I’m a programmer – I work with numbers everyday – but as a child I never learnt any maths – and by maths I mean the sort of thing that’s being taught in our schools; I never learnt my times tables, I never learnt any algebra – I never even learnt to count in any sort of formal context. And yet I manage to do a job that deals in functions and coordinates and formula pretty much every day of my life with no problem whatsoever.
As a family we have an amusing little anecdote about my sister’s first experience of school type maths. In order to be allowed to skip maths while doing an arts course, she was asked to do a maths functional skills test – bear in mind that like me she’d never done any maths whatsoever; no multiplication, no addition, literally nothing – so she sat down full of trepidation to do her first ever test.
What she was confronted by was a multiple choice paper with questions that were so unbelievably straight forward she thought it was some sort of a joke – then, because she has a warped sense of humour, she decided to try to get every single answer wrong. When the results arrived she was somewhat miffed to find she’d got one right! Later, when they asked her to resit the test due to what they decided must have been a technical error, she passed with flying colours making sure she never had to sit it again! And yet this is a test that a third of school children, despite 13 years of ‘maths’ education, continue to struggle with up until the age of 18.
So what on earth is going on? The answer is surprisingly straightforward. We did learn maths, we just didn’t learn maths in the way that leaves 20% of the population “so fearful it makes them feel physically sick”. 1 The fact is all humans are innately mathematical. It’s not just humans, it turns out even 3 day old chicks are able to do subtraction. 2 So if we’re all so mathematical what is going so wrong? Why do almost half of adults dislike maths so much? And it turns out the answer is numbers: it’s those pesky Hindu-Arabic squiggles that are ruining maths for so many of us.
Numbers from a 12th Century manuscript
As with most problems in life, to understand why I find it’s best to think about cake. So imagine I have a cake and five people are coming to visit, how many pieces do I need to cut the cake into? Well if I include myself – which I definitely will – I’ll need six slices. But what happens if one of my friends can’t make it. Do we save a bit for them? How much do we save? What happens if two friends can’t make it? What happens if one friend turns up and doesn’t like the cake? Do we share the uneaten piece or play rock paper scissors? And now I think about it – how big a cake should I buy and what effect does the size of the cake have on the the size of the slices?
In real life, with real cake, all this stuff is incredibly easy – I’m not going to sit there, beads of cold sweat forming on my furrowed brow, pen and paper in hand, clock ticking ominously in the background while I look blankly at the cake and wonder how on earth I should divide it – in reality it’ll take all of 2 seconds and most of those 2 seconds will be spent realising that a blunt knife is rubbish for cutting cake. But the moment you abstract the real life away and start using numbers exactly the same concepts very quickly get orders of magnitude more difficult to grasp. The fact is concepts that a five year old could easily grasp in a real world context are making adults cry when abstracted into numbers. A 3 day old chick may well be able to subtract 2 from 4 if that 2 and 4 are pellets of food but it sure as hell can’t internalise the numbers 2 and 4.
And the really important and frankly silly thing about all this is that it’s not the numbers that are important, it’s the concepts that really matter. If you can understand all the different ways you can divide a real cake, if you understand that different size cakes will affect the size of the slices but not the number of slices, if you understand that if you play rock paper scissors you may or may not get an extra slice, if you understand that a person not wanting a slice throws up all sorts of interesting issues, then you actually understand the numerical concepts you will actually need in life. And the better you understand these real life concepts the easier it will be at a later stage to abstract them into maths. When we come across a new idea, any idea not just a mathematical idea, the way we learn it is to link it to what we already know. If as a child you come across the idea of fractions before you have a deep and innate understanding of dividing real things you simply do not have the necessary understanding on which to link these new and very abstract ideas. For many children this is a disaster and leads to a wholly predictable life long dislike of maths.
On the other hand, if like myself and my sister, you have the concepts cemented in before you come to all this weird and wonderful number stuff then maths is no more complex than any other subject. From the moment we wake up to the moment we fall asleep we are all doing maths – the time we wake – where our socks are – why our socks are always mismatched – how quickly we eat our toast – why our toast is burnt – why there are no spoons in the drawer – why we are in a hurry – the list is genuinely endless and the simple fact is the more you live and the more you see the patterns that real life creates and the more concepts your brain is allowed to really internalise and master the easier maths will be. That’s not to say we all need to go and study maths at an abstract level – some of us will but most of us won’t – instead it’s just to say that simply by living and experiencing the real world numerical concepts we can all become numerate and if, later in life, we need to abstract that numeracy into ‘maths’ then, as my sister proved, it’ll actually be very easy.
Does this mean that no one should be teaching maths? No of course not, many children not only grasp the abstract concepts of traditional mathematics but absolutely love them. If your child loves maths then by all means maths away. However, for those of you who have children who simply don’t enjoy the abstractions it’s nice to know that they are not what’s important. Back in 1935 a famous educator called Louis Benezet tested out exactly these ideas3 and proved conclusively that learning ‘maths’ in a traditional way was not only a waste of time but positively harmful for many of our children.