It’s 2016, and I’ve been swindled into a math competition.
I’ve always been “good” at math. The monotony of it suited me; the rote memorization of formulae and obvious pattern recognition, while anxiety- inducing in others, came to me instantly. It also meant that, once I understood something, I also didn’t care to spend an hour and a half doing problems that varied on such simple themes. And so, in Grade 10, I had fallen into the habit of looking at the class lesson plan, and then spending the rest of my time reading on my phone, only sometimes looking up to answer questions or write tests that came back with perfect scores.
And so, my Grade 10 math teacher, frustrated with my complete and utter lack of care and respect for her class, decided that the best way to keep me off my phone was by signing me up for the University of Waterloo’s CEMC Mathematics Contest. It was a simple competition, she had told me, where they would test students on their math skills. It seemed easy enough; I was good at math. Surely, it couldn’t be that hard.
I took the test in February. I had not done much in the way of preparation; a few lunch hours were spent doing photocopied sheets of Nelson textbook problems deemed ‘too hard’ for my small class. It was on one of these lunch hours that my math teacher handed me a stack of official-looking papers, a small notebook, and told me ‘good luck.’.
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The thing about math competitions is that they suck.
It’s not the fact that they’re hard; it wouldn’t be a competition otherwise. It’s rather the questions themselves, and how you are expected (or, usually, not expected) to go about solving them. An example, derived from my aforementioned math contest:
In the diagram, P Q is perpendicular to QR, QR is
perpendicular to RS, and RS is perpendicular to ST.
If P Q = 4, QR = 8, RS = 8, and ST = 3, then the
distance from P to T is what?
Looking at the question from a distance, it’s clear that no Grade 10 student, armed to the teeth with primary trigonometric ratios and the Pythagoras theorem, would be able to solve this question using what they’ve been taught in class. This is a question that requires more than rote memorization; it requires something that has been scrapped from the mathematics curriculum altogether. Creativity.
From the moment we step into a math class, we are told how the world works. We are given formulae to follow and notation to use, and are punished for any slight deviations regardless of the outcome. Jargon and definition become paramount, when in truth they are simply shortcuts for longer explanations. There is no room for discovery, no room for play or abstract thought. Why, then, are teachers shocked when students complain about such a militant subject? A good example of this is basic geometry. Here is a basic problem:
What is the area of the triangle inside the rectangle?
In true high school fashion, the majority of us would begin to reach for our pencils, aching to write down an x, a y, or an △ABC. Notion and jargon; both useless in the grand scheme of actually answering the damn question. Rather, reach for your pencil and do one thing:
With a single line, we’re able to see two rectangles, each with a triangle taking up half of its area. Therefore, the triangle must make up half of the rectangle! With that observation in mind, students are then led to the universal conclusion that the area of a triangle is the base, multiplied by the height (area of a rectangle) divided in half. This is what mathematics can be; a simple puzzle followed by an elegant conclusion; an exercise in logical thinking. But instead, students are given the formulae up front and are then subjected to a barrage of numbers and mind-numbing questions. There is no work to be done here. The hard part was done for you.
What we fail to show our children is the actual point of mathematics. When a child asks, “Why do I need to learn algebra?” adults reply, “So you can use it in high school.”. When a high schooler asks, “Why do I need to learn calculus?”, they are met with “So you can use it in university.” And it is only then, fourteen years after their first math lesson, that they are given the good news that they never have to take a math course ever again, if they so wish (and boy do they wish). There’s a reason math departments are so small-and don’t get me started on the graduate programs.
And the few who stay are suddenly shown that – to their absolute horror! – math is not about being able to follow orders, but being able to think creatively. It’s being able to pose questions and throw together answers based on past experience and present inspiration. How many children, creative, intelligent children, have been turned away from mathematics, simply because they refused to conform? How many marks have been deducted for improvisation, even when the method was sound? They are instead filed into the more ‘inspired’ jobs, such as art or music, as if integration wasn’t invented because a musician thought he was being scammed on wine barrel prices. Math is a reactionary subject at heart; why do we teach it as if it is laid out in stone? If Newton could come up with calculus to figure out how planets orbited the sun, should we not also be giving out students room to make their own, smaller discoveries?
There are teachers out there who understand this,; ones who present problems without giving students any sense of how to even begin to solve them. And while these methods can bring out the genius in a class, they are also wholly inefficient with the current “teach to the test” atmosphere that has engulfed our school system. When you’re given 30 students and 194 days to teach them, you can’t blame them for not going beyond their lesson plans-their paycheck is on the line! The first teacher I ever met who truly embodied this idea of discovery in mathematics was my physics teacher-a subject unconstrained by the horrors of the standardized test. To allow for such creative freedom to take hold, a complete overhaul of the entire mathematics curriculum would need to occur.
Perhaps this might be of interest in the next provincial election.
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My Grade 10 math teacher shared my results in March, looking unbearably proud for someone who wasn’t of any help. I ended up somewhere in the 80th percentile that year. Not bad at all, considering I had absolutely no idea what I was doing. Halfway through the test, I had realized that I would have to use some innovative thinking to complete the contest,; something I realized I had a small, quiet talent for. That giddy, light feeling of puzzling out a new and foreign problem lingered for days after the competition, and I ended up participating in another competition years down the road; the Sir Issac Newton physics exam, which I did considerably worse in. But the contest had served its purpose; it got me thinking about math, and the wonderful things it can bring about if we let our minds wander.
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Remember my math contest question? It’s not hard to solve-all you have to do is think a little outside of the box.
By completing the square, we are given a much easier puzzle to work with. We know RS = 8 (cm? mm? It doesn’t matter!), so QU must be 8 as well. ST is 3, so the new line UT must be 5. PQ is 4, so PU must be 12. We can then use Pythagoras’ theorem (we don’t have to reinvent the wheel every time, do we?) to figure out the distance from P to T is 13.
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My math days are long behind me; I burned my calculus textbook on a gorgeous summer day in 2019. And yet, I continue to cut my teeth on puzzles. I am now a genetics research student, constantly looking at new problems in science and the interesting, creative ways we try to solve them.
