Teach maths as if it were music. Opinions by David Coulson, Sept 2011
Let’s take a look at the parallel worlds of music and maths. Have you evernoticed how good musicians are at maths, and how good mathematiciansare at music? There is a stronger correlation than many of you wouldknow. The same neural resources that enable a mathematician to readalgebra also serve a musician when (s)he is reading musical script. Bothhave good memories and both have well-developed ability to focus onthings that are abstract and imaginary.
Music and maths share the characteristic of uselessness. I say thatguardedly because I love music as much as everyone else. But no-oneneeds music any more than they need maths, and yet people who becomegood at either or both of these things spend years in training and do sobecause they love the experience of ‘playing’. Neither of theseprofessionals needed to become professional. Both of them chose tobecause there was something nice about their chosen profession. Music toa highly-trained musician tickles the emotions, just as maths to a highly-trained mathematician tickles the intellect.
But from there the parallels end and become contrasts. See how differentlymusic and maths are handled at school. No-one is forced to learn amusical instrument. Everyone is forced to learn maths. A small minority ofour world population become good enough at music to entertainothers, but their presence is always welcome. By contrast, I don’t think Ihave ever known a mathematician who gave an algebra recital to anenthusiastic audience.
When kids ask me why they need to learn something like trigonometry, Itell them honestly that they don’t need to at all, but that it is a confoundededucation system that is forcing them not just to learn it, but to learn itonly for the sake of a series of exams, which will grade them as failures ifthey don’t learn it. And when they ask me the next two or threequestions, I find myself comparing maths to learning a musical instrument.At first the musical instrument is hard to play and therefore unpleasant.But over the course of time, it gets easy, and then all kinds of interestingways of playing with it become possible – none of which can be seen untilthe student has mastered it.
Most people hate maths because they were dragged, kicking andscreaming through the initial displeasure of learning math’s ‘basic scales’but never got as far as seeing it as a thing to play with. By playing withmaths, I’m asking myself – for completely pointless reasons – how muchrocket fuel would be needed to send someone like me to Mars. I’m askinghow much of me is pure water, how much oxygen I have breathed in andout over my entire life and what is the probability of breathing the samemouthful of oxygen twice in a lifetime. NONE of this is useful. Mathsalmost never is. It’s just something for us to play with if we get good atit, like a musical instrument.
I swear, if music was taught today in the way that maths istaught, everyone would hate music. We would have, forexample, everybody from the football player to the class bully sittingalongside the little music lovers. We would tell them all that they had tobecome good musicians in order to get a good job. We would teach themall to play the same instruments, the same set pieces of music, and all theset pieces would be awful things that no-one would ever play at a beachparty.
There would always be more work to be done than time in which to doit, so everyone would be rushing and taking shortcuts. The music teacherwould be a disillusioned English teacher who drew the short straw and hadto take the class that no-one else wanted to teach. The music would belearned from pieces of paper downloaded from the internet and everything– every little bit of progress the students made in the same boring direction– would be graded. Each week, an assessment. Each term, an exam. Eachyear, a certificate that separated the top half from the bottom half.
If maths was taught in the way that music is taught – optionally, by expertsin the field, by aficionados, for the sheer pleasure of it, more studentswould come away from the experience loving it. We only need a smallpercent of mathematical geniuses in the world, and we can easily identifythem in their youth because they will be the ones who are prepared tolearn the basic dreary scales of mathematics. The rest we will not scar bytorturing them with it. And everyone will be happier, from the teacherdown to little Jimmy who’s come in to learn the times table and doesn’tknow yet that he will one day create the language which unites QuantumMechanics with General Relativity.
Why did I eventually become a maths teacher when there are so manyother, more attractive careers to be had? For the same reasons that a goodmusician eventually becomes a music teacher. When I teach a bit of mathsto kids (particularly the little ones) for the first time, I see their faces lightup, not just with a glimmer of understanding, but a joy at understanding.They smile at me as though I had just given them a dose of medicine thattasted unexpectedly sweet. I’m not teaching them the notes on the pagebut rather offering them reasons for enjoying the notes on the page.