Having enjoyed studying Mathematics at Queen Mary College, London University, Jeff became a maths teacher in 1981 to share his enthusiasm for the subject with others. He remained at his first school for over 33 years, gradually moving into school management. In 1984 he became involved with Cambridge Assessment and still enjoys the assessment process, looking to ensure that candidates have fair and accurate outcomes.
Jeff feels fortunate that in 2014 he became involved with the training and support of teachers for Cambridge International, helping others understand that teaching is more than just the sharing of knowledge. He feels privileged to have been able to visit many different countries and meet other teachers with whom he shares this enthusiasm. However, when he is at home, his weekly highlight is the Norfolk Broads Concert Band rehearsal.
1. What’s your earliest memory of doing mathematics?
Learning my tables at a one-room school back in about 1963 or 1964. The school was run by one lady who did everything, and we were all in there together. It was just mornings, but one of the things we did was learn our tables on a regular basis.
We also did things like practise drawing reflections by having a grid and copying what she did on the board, then putting it onto our grid. So that’s my earliest maths.
2. How has mathematics education changed in the time you have been involved in it?
It’s come back to where I started, because when I started teaching back in 1981 — this is the point where I start feeling really old! — it was quite an investigative approach. The school I started teaching at used the Cambridge Schools Maths Project material which used a lot of investigation, and that developed really good mathematicians who problem solved. Our weaker students would come along and have a really good lesson with us where they wouldn’t cope in any other subject – that was the level of engagement with that investigative approach. By the early ’90s, my Year 8s could solve quadratic equations without thinking about it, and they’d done it through an investigative approach and hadn’t been taught how to solve them directly.
But then I saw how much weaker students became at maths when we changed our style, because they were being told how to do things rather than working them out. It was not a pleasant experience because we were trying to do things and encourage our students to adopt a style of mathematics or a style of learning that wasn’t appropriate.
Now I'm really seeing it go full circle, and that took 35 years. That’s how it changed for me: I saw what was a really good way of doing things disappear and then saw it become quite difficult to engage students. If you’re not good at maths or don’t enjoy maths, then you don’t want to be there. But that’s starting to change again in that there is much more engagement. A lot of my work is involved with the international side. I do training for international mathematics, and it’s quite interesting to see how different approaches in most of the countries where I do training compare with how we do things here, and the desire to do much more interactive learning, much more practical learning, linking it into things and changing to that. You do maths, but maths isn’t the whole point. The maths syllabus isn’t just about learning maths; the maths syllabus is about developing a good citizen, and you’re doing maths as a side bit. So, it’s a different way of doing things.
3. Tell me about a time in your career when something totally flabbergasted you.
It was when I was doing some training in Pakistan, where we were looking at the approach that the school was taking. What really flabbergasted me was that the teachers wouldn’t believe that their management wanted a different style of teaching. I spent a week explaining the concept that they were being asked to use their professionalism, they were being asked to do things, and it took them the whole week to get there.
That was the thing that really surprised me: when you’re telling people something that they can do and they don’t believe that they can do it. And then there's that sudden shock that, yes, what you’re saying is good.
On the very last day, they gave us a gift, which has stuck with me in my memory. It was a bird cage that they had manufactured and had attached the Pakistan eagle emblem to the top of it, with a little poster which said, 'Thank you, Sir Jeff, for setting us free from the cage.' That gift really knocked me absolutely beside myself because they had spent quite a lot of effort manufacturing it.
4. Do you practise mathematics differently in company?
I think I’m probably less positive about what I can do when I’m in company. It’s the uncertainty factor because I think sometimes I suffer, like many people, from imposter syndrome, where you’re doing something and you think, 'Actually, no, I’m not sure here.' So instead of putting myself forward as the person coming up with the solutions, I ask everybody else what they think.
I’m quite happy working by myself, but if I’m with other people, I’m much more reserved. So for me, the question is: Do I want to go in and do maths with other people? Actually, on the whole, no, because if there are other people, I don’t want to do maths: I want to do something more social.
5. Do you think a brilliant maths teacher is born or made?
I think it’s both.
I think you actually start off with a desire to share what you like doing, which is where it comes from; you understand that you like what you’re doing, and you’ve got confidence. But a good maths teacher is also made because they reflect on what they’re doing and improve. If you don’t do that reflection, then you don’t improve, you don’t change and you don’t get better.
To me, a lot of it is communicating. One, that it’s enjoyable. I know that some of the teachers they appointed at my school had all these high qualifications, but they were useless maths teachers because they were brilliant mathematicians but couldn’t communicate their joy of mathematics. I think society has made maths this subject where there are a terror of maths and a fear of maths. Some of that is because people have been forced to do it in a way that isn’t interesting or exciting. We learnt tables so we could do problem-solving quickly in our heads. I can remember that once we moved on from tables as a kid, the mental arithmetic we did was quite exciting because they were all questions she made up that were relevant to us as four- or five-year-olds. It was that which actually made it interesting, I think.
Two, if you think you can do it, you probably can, because the reality is that most people can do much more maths than they think. My decorator comes around to my house on a regular basis and tells me that he cannot do any maths. Then he’ll go into a room that we want decorating, and within about five minutes has priced up the job, worked out all the materials he needs, the amount of time he needs, and how much he’s willing to come down when we say, 'Well, that’s a bit expensive.' So there’s all that maths that’s gone into it, yet he says, 'I don’t do maths.' I think, yes, you do. You just don’t realise that you do it.
6. What’s the most fun a mathematician can have?
Playing music; You’re applying your skills: the logical thinking and the processing you do in maths are very much in line with a lot of playing musical instruments.
I think it’s quite interesting because I know several mathematicians who are involved in music and who get quite excited about the music they play. We might talk about a little bit of maths, but we’re much more interested in talking about the performance we’ve just done, or wherever we’ve been, than talking about maths. So it’s actually doing something that involves maths.
A lot of musicians are quite mathematical, and you think of some of the pop stars who studied science. Brian May, who is an astrophysicist, is a good example. You can’t get much more mathematical than that, in fact. But he plays the guitar, and the way he plays it is simply because his mindset works in a way that puts things together without thinking about it. It’s that knock-on effect. And it is that bit where you suddenly recognise that.
I play the clarinet. For a long time, I played in a worship band in my church, and it was entirely by ear. I had some dots in front of me, which I never played because I needed to know what the singer was going to do. Everything was done by listening and playing in with all the other instruments. As they described it, because I played the clarinet, I was 'doing the twiddly bits around the edge'. It was about listening to where the 'twiddly bits' should go, and that’s mathematical thinking. I can hear this is where it’s progressing to, so it’s a bit like problem-solving with theories: this is where I think it’s going to go next.
Now I play in a wind band, although not at a high level. I was much better when I was younger. But it’s still about listening, putting things together and thinking through the processes. It’s that logical thinking: what I’m hearing is matching into the sound sets, I’m balancing the sounds, and I’m being adventurous.
7. Do you have a favourite maths joke?
Why was 6 worried about sitting next to 7?
Because 7 8 9.
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