Average

The year was 1991.

It was the last time the Red Hot Chili Peppers would have an original musical idea. Terminator 2 came out, and everyone loved it, because back then an apocalypse created by rapacious humans and unfettered machine intelligence seemed like a bad thing. I got what was my first perm, and should probably have been my last, but I was never a fast learner. I was skinny, and the perm made my head triangular, so I kind of looked like a lampshade. But that was the least of my worries. Because 1991 was also the year I sat School Cert.

Ah, School Cert.

I’ll have a go at explaining what School Cert was like, in my world at least. You’d make it to fifth form, or what is now year 11, and adults would nod knowingly. School Cert this year. If education had been child’s play to that point, then School Cert would make you knuckle down. Your ability to get a job would likely depend on it. The real world had arrived, and School Cert was above all else meant to teach you this lesson: the real world can be harsh.

To get School Cert, you had to take a set of national exams, passing a minimum of five subjects. I knew I’d do fine in music, and would muddle through another three subjects. But maths was my Achilles heel. I experienced what’s called maths anxiety, which is pretty much what it sounds like, and is fairly common. Kids with maths anxiety worry they can’t do maths - and the worrying often lowers their maths performance, spurring more worry. Maths anxiety can be instilled by parents and even teachers who feel worried about their own maths, and might say things like, ‘I never understood that stuff either’. It’s reinforced by teaching methods that focus more on passive learning than digging into actual concepts. The sad thing is that maths anxiety can persist even into adulthood and hold people back in life.1

Maths anxiety can be underpinned by a myth that high school me believed without question: some people are naturally good at maths, and some simply aren’t. I wish I had a dollar for every time I’ve told myself I’m no good at maths because then I’d have, f*** it, I don’t know, counting is hard. But having told you I’m not a maths person, maths is the very topic I’m going to have a crack at today.

Grown-up me thinks very differently about stuff like this. Nowadays, my mantra is ‘Be brave enough to suck at something new’ - a conscious rewiring of my brain over years that meant pulling on my big girl pants. Simply put, I realised I was at risk of role modelling can’t win, won’t try to my kids. Giving our kids something better is all any of us wants.

But back then in 1991, when my mum handed 15-year-old me the just-arrived letter with my School Cert results, I braced myself a little. When I opened the letter, I was gobsmacked.

Why are we talking about school assessments? You’ve probably got a hunch.

Our kids aren’t doing so well educationally.2 There are debates about the extent of the problem.3 And there are debates about the causes of the problem. It’s not fair to lay all the blame at the door of schools, or even the education system, but we have to ask what role NCEA is playing - and a Government announcement on NCEA’s future is imminent. We need change, but I think we have to be really careful not to throw the baby out with the bathwater.

Our kids’ educational troubles have created some nostalgia for the ‘good old days’, including a call from Tim O’Connor, headmaster of Auckland Grammar, for a return to something called ‘norm-referencing’.4

Norm-referencing essentially means shoving everyone on a bell curve, and it was the basis of School Cert. For any given School Cert subject, kids were ranked along a bell curve from the worst-performing to the best-performing. Then a line was drawn through the bell curve, so the kids on the left of the line failed and the kids on the right passed.5

[Image description: A bell curve that is high at the peak and low at either end. The middle is labelled ‘you are here’.]

The bell curve basis for School Cert was crappy.

If the crappiness isn’t immediately obvious, let’s a imagine a scenario in which a bell curve is applied to another kind of test you’ve probably done. Cast your mind back to when you sat your driver’s license. You stressed and practised and stressed some more, but when the day came, you did just fine. When the test was done you exhaled with relief, unclenched your white knuckles from the wheel, and turned to the tester. Great work, the tester said. You’re a perfectly safe and competent driver. The problem is, 50% of other people who sit this test are better than you. And so I can’t pass you.

You’d be livid, right? You’d say that what matters is that your own driving hit the standard, not how it compared to anyone else’s.

