When 5 minus 3 doesn't equal 2

I am incredibly fortunate to be self-employed in a one-woman company that designs, produces, publishes, and distributes card and board games for the family and casual market. There is no pressure on me to generate big profits in the short term, so I can grow my Cheeky Parrot Games at a manageable pace, in a way that aligns with my values, and allows me time to pursue other interests, especially an involvement in progressive politics.

Recently I was promoting my games to attendees at the Primary Maths Association's yearly Auckland seminar. The PMA kindly allows vendors to sit in on the keynote speech and workshops and hence I had the enormous good fortune to sit in on a workshop run by Steven Arnold of AUT. Steven's talk, the Ideas Within Mathematics, Sustainability and Ecology promised to pose the question: what does the narrative of mathematics have to offer the human understanding of our world in the context of sustainability? but what lured me in was his rather cheeky take on subtraction:

The idea of subtraction is to take away. We can't take away in a finite planet. If I have 5 lollies and 3 are taken away, how many lollies are there? 2 is the traditional answer, but 5 is the correct one. There still remain 5 lollies even if you can't see them.
This he extrapolated to an even more relevant topic: If I have 5 rubbish trucks and 3 are moved out of sight, how many truckloads of rubbish are there? 5.

I was so taken with Steven's presentation that I would like to paraphrase some of his points, interspersing my own thoughts and relating it back to the industry I belong to. Steven began by inviting us to judge our own ability with mathematics; would we place ourselves in the top, middle, or lower third? Curiously in a roomful of maths teachers, only two or three raised their hand for membership in the top tier with the majority, about ten people, nominating themselves for the middle, and the remaining two or three choosing the lower group. Steven commented that our idea of our own mathematics ability is fixed at an early age, and those who self-identify as being poor at maths, besides usually being female, can also usually remember a precise incident in which they were shamed or belittled. Indeed, one attendee vividly and painfully recalled her work being held up by her teacher in front of the whole class as an example of what not to do.

Steven questions why, when so many subjects are worthwhile, mathematics is given such pride of place in the curriculum. No one would ever say, as they might for drama, that "we'll fit in a bit of maths after recess on Friday afternoons". The seductiveness of maths is that there are always right answers, it is black and white, and it can be easily measured and scored. Maths lends itself to the patterns the neurotypical human brain is primed to seek out.

One reason why some girls struggle with maths and boys often embrace it, is because girls tend to be more verbally precocious when they arrive at school. We recognize that language, unlike maths, is loaded with shades of grey of nuance, tone, and context, not to mention inconsistent grammar and spelling rules. However, from Steven's perspective, maths is a language like any other, beautiful and worthwhile, but at the same time a fallible and incomplete way of reflecting and capturing reality.

Certainly there is a tyranny in thinking that bigger is better, reflected in the thoughtless comments we make to children like, "Wow, now you're seven," as if that is better than being six years old. Height works in much the same way; tall is valued more than short. And of course test scores are the biggest tyranny of all. Is the child who scored 80 any better, smarter, or harder-working than the one who scored 75? What is the rest of the story? Perhaps the child with 80 has been on a slow downward slide when that 80 is compared to marks earned in the 90s from earlier in the year. And perhaps the 75 represents a spectacular effort from a child who doesn't speak English as a first language, who has less time to study because of responsibilities at home.

Furthermore, there is often no meaningful correlation between a number and the experience it might be expected to capture. The temperature scale illustrates this. Do 10 degrees feel like half of 20? Is -20 degrees the opposite of 20?

Perhaps the most tyrannical concept of all is the equals sign. Steven, who is a passionate Montessori advocate, displayed some of the materials used with young children: alt Would four of the shortest rods truly equal the one that is four units long? They can't be used in all of the same ways.

Maths underpins economics, considered by its practitioners to be "the most scientific of the social sciences". Economics has gained its own pride of place at the university level*, often to the detriment or even complete sacrifice of humanities and hard science courses or departments. Neoliberal economics concepts (trickle down theory, deregulation of financial markets and industry, privatization) underpin and justify some of our most disastrous politics. So isn't it high time to take a critical look at mathematics?

Indeed it seems high time to take a critical look at how we educate our young, full stop. It seems clear that blindly continuing traditions that are, after all, just 150 years old but arose from a vastly different era, hasn't been serving humanity well, as we continue to pollute and overheat the planet at an unprecedented pace and to kill each other more directly in pointless and costly wars.
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In the Chain of Command double episode of Star Trek: The Next Generation, Cardassian Gul Madred seeks to break Captain Jean-Luc Picard's will, by insisting Picard say he sees five bright lights.

I suspect Steven's message sat uneasily with many of the teachers present. After all, it is unlikely they entered the profession to crush children's spirits with a view to conforming them to fit into a dysfunctional society. It is also unlikely that individual teachers with bills to pay can do much to reform the educational system; for that reason I hope Steven will be able to bring his message before policy makers. They might be advised to look to Finland as a model. Finnish students are high achievers, to be sure, but they are nourished in a system that is so nurturing, de-politicised, and non-competitive, that the Finns were happy, off-the-record, to fall from the number one spot in PISA testing because they believed that their fifteen year-olds were experiencing too much pressure to maintain that ranking.

I think there is also something to be learned from the evolution of board games over the past few decades.

In preparing for the PMA seminar, I pondered the five key competencies the New Zealand curriculum is meant to enhance in students:

  • Thinking
  • Relating to others
  • Using language, symbols, and texts
  • Managing self
  • Participating and contributing

and realised that a good modern card or board game exercises all of these.

Unfortunately, although there is an avid board-gaming community in New Zealand, for much of the greater public "board and card games" still conjures up sentimental classics like Monopoly, Risk, Scrabble, Hearts, and Euchre. This is unfortunate because modern board games leave these old titles in the dust when it comes to creating an enjoyable collective experience and rewarding strategy far more than dumb luck.

Many of the pioneers of modern board games come from Germany, a country that did some soul-searching in the wake of World War II and concluded that children needed more uplifting playthings than toy soldiers and games where one person triumphs by eliminating all the others. Settlers of Catan, invented in 1995, was one of the first of the new "Euro" games to achieve success and popularity beyond Europe. There are three hallmarks of a Eurogame. First, they are aesthetically pleasing, often with custom wooden bits which are fun to stack and fondle during down time. Second, the games often entail an element of cooperation instead of pure dog-eat-dog competition. In round one, A might trade resources with B, shutting out C, but in a subsequent round, A might ally temporarily with C to achieve a mutual goal. Finally, no player gets eliminated. All are involved until an end point is reached or one player reaches the winning conditions. For the losers, there can often still be the satisfaction of achieving particular goals, like completing a route connecting two cities in Ticket to Ride or finishing off a large city before the last Carcassonne tile is drawn, which means it will earn more points.

Just as the teachers may have been discomfited by how Steven's talk challenged their practices, exposure to Eurogames does not necessarily lead to their being happily adopted, as I've learned when I've tried to persuade my friends in the competitive Scrabble community to try something--anything--else. And it is fair to say the staggering selection at a well-stocked games shop can be overwhelming, causing people to reach for the tried-and-true, however flawed it may be.

It will no doubt take much political will to overhaul the education system, but thankfully in the meantime parents and teachers can cast a critical eye over the toys and games they choose for the children under their influence, selecting ones that will foster the skills we need to live more collaboratively, with a lighter footprint on our planet.