# What were they thinking??

I do an increasing amount of work in primary schools and with primary school trainees developing maths subject knowledge and pedagogy. Over the last few years I’ve managed to blow my own mind many times just imagining the beginnings of concepts being developed in children. At secondary level (11+), most concepts at their basic root are pretty much embedded and understood or at least taken as ‘the way it is’. For example, a square is called a square, and the number after ten is called eleven. When I wrote the book ‘Yes, But Why?’, I really enjoyed putting myself in the position of a student being told all these strange and mystical maths facts and I tried my best to explain them to make them make sense. At a younger age, concepts must be even more mind boggling at first. An example I’ve used before is counting.

We count in base-10 (ie we use 10 symbols (0-9) and then start combining them. Imagine learning this for the first time, and getting to the number 9, then being told we start to use them all again. It’s weird right? And why do we use ten symbols? Why not five, or sixty? Does everyone count using the same system? (spoiler: no). These are thoughts we as adults probably don’t have, but they fascinate me. Who decided to call a square a square and not a quadrangle or a a tetragon? What were they thinking? Why are we using 360 degrees, and why are they called degrees? Where do these weird mathematical words come from? We’re used to using terms like polygon and acute angle, but these words are weird! “I’m going to find the mean of this data set”. The what?? Who decided to call it that? I “can’t subtract 3 from 1 so I need to borrow…” – you’re doing what now?? Can I borrow from elsewhere? Can I just move everything around? Also who decided that we should stack numbers like that to add or subtract them? What were they thinking? How did that idea become so popular?

Trying to think ‘like they do’ is a good first step into empathising with how abstract even the little details can be in mathematics, and how easy it is to misunderstand or misinterpret things. Furthermore, it’s a great exercise in testing your own subject knowledge, and figuring out what might be beneficial to incorporate into your own teaching and explanations to prioritise what must be prioritised – making maths make sense.