But the crappiness of the bell curve, and of education assessments based on it, can run far deeper. This deeper story is the one I wanted to tell - but to do that, I actually had to learn about maths, God help me. I discovered that maths is beautiful; but like anything, it can be misused and even weaponised.

Forgive me in advance for any limitations, and hang in there, chums.

Okey dokey. This is where I admit I tumbled into a rabbit hole, but it was kind of fun, so I’m going to share it with you before I climb out again.6

We’re heading back in history - and this time, way back. We’ll meet some of the key thinkers who came up with the concepts behind the bell curve, picking ones whose lives and discoveries show how maths can sometimes join forces with other ideas, for better or for worse. I can’t say for sure there weren’t other (maybe non-male, non-European) key thinkers who also came up with bell curve concepts, but these are the guys who appear in the history books.

We’ll start with Abraham de Moivre, born in France in 1667. This is a man who took his maths seriously. De Moivre was interested in probability, or the likelihood that something will happen. The guy never managed to land a proper job, which makes me feel better about my own midlife crisis, and ended up applying his incredible discoveries to the emerging industry of life insurance, but also to understanding gambling.

Working as a kind of consultant, de Moivre got called on by gamblers to figure out the maths behind things like coin flipping. Say you’re betting on heads. You’ve got an equal chance of heads or tails. If you do only a few coin flips, you might not get a fifty/fifty split between heads and tails, but the more flips you do, the closer to fifty/fifty the split will become. The gamblers wanted to know what was the chance of beating the odds, and getting heads 60% of the time? Of course, the probability of 60% heads isn’t as high as an even split - and the probably of doing better than 60% is even lower.

De Moivre drew this all out in the first bell curve, aka the ‘normal distribution’. In the middle of the bell, at the highest point, was the norm, or the most likely outcome of doing lots of coin flipping - a fifty/fifty split. The edges of his bell curve tapered away, until the very outer points showed the least likely outcomes of a lot of coin flipping: getting heads every time or getting tails every time.

Next up, we’re going to meet a dude called Adolphe Quetelet, born in 1796 in Belgium. Quetelet was a really out-of-the-box guy who took probability and the bell curve in interesting directions. Jobwise, he did better than de Moivre, scoring an astronomer’s role in Belgium’s first observatory. When revolution overtook the country, it not only messed with Quetelet’s career plans but got him thinking. He’d been using probability in astronomy, an area of study that all seemed orderly and nice - but could these same ideas to be applied to the messiness of humans?

Quetelet did something incredibly innovative: the first serious number-crunching of human statistics. It was now the 1800s, and governments were starting to collect data on humans, like their births and deaths and marriages. Quetelet got his nerdy hands on a set of measurements of the chest sizes of Scottish soldiers - and guess what? The measurements made a beautiful bell curve. Quetelet was able to come up with an average chest size for the soldiers, and eventually the concept of the ‘average man’. And ‘average man’ wasn’t just a numbers thing in Quetelet’s eyes. He thought that average men were nature’s true intention - physically and morally better than other men, who were deviations.

Quetelet’s work number-crunching people would in time become known as the Quetelet Index—today called the Body Mass Index. And Quetelet wasn’t done. He went to town measuring not just human bodies but other human phenomena, from births to crimes to poverty to suicide. As an aside, Quetelet was once crunching a data set of the heights of 100,000 military conscripts when he noticed something hinky. He was expecting a normal distribution, but instead found a whole bunch of blokes either just below or just above the height soldiers that were meant to be. Was the bell curve a crock after all?

It turned out the conscripts had been fibbing about their real heights to try to evade the draft. There’s nothing in nature so beautiful that humans won’t mess with it, but on this occasion, you can see where they were coming from.

