Maths at School

I was amused by a recent back page article in the Guardian Weekly arguing that too much maths is pushed at too many children at school. According to Simon Jenkins, it has become a bit of an obsession to keep up with other nations in the PISA rankings, and more and more effort is expended on getting kids close to the high level of Chinese and other Asian kids. Maths is chosen for focus because it is easy to measure and seems to have some relation to the sort of careers that determine competitiveness. But for many kids maths is a torture, and for most the maths taught at school will have little practical benefit in later life.

The article was amusing, and so were the letters published the following edition. Three were chosen, doubtless from many, all of them against the proposal. The first took the traditional view that maths, even where not directly practical, was excellent brain training. The second had the stronger argument that maths is the basis for many practical things, notably engineering. The third simply sneered that Jenkins was probably rubbish at maths.

I find the article useful because it made me think about something in a new way. I had sailed through maths at school, almost at prodigal level, and did not really exercise much thinking in choosing the subject for college. At college, a few things happened. First, I started failing. That was partly because I had never had to think about maths before and did not take well to working through struggles. Next, the syllabus caught me out, because, before it was possible to specialise, many courses assumed some knowledge of the branches of maths associated with science, knowledge that I was lacking due to prior choices, and a lack of interest or talent. Lastly, I started wondering what the point was, in a subject that had long ago discarded anything as simple as numbers and where each concept only seemed to serve the next, even more obscure, concept. We spent half of one term proving that if you had three infinite parallel lines and moved your pencil from the top one to the bottom without a break, you were sure to cross the middle one. Now who would have guessed that! I left college wishing that I had had the courage to transfer at some point to Economics.

So, comparing the ultimately unsatisfactory experiences of Jenkins, a mathsophobe, and of me, a mathsophile, what lessons can we draw?

First, I don’t buy the argument at all about mind training. Sure, maths does train the mind to think logically, to follow steps, and things like disproving by counter-example, all of which have common application in everyday life. In the same way learning Latin helps the mind understand sentence structure, tenses and declensions, and even the origin of some common everyday words. But that does not mean we should still all learn Latin. Surely we should all learn modern languages instead, which have the same mind benefits and might actually be used to converse with real people on planet earth. There must be practical maths applications with the same combination, if our starting point is everyday use rather than something ethereal.

The argument about engineering has more dimensions. The world surely needs engineers and scientists, and engineers do require strong knowledge of much of the maths we learn at school. Trigonometry and calculus are two sub-disciplines that are essential. To reach a level in these disciplines that is good enough to become an effective engineer requires a large set of more basic skills. Perhaps as much as half of the school maths curriculum could be seen as a primer for engineering.

But while the world needs many engineers, it does not follow that everyone needs the knowledge that engineers have. For people who are not engineers or in science and technology, that same curriculum has little or no everyday value. Most people would be better off being taught basic DIY skills. I was never going to be a scientist or engineer, and indeed those branches of maths were a lost opportunity for me. It was especially wasteful at college to reintroduce topics that I had already dropped at school. How disheartening it was to sit through a three-hour exam and finish useful input after five minutes!

It would be possible to divide up the subject somehow. Perhaps maths for maths, maths for science and engineering, maths for business and economics, and maths for living would be a good segmentation. Maths for maths would prove things about parallel lines and ultimately lead to more research and more maths, for brilliant specialists. Maths for business and economics would have focus on cash flows, cost types, statistics and probability – all topics I would have retained passion for and have used extensively in later life. Maths for living would be compulsory, and focus only on things that most people could benefit from, such as budgeting, probability, percentages, loans and so on.

To a small degree this happens. Pure maths is sort of maths for maths, applied and applicable the other specialities. But it is all too little too late, and maths for living would be a big step forward from the sort of courses taught to the majority in most schools, especially if it filtered back into junior schools. Probability is a big challenge for many at high school, but is a key life skill, and perhaps starting earlier would help.

What stops this happening? Well, I see three blockages. One is the sort of traditional thinking about training the mind and beating the Chinese. The second is the practical challenge of managing many parallel streams with limited teaching resources. And the third is the requirement for kids to make choices before they are mature enough to do so – did I really know at eleven that I would lean towards business and not science or research?

The first blockage is lazy, and Jenkins does a good job at exposing. This is the one that leads to pointless torture of generations of kids, failing at subjects they have no talent or passion for and will never find need for after school. The second blockage is where technology can make a step change. Once we all learn partly in classes and partly from computers, much more flexible curricula become feasible to manage.

The third blockage is more problematic. In Germany and the Netherlands, kids are streamed into completely different schools at eleven, some groups prepared for college and others more vocationally. I have always been against this system, because it is very young to essentially condemn kids along a particular path, especially considering all the contextual factors involved like family background and aspiration. But I am coming to see the merits of the approach, so long as tracks to deal with exceptions are available. The vocational group could all take maths for living, with a small dose of science or business thrown in for some depending on talent and ambition. The academic group could be further split at some point between researchers, engineers, business people and non-mathematicians like linguists or historians. With the help of technology, it is all very possible.

Such thinking could have spared the Jenkins much torture in his teens, and me a lot of wasted education in my early twenties. Might we have chosen the wrong path too soon and thereby blocked our own path? Possibly, but that risk has to be weighed against the massive benefits of targeted education. My own path towards Economics would have seemed far less of a leap had my school maths been focused on maths for business.

It is a shame that traditionalists and trade unions conspire to prevent education moving forward s quickly as it could. Such tailoring might not beat the Chinese at PISA tests but would surely lead to happier kids and ultimately competitive advantage. The same thinking could apply to many other subjects and the balance between subjects. For example, modern languages are still sadly neglected in the English-speaking world, due to a mixture of arrogance and the fact that languages are less about academic research than practical value. I was lucky enough to start French early and have good teachers, and somehow my French is still much better than my other languages despite all sorts of later-life efforts. This leads me to wonder if the brain finds language easier at a younger age.

Thank you, Simon Jenkins. Our talent profiles are so very different, but you helped me think about a subject in a broader way. I can only hope that some of the people designing education systems have open minds and not just PISA targets.