The Numbers Game
Not everybody hates maths — and perhaps the rest of us shouldn’t either, discovers Kim Knight.
You have 42 coins. One is fake and the wrong weight. How many pints of craft beer does it take to work out if the counterfeit coin is lighter or heavier than all the others?
I first read about Mathsjam on Twitter. It was cancelled, said the post, because police had asked Aucklanders to avoid the central city. The Skycity Convention Centre was on fire. “I don’t want anyone breathing in toxic fumes,” wrote Dr Nicolette Rattenbury. “See you next month!”
On the second to last Tuesday of every month, in 118 locations around the world, people go to the pub to do maths. It’s an adults-only event, held on licensed premises where participants download that month’s “shout” — a sheet of problems posed by numerate compatriots in Milan or London or wherever — and work together on solutions.
The next time I tried to go to Mathsjam it was cancelled because the entire planet was having a maths lesson. Remember when you didn’t know what exponential growth was? Remember when you wondered whether maths would ever apply to the real world?
“Covid-19! Covid-19!” says Nicolette. She’s the organiser of Auckland meet-ups (there’s another group based in Christchurch). Her dark green T-shirt features Darth Vader and the caption “I find your lack of calculus disturbing”. She orders a glass of Elvis Juice Grapefruit IPA and takes a seat. It’s a small turn-out tonight, just two other people — Jonny (35, tie-dyed T-shirt, Amarillo hopped beer) and Louis, who has an Epic IPA, a ponytail and a T-shirt emblazoned with prime numbers. I ask him how old he is and he begins to count on his fingers.
Jonny: It’s a legitimate technique!
Louis: It comes up less often over time. For a while, you’re 17. As you get through the ages, there are very few thresholds left. How old are you? I’m over 18. I’m over 21. I could theoretically get car insurance, I think?
He is 29 and randomly hilarious. Did you know, for example, the famous mathematician Paul Erdos left Hungary aged 21 — the same year he learned to butter toast?
“He left Hungary when he could butter toast!” This session in the bowels of a Vulcan Lane pub is an anomaly. In June, New Zealand was one of the few places Mathsjammers could physically meet. The location on tonight’s downloadable sheet of maths puzzles speaks to a whole other set of problems: “Your home, yet again.”
“We do get quite a lot of people along who are mathematicians,” says Nicolette, a 45-year-old professional teaching fellow at the University of Auckland’s mathematics department. “We’ve had quite a few computer programmers, a couple of teachers ...
“We don’t just sit here go, ‘Well, obviously this is such-and-such a theorem that I’m using.’ It’s more logic and puzzle-solving and reasoning.”
She’s lugged a crate of maths accoutrements down the stairs. A Rubik’s cube, packs of cards and stacks of paper. I can’t see any calculators. Sample small-talk:
“You know a perfect riffle shuffle?” asks Nicolette. “If you can do that seven times, absolutely perfectly, you will get back to a perfectly shuffled deck of cards.
Jonny: This is something to do with the relationship between seven and 52?
Louis: Yeah, seven seems like the wrong number.
Nicolette: I’m sure it’s seven.
Jonny: You’re probably right.
Louis: I’m sceptical. If you said four, I’d be more convinced.
Nicolette (taking out her phone): Hey, Siri ...
Back in primary school, a teacher amazed me by demonstrating that when a number is multiplied by nine, you can add together all the numbers in the answer and they, too, would equal nine: 9 x 3 = 27. Also 2 + 7 = 9. Magic! “That,” I say, pausing for the laugh, “was the very last time I thought maths was amazing.”
Nobody laughed. “I still think that’s magic,” says Jonny.
Are people who can do maths different from those who can’t? Are they better at, say, saving or making money?
“I think they are better at understanding what you should do,” says Nicolette. “But that doesn’t necessarily mean they’re better at doing it.” Jonny: Impulse control is a separate thing!
Nicolette: We could, say, work out what the expected value is for every dollar that you spend on Lotto. My chances of winning Lotto are very small but, you know, that doesn’t stop you buying the odd ticket.”
Louis cuts to the chase. Anyone who buys a ticket is a complete idiot. The odds are so far stacked against a win, he can’t understand why anyone would spend the money. In fact, he says, if he won Lotto, “I’d be embarrassed that this has worked out for me so well.”
Based on this sample of one, the hypothesis holds: People who can do maths might be a tiny bit different from those who can’t.
Last year, the Programme for International Student Assessment report (which ranks the educational achievement of 15-year-olds across 36 developed countries) placed New Zealand students seventh in the world for science and eighth for reading, but 22nd for maths (down from 21st in 2015). Meanwhile, the most recently available results from the Trends in International Mathematics and Science Study (which tests Year 5 and 9 students in more than 50 countries) showed improving scores for New Zealand but still ranked us behind England, Ireland, the United
States and Australia for maths.
“Something that people don’t understand is that maths is creative,” says Nicolette. “People think of it as being a very dry subject.”
More crucially: “People feel proud to admit they are not good at maths. Nobody proudly says, ‘Oh well, I can’t read.’”