Last but not least, it’s time to meet Francis Galton, born in England in 1822. Galton was really smart, but he’s not remembered fondly for reasons we’re about to see. He took Quetelet’s ideas, both good and bad, and he ran with them. Much of his work focused on gathering data by measuring the size of sweet peas, and whether their seeds would in turn grow into sweet peas of different sizes. Galton gave us the idea of standard deviation, which is pretty cool. Standard deviation describes the spread or dispersion of data. For example, the size of sweet peas might fall into a bell curve, but what’s the gap between the very smallest and very biggest sweet peas? Are smallest and biggest not so far apart, or is there a heap of difference between them?

But if Galton was willing to give peas a chance, he wasn’t so kind to his fellow humans.

Galton was the cousin of Charles Darwin, and he was influenced by Darwin’s ideas - but also by Victorian colonial racism. He brought these things together with the bell curve and probability in a pretty ugly way. Sweet peas had put a few notions in Galton’s head, and he wanted to try them out on people. He figured that all sorts of human attributes could be measured, and would be found to sit on a bell curve: not just things like height or chest size, but also intelligence. Worse than that, he thought intelligence was hereditary. Even worse still, he thought that some races, as well as working class people, had naturally poor intelligence - a fate they were destined to pass on to their children.

Galton believed in the bell curve; but he also believed in different bell curves for different races. In his thinking, white people had a bell curve that showed they could be more or less smart, but were on average smarter than other people. If you wanted to make society smarter overall, Galton thought, you needed to stop less smart people having babies. These days, Galton is described as the father of eugenics. He even coined the term.

Where have we landed?

The bell curve is pretty great for describing some stuff. Coin tosses? Yep. Men’s heights or chest sizes? Sure. The size of peas? Why the hell not? These things are random. Nature has a way of serving up random phenomenon in a natural distribution (although there are other kinds of distributions in nature too). But beyond that, we start getting into tricky terrain - especially when we start trying to quantify human attributes like intelligence.

Critically, the bell curve isn’t always good for describing non-natural things; that is, the things people tinker with. Tinkered-with things aren’t random by definition. Education systems deliberately try to change kids’ outcomes by increasing their skills and knowledge. Education assessments try to measure how well that process is going. Why then would we expect the results of education assessments to form a nice neat bell curve?

Our next rabbit hole awaits.

In 1994, three years after I sat School Cert, two guys by the name of Charles Murray and Richard Herrnstein published a book. It was a controversy, a travesty, and of course, a best seller, influencing the agendas of some fairly shitty politicians for years to come. I haven’t read the book because life is both too short and too full of other, better books that don’t deserve to be printed on a scented two-ply. So I’m going to rely on critiques rather than the primary source.7 You’ll see why.

This book is called The Bell Curve: Intelligence and Class Structure in American Life. It’s a case study of eww, but it teaches lessons that are still subtly relevant today. Let’s dive in.

There were red flags from the beginning. The Bell Curve was released without advance copies, meaning critics couldn’t scrutinise it - a suspicious sign, given the book was meant to be based on rigorous data. It was launched at an event hosted by a right-wing think tank, its shocking conclusions quickly making it into headlines, but not reputable academic journals. By the time further analysis revealed the book’s data was a shit show, the damage was done.

Here’s what The Bell Curve argued. ‘General intelligence’ is an essential human quality, measurable through IQ tests. During the twentieth century life had got more complex, making intelligence ever more important - and that meant smart people had inevitably risen to the top roles in business, government and professions. Smart people were inevitably getting richer and more important, and not-smart people were falling further behind.

So far so eww, but it got worse. Murray and Herrnstein argued that Black people were over-represented amongst the not-smart. And the news for the not-smart was all bad: because intelligence was mostly inherited, nothing much could be done for these poor, non-smart souls. Trying to give them opportunities would only be a waste of money. Jobs suitable for non-smart people would be the best these folks could expect.

In (my) summary of Murray and Herrnstein, the bell curve was destiny - not just in the sense that people’s intelligence could be neatly plotted onto it, but that their life outcomes would be determined by it.

