Let's Talk About Maths
This year I decided to stop thinking “I’m bad at maths” and to start acknowledging that I was taught maths badly and that put me off.
I stopped saying “I’m bad at maths” a couple of years ago after two things happened. Firstly, a friend said he found it perturbing how people in New Zealand could say “I can’t do maths” with humourous pride in front of all their colleagues, while no one would say “I can’t read” in the same way. Secondly, the person in charge of numeracy at school said more or less the same thing to the collective teachers of our school and asked us to reflect on what message that sent to students.
The second statement wasn’t so impactful because I had spent years feigning enthusiasm for swimming and maths so that I wouldn’t put my daughters off either thing. What my friend described though was something I had done for about thirty years.
At the time this made me think about our collective cultural conditioning here in New Zealand. Somewhere along the line we have broadly agreed that maths is hard, and that not being good at it is normal. You can tell it is a cultural idea by getting on a plane and travelling to Asia. In Asia this is not the general view. We know this because in New Zealand we racially profile Asian kids as being “good at maths.” Which is stupid. Is the Asian brain different? If we accept that it is then we’re on the slippery slope to giving all Māori kids guitars and all Pasifika kids a rugby ball. So, let’s not do that.
If everyone can learn maths then why don’t we in New Zealand?
Bad curriculum and low cultural expecations.
The first school was experimenting with the radical notion of open plan classrooms. I remember it as chaotic. If maths was taught, I missed it. After a year of that I switched to a private boys’ school until Year 8. This was very traditional in its approach and they got half of maths teaching right. The bit they got right was the relentless focus on learning basic number facts until we had them automatically. The bit they got wrong was using the “sink in shame or swim” approach. (About swimming please see this post.) I do not have a natural affinity for maths, we all sit on a continuum in all subjects, and I needed some more time and more practice with some of this stuff, but time and support was not what this school did.
We can all remember crucial moments from school. These moments become emblems; symbols we use to define ourselves. In my Standard One class we did times tables drills. We all stood up and recited the times table in a chain. If you hesitated you sat down. It was shameful to sit early, and wonderful to be last person standing. Of course I hesitated early, maybe I was first to falter, and maybe it was a simple sum. The teacher made her displeasure clear. That was an early blow against maths for me.
When I reflect on it, honestly, in front of you on this page: I am still a bit insecure on my times tables. Once we get into the sevens and eights I can still falter. I can get there in a few seconds but I don’t have the automaticity that would have helped me with the next stage in the maths learning hierarchy. Now that I listen to a podcast by a maths lecturer (life is full of surprises) it is clear to me how - in her words - “relentlessly hierarchical” maths is. You need to learn A to do B, B to do C, and so on. Which means that I, and a lot of people, who got a bit iffy on maths facts at a certain point (fractions is where I get seriously clueless) are ruled out entirely by the time they get to algebra. As a result I simply sat in maths class in Year 9, 10 and 11 and passed School C purely on the basis of the drilling I had picked up from primary and intermediate.
Take two in my maths journey was watching my daughters go to school and do maths. Daughter one survived a numeracy programme due to a natural aptitude for maths and being friends with a small cohort of bright girls who were similarly inclined. Looking back on that programme it was pretty ropey. It was a multiple strategies approach with hallmarks of discovery learning. The fact that number one daughter did well was lucky. For quite some time the narrative was that she was good at maths, but she became a bit unstuck in Year 11, and then was out of her depth in Year 12. Looking back I beleive it is because she was left to explore too much, and not directly given the methods she needed, and then made to practice applying those methods.
Number two daughter had a worse time of it. The problem was clear in intermediate as the students were left to self select into groups working mostly independently to solve different types of problems. Her confidence collapsed. There was minimal guidance. It was the opposite of my experience at primary school: a safe, friendly environment in which it was ok to drown. How about you just go back to the paddle pool and don’t worry about actually learning how to swim?
Being privileged, anxious white middle class parents we sent number two daughter to KUMON. This is a Japanese model which is relentlessly hierarchical. It has given number two daughter lots and lots of confidence because she has proven week after week that she can do maths skills that become increasingly complex. She is near enough top of her class in maths in Year 10. My problem is with the people who run it. Not supportive and not friendly. They remind me uncomfortably of my Standard One maths teacher. On a side note, it is noticeable that most of the clientelle are Asian. Cultural expectations of maths are in the flesh.
In a subject like maths that is so hierarchical, and represents one of the great achievements of humanity’s collective insight, why has a methodology that is so ineffective flourished for so long? If we are standing on the shoulders of giants why are we pretending that we aren’t? If there is a very, very sensible way to teach maths that those giants have provided why are we telling the students “don’t look down at what you’re standing on: just have a go at spontaneously inventing maths for yourself!” As I said to another friend, sitting at the time at her son’s swimming lesson, it would be like chucking everyone into a pool and saying “invent swimming!”
We clearly need to take the well established route that takes students from addition to algebra and couple that with a supportive approach. I understand the concern about making students feel bad. I remember my Standard One maths class 47 years after the fact. Here’s what I know: feeling like you can do something you couldn’t do before is the best feeling you can have in a classroom.
I handed back the post test results in my religion class at the start of this week. It was a test out of 16. The average score on the pretest was 2. The average score on the post test was 12. Regardless of all previous results, students who were in class 90-100% of the time got an average of 89% on the post test. The EL student who got 0% on test one got 50% on test two. The vibe in the room was great. Students wanted to take their tests home. This is Year 13 on some random nine lesson sessions on Judaism. Being able to do something you couldn’t do before is awesome. If we are concerned about students feeling good (and we should be) then we need to teach them really, really well.
Coming to the realisation at 52 that I am not naturally bad at maths is actually quite moving. Even if I have joked about it, I have also felt a little ashamed about it. What we think about ourselves is so powerful. So constraining or so liberating. We teachers, we need to be the liberators. What a job that would be.