity.

Make numeracy compulsory, but not maths

Reducing the amount of compulsory maths means more time for a broad range of subjects, and more time for those students who struggle with numeracy to master it before being forced to move on to more complex topics. As we have seen, though we spend a huge amount of time learning maths, the outcomes are embarrassingly poor. We should teach students based on their ability, not their age, and we should spend as long as is necessary to make it click. Leaving school without a firm foundation in numeracy should be unacceptable and near impossible. It does a disservice to our students and our society. Raising the base numeracy level of our entire country will have huge and lasting positive effects.

The maths outside of numeracy that is not strictly necessary should still be taught, but only to those who want to learn it. We should also go a step further and free it of the constraints of qualifications like GCSEs which undermine innovation in education.

Let teachers teach

School 21 (where I briefly taught) is so named because it is intended to be a school that teaches 21st century skills. In practice I found it was not dramatically different from what I experienced during my own schooling. But then how could it be? You can make your approach to education as innovative as you like, but at the end of the day you’re still hamstrung by the need to have every child pass GCSE Maths. Acclaimed Maths teacher Dan Meyer says that he “[sells] a product to a market that doesn’t want it, but is forced by law to buy it.”. We must let teachers teach. In A Mathematician’s Lament, Paul Lockhart writes:

if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education

As a maths teacher I was encouraged to find ways to make maths fun and interesting and relevant. My colleagues and I would share resources and ideas, attend events, and concoct ‘real-world’ applications for today’s learning objectives. The pool of particularly good and engaging resources is growing and the quality of maths teaching is probably improving, but we are optimising a not very effective solution, we are finding a local maximum rather than a global one. We have failed to see the wood for the trees.

The truth is that maths already is fun and interesting once you free it from the shackles of rote-learned formulae and contrived scenarios. It is, however, mostly not relevant, and that is okay. Things do not have to be relevant to be worth teaching and exploring and enjoying. We should accept this and be open and honest about it with ourselves and our students.

If you visit the comments section of any popular mathematics video on YouTube by 3Blue1Brown, Numberphile, or Matt Parker you will see the common refrain ‘I wish my teacher had taught maths like this when I was at school’.

These channels have between then more than 10 million subscribers, and not a single one was forced to subscribe. They chose to. The videos contain no exercises to complete, no curriculum topics to tick off, no exam questions. Instead the presenters ponder problems (sometimes relevant, sometimes absurd, but crucially not in any way contrived) and then go where the problem takes them using maths as needed with no preset agenda to shoehorn in an example of fractions or simultaneous equations.

As Lockhart puts it:

Problems will lead to other problems, technique will be developed as it becomes necessary, and new topics will arise naturally. And if some issue never happens to come up in thirteen years of schooling, how interesting or important could it be?

Intrinsic motivation is key

You have to want to learn. Intrinsic motivation beats extrinsic motivation every time. Once you crack that, the rest is easy. Kids, even kids who get written off as low achievers, have a boundless enthusiasm for learning when they have the right motivation. Ask them about their football team or their favourite video game and they will be able to reel off facts and statistics without a problem. Why? Because it’s something they care about. They’re motivated to learn about it.

Forcing people to do maths against their will is a sure-fire way to make them hate it and drop it at the first opportunity. It goes against everything we know about how people learn effectively, and how people want to learn. Instead we make the case for maths on its own merits, and if some people are not convinced that is a shame but it won’t mean the collapse of our civilisation any more than the fact that many people cannot play a musical instrument.

Teachers hate reducing a subject they love to teachable chunks and exam questions, but they have very little flexibility. They can try to make it a bit more engaging, show an interesting video, find some examples of maths ‘in the wild’, but ultimately they’re constrained by the fact that after next Thursday they need to move on to the next section of the curriculum.

We must discard the maths curriculum and let students explore and create maths like they explore and create in the arts. It is freedom to learn that builds mental discipline, hones the kind of thinking that solves problems in science, engineering, and economics, and develops an appreciation for our mathematical cultural heritage.

J. Dudley