Appalled critics of The Bell Curve had plenty to say, especially after they’d had the chance to pore over the data the book was based on.

For a start, the critics said, the concept of general intelligence the book relied on was crap. Humans have all kinds of ways of being smart that aren’t easily wrapped up in a single concept of intelligence. And whatever level of intelligence a person’s born with, it won’t be enough to trump all the other things that affect people’s lives, like their family backgrounds or resources. However, intelligence can be influenced by things like education, training and public health. And critics pointed out that the IQ tests The Bell Curve cited were actually measuring education levels more than intelligence.

And what about the idea that smart people inevitably rise to the top? Critics of The Bell Curve were scathing of this too. For a start, mass IQ testing was too new in 1994 for anyone to make this type of claim. But where high IQ people were clumping together in particular professions, that was because IQ testing was used as a gateway to get into those professions. (It’s a little bit like setting a thousand dollar joining fee for a club, then wondering why only reach people join - while also assuming that other clubs without fees must not have rich members.)

OK: why look at The Bell Curve? Research on intelligence, and life itself, have moved on. I think this case study matters because it shows so clearly not just how the bell curve can be misused, but how all sorts of shitty ideas can be hitched to it - sometimes in ways that are tricky to disentangle.

Am I saying that these eugenics-tainted ideas from The Bell Curve are present in Aotearoa today? Well, not exactly - but nor do I think we’ve consigned this stuff to history as much as we think.

Funnily (or not), it was the corporate world - the harsh ‘real world’ we’re meant to educate our kids for - that helped lead the charge against the bell curve. Microsoft dumped the bell curve in 2013. Before then, it had used a normal distribution for performance management - but all this meant was that top-paid positions were rationed to a small number, meaning most employees would never have a chance at them no matter how they tried; and the least performing people were always deemed losers, even when they were perfectly capable.

The bell curve is still used in some education systems, but it’s gone out of fashion.8 Looking back on School Cert days, and defending NCEA, Ronan Bass does a great job explaining why.9 Essentially he asks, what kind of education system fails half its participants by design - especially when the failed kids were more likely to be Māori and Pacific, low income or rural kids, neurodiverse kids, and kids for whom English was a second language? Some of these kids experienced more than simply shame or a sense of failure. Being shut out of higher education and employment left scars on their own lives and sometimes their children’s.

Maybe School Cert wasn’t based on ideas as egregious as The Bell Curve, but it managed to quietly produce a similar social order - with some kids assured they were destined to win as surely as others were reminded they’ll inevitably lose. And as in The Bell Curve, this order of things seemed kind natural, just the way things are meant to be. When I saw the call for a return to the norm-referenced ‘good old days’, I’ll just say I wasn’t surprised it came from an affluent boys’ school.

School Cert was improved over time and eventually replaced by NCEA. When it finally seemed the bell curve had tolled for the last time, I remember thinking, hallelujah. My own kids would never be subject to it. They would earn their qualifications or not; but either way, they’d be held to a standard, not ranked against their peers. I wanted better for my kids. I believed, and still do, the bell curve subtly but deeply affected the way I understood the world - and myself.

Like I said, I had a can’t win, won’t try mentality, especially when it came to maths. And although I wasn’t much good at maths, I understood the bell curve implicitly. I could try my best, but it wouldn’t help that much - especially if the others around me were trying too, and I couldn’t overtake them in the rankings. Like most kids, it’s fair to say that me and my mates were raised for the world around us. In Southland, at least, you didn’t need academics quite the same: numeracy and literacy were enough to be on your way. After all, when I was a kid, you could leave school and get a perfectly good job at the Tiwai smelter, or maybe learn a trade. Even if you’d missed School Cert, you might still be able to get an OK-paying job in a shop.

