On Being 'Good' at Mathematics

I've no idea what it means to be good at maths. I studied the topic at university, through to a PhD, which can certainly be an impressive qualification to throw around. But don't be fooled: I've no idea what it means to be good at maths. Instead, what I *can* tell you, is why I enjoyed studying it.

First, some context. I'd like to talk about the young adults that I've mentored in the subject.

These students I've worked with have been extremely bright and responsive, and pick up the top-level concepts of the syllabus pretty swiftly. As visualisers, as problem-graspers, they are SO GOOD. But after that, their basic arithmetic & algebraic processes tend to be lacking. So even after correctly codifying even a complex problem (such a huge skill to have!) transformations toward a solution hit all kinds of stumbling blocks, which is often why I've been paired to work with them. Maths gets hit particularly badly if someone is robbed of the fundamentals, and those impacts can resonate severely down the line.

Crucially, this nukes the student's confidence. Because they've failed to reach the answer, they assume they're 'bad' at maths. But it's more that they have so little experience - both of hitting fundamentals and of processing mistakes - that minor slips feel like fatal crashes. I love working with these willing, capable (and often very anxious) young adults, but we only have so much time together. As much as ticking off exam crtieria, the goal is to make sure we deal with mistakes properly: Stop, identify what went wrong. We don't move on until we spot what went wrong. No exceptions. Found the mistake? Great, NOW KEEP GOING!

KEEP

GOING

So much of teaching is about simply just being there with someone, to correct the wobbles as they discover their own sense of momentum.

And maths, for me, was never about this perfect, machine-like precision of behaviour, of robotic recall and lofty detachment. It was about using your mistakes to improve your understanding, something which it's *brilliant* for - it can be tremendous scaffolding for brains - but we hardly ever discuss this aspect of it. So much of our perception of the topic involves a circus-like fascination with misrepresentative extremes: "Roll up, roll up, here's a 5-year-old who can perform insanely hard calculations in their head, as easily as breathing! My my, maths is so alien and impenetrable!"

My experience couldn't be more different from the performative sideshow that would often couch the topic, if it ever appeared in the news. And yet, if I tell you that maths can be emotionally engaging, I'd probably sound even more unbelievable.

Here's the thing about mistakes: You *will* make them, all your life, that is never in question. But what you can control, is how you respond to them. And maths felt like such a tangible framework for exploring this process, that I started to really enjoy it. Realising the pattern behind certain errors could show you exactly where to best apply your concentration, while also helping deal with the emotional backlash of frustration and anger that we hurl at ourselves whenever we slip up. After six years of study, that's the most important thing I took from maths. That's why I enjoyed it.

I don't care whether someone wants to progress in maths, or not. Entirely up to them! But I hate that people consider themselves unsuited to the topic, because they've received a poor grounding at an earlier stage, and because we have such a dysfunctional perception of how we can engage with the topic.

For me, maths is a form of communication, but one that's just as potent for entering dialogue with yourself, as with other people. Good communication relies on a mutual appreciation of limitations, and this principle applies as much in maths, as it does in any language, or in any methodology for interpreting the worlds that are around us, the worlds that are in ourselves, and how the two may interact. Of course, for many people, for various reasons, it may not be a language they can engage with, and that's absolutely fine.

There are also lots and lots of people who *can*, but are denied a chance to ever know it.