OPINION
One of my colleagues brought his daughter to work for a few days this week and I can totally, see why 12-year-olds are leaving school.
In another week or so she’ll be back at her school, poor girl. It’s a good institution, one of the best in Auckland. But when I asked her if she was enjoying her time there, she said it was too slow for her. It wasn’t a waste of time, since she had heaps of friends, but the learning wasn’t moving fast enough for her brain. You could see the lights fading from her eyes.
Nevertheless, last month teachers got a 14.5% pay rise. They are being rewarded for bad behaviour. Listening to this 12-year-old talk about her woefully bad teachers, I was reminded of the adage: if the problem can be solved with money, then it’s not a real problem since more money can always be found. The bottleneck is always, as Peter Drucker said, at the top. But teachers have the lowest IQs of any profession that requires a university degree, so I’m not surprised they can’t see the problem.
Unfortunately, schools are a fact of life. Can’t get rid of them. Everyone knows they are a waste of time – even the 12-year-old I talked to – and the teachers seem only to care about their pay packets. So, I’m glad people like Alwyn Poole exist to pressure the education system. He’s managed to convince multiple political parties to discuss education this election.
In my estimation, the most urgent election issue for New Zealand is the sorry state of maths education in our schools. Nothing – and I do mean nothing – is more important. Everything spirals either up or down from the quality of maths education.
For a start, if I were the Emperor of New Zealand, I would set the minimum age a person could be a teacher at 50. The older I get, the more I see how dangerous it is for the young people to have all the voice and none of the wisdom, while the older folk have plenty of wisdom but none of the voice – due to their own selfish choices. Retirement villages are a cancer on society. Old people have a responsibility to turn around and ensure the youth don’t make the same mistakes they did.
Young people (I’m talking 20–35) simply do not know enough about the world to teach effectively. All they can do is teach students what to think, not how to think. And maths is the only way to train your brain in ways to think differently.
Good maths education is not intuitive. Nothing of value in human experience is intuitive. All that comes naturally to the human animal is eating, defecating and killing. In maths, there is nothing intuitive beyond the addition of natural numbers less than 10. Subtraction is not intuitive, nor is the concept of zero. The postulates of Euclid are not intuitive. If they were, Euclid wouldn’t get any credit for them. Fractions? Forget it. And don’t get me started on calculus.
People aren’t “gifted” at activities. Babies don’t even know how to sleep peacefully through the night. As any parent will tell you, they must learn how to sleep. We are creatures of noise, madness and chaos. Everywhere in the world where people live together, and the inhabitants are uneducated and idle – regardless of culture, race, or time – all of them share a common characteristic: they are noisy, both audibly and visually.
By contrast, there are two places where people can congregate in large numbers which are quiet: churches and libraries. These cloisters are quiet because they are where people go to get on with the work of engaging with the unknown. Understanding is a function of work. And the first point on that function is (0,0) – you must accept that you don’t know anything.
Most mathematics lessons before calculus are about computation. Mastering computation takes work. Not a little work, not 15 minutes a day – it takes a lot of work. Over and over and over again, like running beep-tests in basketball drills. Or endless scales in piano practice. Most of the work is practice for the interesting maths later on. If you’re willing to put in the practice, calculus teaches you composition, the system and patterns which not only produce order but define that order.
To understand something, you must recreate it. Once you can do this, you will stare at the result for hours wondering what you just did. The sun goes down outside, and you don’t notice because all you see is how the starting point of the equation so obviously contains the brilliant insight at the end. The world you know, the same world you lived in as an infant – all wood, metal and separate pieces – starts to look thin and you can finally perceive the fields and flows that have always been there. And you wondered why you ignored them, and what else you might be ignoring.
The field of mathematics doesn’t matter: fluid dynamics, electromagnetism, topology, physics, aerodynamics. In each of these, you are listening to different music sung by the universe. Even if the form of the music is unexpected, maths lets you know how to listen, and how to hear it. The music in planetary charts sounds like Bach with the beauty of periodicity or synchronicity, some counterpoint within the unity.
Looking at the data from an atom smasher sounds a bit like Mozart. Maybe Stravinsky. Probably more like Xenakis. The data is discord and unpredictability in an irresistible force. It’s an energy. Charlie Parker. Ornette Coleman. A force with its own internal order invisible from the outside. A fixed beginning with a very definite and different ending.
A big part of the reason people suck at maths is because teachers don’t know what’s important. The point of memorising multiplication tables, for example, is so that seeing the patterns in the tables – like the relationship between the 2 and 3 with 6 – becomes intuitive over time. For the same reason that it’s useful for a child to see a picture of a farm to understand farms, it is worthwhile for them to see the landscape of multiplication to understand what happens to numbers when you compound them.
When a student visualises a memorised table in their mind, they will discover things that are missing from it, like 11, 19 and all the other primes. They might recognise how some numbers show up a lot, like 24, and others infrequently, like 21. When the student thinks about these tables, patterns feed their memory. The student begins to learn unspoken things about mathematics, completely independent of the simple act of repeatedly recalling the table.
Funny how kids have no problem memorising the characters on their TV shows but for some reason, according to teachers, can’t be expected to remember the names of planets or the identity of half a dozen species of tree in their backyard. The idea that kids don’t have to memorise multiplication tables because they have iPhones is beyond ignorant. People have had abacuses for thousands of years, then soroban, slide rules and calculators – and it was still worthwhile to memorise the basics.
If mathematics were a religion, we’d say this process of memorisation is like taking a passage from the Bible or zen koan and meditating on it. Maths isn’t a religion, of course, but the iterative process of thinking through a problem is the same. You ponder something deeply, see it in your mind, and your mind gets so familiar with this conjured image that it develops the specific power of detecting new patterns – or of spotting existing patterns that might otherwise stay hidden.
Memorisation is the basis of inquiry, investigation and all answers worth knowing. It allows you to prepare and answer your own intelligent, probing questions. Without doing the hard work to instil the basics – with a clear strategy articulated to the child for why this is all happening – education is nothing more than instructions for using tools. The robots can do that.
The emphasis here is on the work. Again, there is no intuition or natural talent in education. The child who sits at the piano for hours after other children grow bored does not have a natural talent for music. She has a natural talent for work. The same goes with reading. The joy is in the figuring out, in the trying.
There is only comfort to be found in doing the work of learning properly. All that is great in this world comes from inhuman amounts of effort. The only way to create order out of disorder, to create a pattern out of noise, is to work. Work fights entropy. Bach and Beethoven worked. They suffered. They were possessed of Plato’s daemon – driven to study and study and study and slowly learn to see the patterns. They learnt to recreate those patterns and then dared to wrangle the forces underlying those patterns, set to work on the deep forces themselves, and created new patterns, surprising and unexpected even to accomplished musicians.
Maths – not computation, but maths – requires concentration, devotion and humility. A mathematician is a good listener. Maybe he thinks he’s listening to God, or the Universe, or the white noise of bombinating quarks. He isn’t working his systems of equations by mechanically jostling symbols around the page. The good thinker listens and wonders where he’s heard the music before.
There is a lot to learn when kids are kids, but maths is about making good adults. If there’s time left over, they can learn to program computer code, knit, bake cookies or build furniture. Empowerment doesn’t come from technology. It comes from knowledge. Wisdom. Understanding. Maths.
If students aren’t being taught the love and understanding of maths, with the precise goal of knowing how to see patterns in the world, then it’s probably time to purge the teachers and start again. You should be demanding change, not asking for it. Or do you want to keep experimenting on children?
I guess it’s your choice this election.