The problem of mathematical education

Photo by Travis Nguyen / Photo Editor

Why the way mathematics is taught does a disservice to its students

“What are you studying?”

This is the question all university students continuously face. It’s an easy icebreaker, a well-meaning inquiry, a pointed question and just about everything in between. 

As an Arts & Science student, I have a lot of flexibility in what courses I can take. At the moment, most of my courses are in math or political science. Without fail though, whenever I explain this to someone, they immediately latch onto the former. I’ve gotten reactions ranging from horrified, “You’re taking more math courses?” to strained comments such as, “Wow! I could never. But good for you.” 

I can count on one hand the times I’ve received an enthusiastic or an equally excited response. Because I do find math exciting. That’s why I’m studying it — not because I’m exceptionally bright or talented, but because even when I find it difficult and frustrating (and I often do), I enjoy math.

What I don’t enjoy, though, is the way it’s often taught. Math, like any field, relies on its students having a solid foundation. You need to be able to count, then you need to be able to add, subtract, multiply and divide, in the proper order, and then you need to understand functions and transformations and so on and so forth. 

If you’re missing even a portion of one of these building blocks, it’s incredibly difficult to move forward. That’s likely why there is a strong emphasis on this kind of computational learning in mathematics, on memorizing multiplication tables, formulas and theorems. But to have a truly strong foundation in mathematics, you also need to be able to solve problems, to think and reason mathematically. 

But this deep comprehension is more difficult to teach. It’s not easily tested and it takes different students different amounts of time to arrive at this point. When you only have so many weeks in a semester to cover a large range of material, it’s not always possible to help everyone achieve this understanding.

This kind of deep comprehension is why I love math. I enjoy understanding the theory behind computations, deriving theorems and proofs and working backwards to see how and why certain formulas and theorems work the way they do. It’s thrilling to finally figure out the way to solve a problem, to watch as all the pieces come together, all the numbers and variables lining up and falling into place. 

Most of the work I do, at the Silhouette and otherwise, involves this same kind of problem-solving: working with the pieces of information I’m given, figuring out how to find the pieces I’m missing and coming up with a solution. It’s this deep comprehension that allows me to connect mathematics to the other areas of my life, but it’s also the one consistently missing from math education. 

Over the years, there has been debate, particularly at the elementary school level, about how we should approach mathematical education. There is the traditional approach, which has been heavily endorsed by Premier Doug Ford and his government, which relies heavily on computation and rote memorization. On the other hand, there is the more recent “discovery” or inquiry based approach, which instead encourages problem-solving and experiential learning. 

Most math teachers would argue that you need a mix of the two to ensure success and I would agree. Computation with comprehension clearly isn’t working, but comprehension needs computation to be clear and concrete.

But that’s still not the way it’s typically taught. In my experience, math education is also often fragmented, with approaches varying from teacher to teacher and curricula from place to place even within Canada.

Additionally, the topics themselves are rarely linked together in a cohesive and clear way that highlights the remarkable network of connection that actually exists between them and the rest of the world.

All of this comes together to contribute to the most insidious and damaging belief about mathematical education: the myth that you’re either good at it or you’re not. 

The number of times I’ve heard people say “Well, I’m just not a math person,” or “Math isn’t for me,” is too many to count. When I ask people why they say this, they’ll give me an anecdote, usually from elementary school, sometimes high school, about how they couldn’t figure out fractions or understand derivatives. 

Students are sorted into these camps early and often get stuck within them because this myth allows no room for improvement or growth. And when we not only deny students the opportunities to improve, but also teach them from a young age there are certain things you just can’t get better at, this is where the damage is done. 

Developing a strong comprehension of mathematical concepts and understanding how to think mathematically are key to helping students improve and ultimately debunking this myth. I’m not saying everyone would love math if only they could understand it. The same way not everyone loves English or Chemistry, there are going to be people who won’t enjoy math but I think a great deal more might if they could see it this way.