I’ll confess something – I harbour a lot of unresolved annoyance at my maths education. Growing up in the United States, I was subjected to a the type of maths teaching that was essentially focused on telling what to do and how to do it (in a particular way) – but had no focus on why we would want to do it in the first place!
Consequently, I learned how to find the roots of a quadratic equation, but not what a root actually meant. The result, of course, was that maths were harder to learn and deeply boring. It was only much later, after university, that I decided to reteach myself what I’d learned (in order to prepare for the GRE) and in doing so began to understand maths for the first time.
One big thing to recognise is that maths are simply a version of logic, using numbers and symbols rather than words. Maths aren’t about numbers at all – not really. They’re about relationships – and the more clearly we see the relationships, the easier maths become.
To explain this, I often tell the following story. Like all stories, it’s a lie – but it uses a lie to tell the truth.
Albert Einstein was not the world’s greatest mathematician. By that, I don’t mean to spread the b.s. idea that he was bad at maths – he was fantastically better at it than I will ever be, certainly – but maths themselves were not his forte. After all, he was a physicist! Nonetheless, while working on his theory of relativity, he was confronted by some very difficult maths indeed, maths that he couldn’t do on his own.
So, in the way of all good scientists, he asked for help from others who knew better, corresponding with the greatest mathematical minds of his generation. And with their help, the the theory of relativity was born.
So we might ask ourselves – if Einstein didn’t do it alone, then why does he get all the credit?
I’d argue this: getting the maths right is one thing; knowing what the maths mean is something else again.
When you’re studying for a standardised exam, you need to rewire your brain to think of maths in terms of meaning: the more clearly the maths become a story, the more obvious what it all means, and the more simply you can eliminate answers that are simply insane, or absurd, or just plain wrong.
So – be like (my purely fictional version of) Albert Einstein: focus on the why.