How maths can look for different people

One thing I have found interesting about tutoring maths across different year levels is how differently students can interpret the exact same idea. Before I started tutoring, I assumed that if you knew the maths, you could explain it to anyone. But in reality, I have realised that the explanation has to change depending on who is sitting in front of you.

A concept that takes a few minutes to explain to an older student might need a completely different approach with a slightly younger student. Sometimes I find myself changing the words I use, drawing something out, using a real-life example or even making the question much simpler before building it back up. It can feel strange at first because after all, I am still teaching the same mathematical concept, but the way I communicate it is completely different.

I remember one session where I was explaining a problem and realised halfway through that I was using language that made sense to me but probably meant very little to the student. They were staring at the same question without really knowing where to start. Instead of repeating that same explanation, I stripped it back to its core and explained what the question was actually asking in much simpler terms. Once that clicked, they were able to continue on their own.

This has made me realise that knowing something and being able to teach it are two completely different skills. As a student, I was mostly concerned about whether I understood the answer, but now as a tutor, I have to think about why someone else might not understand it yet. Because of tutoring I have learnt there is no single "correct" way to explain something. Sometimes being a good tutor means being willing to change your explanation completely when the first one does not work.