This post continues the story from my last post about my struggles with maths as a child, into adulthood, and even as a primary school teacher expected to teach it.
Whilst teaching at primary, I started noticing that we teachers make a lot of assumptions about what children should already understand by the time they reach a certain stage. Surely a child who can recite their tables up to 12 x 12 perfectly will have a good understanding of multiplication – won’t they?
Not necessarily, it seems. It’s possible to learn something by rote without having a real understanding of what it means, as I discovered with a small group of year 6 girls who couldn’t seem to grasp concepts such as division and fractions.
I took them right back to basics and gave them counters to put into ‘arrays’.
What does 3 x 4 actually look like? And how can that image help with the understanding of division?
It was like seeing a lightbulb come on when we did this. Despite being able to recite multiplication facts, these children hadn’t realised how this linked to other aspects of maths – and this was what was holding them back.
It was this revelation that made me reflect on my own struggles with maths. I’d diligently learned my tables at school. (Those were the days when teachers could give you a clout for not doing so, and I was more wussy than lazy). Still, that didn’t prevent my head from being the target for the flying board rubber: I was unable to relate that tables’ knowledge to division and, later on, to fractions.
You see, I’d learned how to do something without understanding how it worked.
Same with long multiplication and long division at secondary school: I knew the procedures to follow, but didn’t understand why they worked; this meant that I couldn’t recognise my error whenever I arrived at a totally outrageous answer. Which happened a lot.
Many of the methods children learn in primary school seem long-winded to parents who remember the methods the quick were taught. But often these modern methods help children to understand how numbers work. (And those modern methods help quite a few non-maths-specialist primary teachers as well – myself included!)
One telling indictment on the state of maths teaching in our schools was that, during my second year of teaching, I was given the job of leading maths for the whole school. Yes, you read that correctly: someone who was scared of maths – and was often only one step ahead of the kids, having sat up the whole night before a lesson to learn how to teach it – was responsible for implementing maths procedures within the school and for training other members of staff in those procedures.
The pressure almost finished off my teaching career.
Teaching English had always been my real passion, so eventually I left primary teaching and became an English teacher at a secondary school. I believed that I’d never need to look at another maths problem for the rest of my teaching career. English teachers don’t need to teach maths …
That belief was quashed shortly after I was made form tutor for a class of Year 11s.
The year leading to GCSEs is horrendous – for pupils and for teachers. Despite being an English teacher, I found myself becoming a sounding board for a group of fifteen- and sixteen-year-olds in my form for whom maths was a complete mystery – just as it had been for me at that age. Much of what they said was familiar: ‘I don’t get how/ why that works’; ‘I can’t remember that method because it doesn’t make sense’; ‘I feel stupid having to ask the same thing over and over again’; ‘My maths teacher has given up on me because I’m never going to get a C’. ‘I’ll never understand maths …’
Before I’d really had time to think about it, I had a group of pupils from my form meeting me after school a couple of times a week whilst we went through some of those basics I’d gone through with my primary pupils. We used pens, sweets, bars of chocolate, crisps (the caretaker wasn’t happy about that one) – anything we could count or use to represent something that could be shared/ cut into fractions/ put into ratios …
Soon we’d moved onto stuff I really didn’t want to think about, and I admitted to my students that I wasn’t teaching; I was learning this along with them. And the pressure on me increased as pupils from other forms had began turning up to these sessions.
We used weighing scales to show how algebraic equations work. We nicked Blu-Tac from corridor displays to make balls that we could then investigate to understand how to calculate the surface area of a sphere. We pilfered grapes, strawberries and tomatoes from the staffroom fridge to demonstrate conditional probability. And I completely exposed my maths-dunciness the first time we tried to recognise quadratic graphs (but we all benefitted from my dreadful mistakes – and had a good laugh along the way. Well, they did!)
That year was a huge learning curve for me, as well as for those young people who’d worked really hard, and who’d helped me more than I ever admitted to them at the time.
By the time I left classroom teaching in 2012 (thanks, Gove!) I’d learned enough about maths to know that I could have done my GCSE again and performed extraordinarily well.
Maybe one day I’ll do just that.