Jonny: You’re right. People weave that into their identity.
Louis: It’s like, ‘Yeah, Taurus, bad at maths.’ But
People feel proud to admit they are not good at maths. Nobody proudly says, ‘Oh well, I can’t read.’
— Nicolette Rattenbury
it doesn’t work both ways: ‘Good at maths and Pisces.’
Aquarian. Open to new ideas, happy to ask questions. And now I’m wondering — why do I wear my lack of maths as a badge of honour? Why are there so many variations on the “oh, numbers just aren’t my thing” statement?
“There are a lot of factors and one of them is societal discourse,” says Dr Lisa Darragh, lecturer in mathematics education at the University of
Auckland. “I did one research project where I looked at the way maths was talked about in Young Adult fiction books — and it was way more negative towards maths than it was positive.”
Darragh (who found maths references in 59 of the 136 books she read) said authors portrayed maths as nightmarish, inherently difficult and a subject to be avoided. Meanwhile, maths teachers were depicted as ridiculous, sinister, insane and even dispensable.
“If you wanted a baddie, it was pretty easy to call on the maths teacher!”
One surprising aspect of her research was how often the protagonists fell in love in a maths class. In 15 books, says Darragh, the romantic story was progressed through a specific classroom or project — once each in art, English and French, twice in science and 10 times in maths.
“I thought maybe the authors were drawing on this notion of maths being tense and then romantic tension develops?”
Darragh says there’s no single reason students develop “negative learner identities”. Theories include the impact of formal testing (where students feel labelled by the “brutal and definitive” results of a wrong answer) and parental influence, especially in modern-day parent-teacher interviews, which take place with students present.
“And the parent might say, ‘Oh, well I was never any good at maths.’ It gives permission to not be good at maths and creates this notion that maths might be genetic ... this isn’t helpful, because the first minute you get a bad mark you think, ‘Ah, my natural ability in maths has run out now.’
“But if we failed our driver’s test, for example, we don’t think, ‘Oh well, I’m obviously not a driver.’ You learn some more and you go again.”
Full disclosure: I achieved 51 per cent the second time I sat School Certificate maths and while I have a driver’s licence, I do not drive. Also, it took one explanation at Mathsjam, two independent Google searches and an additional interview before I could confidently explain the concept of a prime number. If I need to know a percentage, I ask a business journalist. If I need to understand why grown adults think maths is fun, I ask a data journalist. Here’s some insight from the Herald’s Keith Ng:
“I love being able to scrawl stuff on a napkin — all squiggles and diagrams and random letters — and then when I implement it in the real world, it turns out exactly as the maths tell me it should. It’s the power to see things that don’t exist yet.
“But getting it wrong is also fun. Sometimes instead of doing what you want it to do, it follows its own logic and ends up with a completely different answer. Tracing that thread and understanding how it got there is a good game.”
Coincidentally (or not, depending where you stand on Kolmogorov complexities) over on Twitter, Herald data editor Chris Knox had just posted, “I like today’s date — 20200707.” When I asked why, he said, “I like that it is almost symmetrical — that somehow makes it better than a fully symmetrical date. But 2 and 7 work better together than say 2 and 6.”
Obviously.
In New Zealand, maths is compulsory up to Year 11. To pass Level 1 NCEA mathematics, students must obtain a minimum of 10 credits. Kim Locke, a high school maths teacher currently working at the University of Auckland, says the basic high school numeracy course is “pretty much life-skills mathematics. You do have to be able to solve problems, but you’re allowed to use a calculator.”
According to the long-time classroom teacher, maths anxiety is real. In extreme cases, she says, students may be permitted to study the subject offcampus or outside a normal classroom setting, in an attempt to relieve their stress.
“There is this feeling of right answers and
— Kim Locke wrong answers and not much in between. Sometimes maths is taught that way, sometimes it’s perceived that way by parents or students.” In fact, says Locke: “Maths is a bit of a journey and an investigation. Mathematical thinking is about how you think about problems, rather than just getting to the right answer.”
Teachers are encouraged to introduce “low floor, high ceiling” maths tasks, which every student can engage with.
“So they’re investigative tasks, where even if you can only just enter them, you get some sort of success. But if you are able to push them quite far, you can achieve some relatively high-level things. Those feelings of success encourage you to go further. Participating in that sort of environment should, one hopes, start to reduce anxiety in some students.”
Back at the pub, the Mathsjammers have moved on to a question I thought would be easy. Which fits better — a round peg in a square hole or a square peg in a round hole? They talk radiuses and pi, angles and areas. It takes ages. But wait, there’s another part to the question. What about a regular n-gonal in a peg or hole?
An n-what?
Jonny: A 3-gon is a fancy word for triangle. Nicolette: A polygon is just a many-sided shape. A square is a regular 4-gon.
Jonny: So, do we think the answer is going to be different? Or is it a four-gone conclusion?
Mathematical thinking is about how you think about problems, rather than just getting to the right answer.