But my School Cert year was 1991, and other stuff was going on too. Years of economic upheaval had transformed economy and society. The Mother of All Budgets was laid down at the moment our fathers were being laid off. Their manual jobs disappeared, leaving them not just redundant in labour force statistics, but in their own eyes. Our mums stepped into the breach, leaving their kids at home for whatever extra hours they could pick up. In this profound dislocation, our parents didn’t know how to counsel their children for a world of work they hardly recognised. All that was clear was this: being a nobody in the middle of the bell curve wouldn’t cut it anymore.

The day I opened my School Cert results I looked, I puzzled, and I looked again. Yes, I’d passed maths with some unexceptional mark: but that wasn’t the surprise. In music, I’d got 97. And I shit you not: in my confusion, I concluded that the 97 must actually be out of 150 or something. (Like I said, I wasn’t into maths.) My music score was the second highest in the country, and I never came close to this honour again in my remaining years at school. But for a short time I got to be a minor celebrity - even having my photo taken for the Southland Times with my f***ing perm.

How did I get a mark like that?

Well, when I was little kid I asked to do music. My parents bought me a recorder and let me go to Saturday morning classes. I learned the basics of reading music. I also spent a lot of time at my Nana’s house. She had a piano and sheet music. Out of sheer boredom - my Nana’s granny flat in 1980s Invercargill wasn’t the hotbed of excitement it might sound - I took my music basics and taught myself to play piano after a fashion. My Nana saw my interest and paid for more music lessons. As I studied, I became aware that music has patterns, and I started dissecting it in my head. By the time I hit School Cert, I’d done literally thousands of hours of practice. My success was about 20% ability, 20% personal persistence, and 60% opportunity and resourcing. If I’d approached maths the same way, I would’ve been better at that too.

The funny thing is, I never put either my musical success or my maths mediocrity down to this influenceable mix of factors. I just thought, hey: nature made me better at one subject than the other. Nature. Success had no more ability to challenge my can’t win, won’t try outlook than my fear of failure.

Was the bell curve the only thing that made me feel this way about school and life? Of course not: but it seemed to offer proof for feelings. And who was I to argue with maths?

NCEA doesn’t work for all kids, and it needs to. But I’m grateful it worked for my two, giving them the skills they need and sparking their ongoing love for maths.

I try to be down with my kids, but if being down with the kids is a bell curve I’m very much at the left of the distribution. Sometimes I get my sons to explain mathematical concepts to me. Last time, after several attempts, I became overwrought and squawked, I don’t understand. The two of them blinked at me and the younger one gently replied, We don’t understood what you don’t understand. Yep.

One of the things I asked them to explain is the Monty Hall problem. This is a probability puzzle made well-known by a game show. A game show contestant is shown three closed doors, and told two doors have a goat behind them, but one door has a car. Of course, they want to win the car.

The contestant is asked to pick a door - say, door number one. The game show host then chooses another door to open - say, door number two. Now it’s the contestant’s turn again. They’ve got the opportunity to open another door in hope of a car. But do they stick with the door they picked originally, number one, or do they switch to number three?

The answer is this: the contestant should always switch doors, because it increases their probability of winning the car. But why? I squawked at my children. Why isn’t it a 50% chance either door?

When I eventually stopped squawking, I realised I was lapsing into my can’t win, won’t try mindset - and I decided I would figure out the Monty Hall problem for myself. I spent a while searching different explanations online until I found one that made sense to me. And then, to prove matters to myself, I took a bit of paper and wrote out all the different door-opening scenarios, until I saw how the puzzle worked.

And I did it. It took me a couple of hours, and it wasn’t elegant, but I did it. I bloody did maths. And I’m not going to lie: I felt proud of myself, as if I’d climbed a bell curve-shaped mountain. I don’t know what I was expecting next, but it wasn’t less than a parade in my honour. Yet when I told the kids, all I got from the older one was something like, That’s nice. The younger one just looked at me silently.

I love my kids, and I want better for them, but they can be dicks. I sometimes wonder if I’d just kept going and had a third child, would I have finally won the car.

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