View related sites
Dr Jennie Golding is a lecturer in Mathematics Education at the Institute of Education at University College London and immediate past President of the Mathematical Association.
1. What’s your earliest memory of doing mathematics?
I think chanting tables at Primary school – and lots of calculations with strange units: rods and chains, pecks and bushels… all very good for the mental arithmetic! I went to a school where a third of our sixth form timetable was general studies, only a third A Level lessons, and a third private study, so maths in the sixth form was always a fairly collaborative affair – excellent preparation for university, so collaborating with peers is something I’ve always tried to encourage students to do.
2. How has mathematics education changed in the time you have been involved in it?
I think the first change I was aware of was the demise of formal Euclidean geometry in schools – that largely disappeared over the time I was at university, though my own experience at grammar school was of five 40-minute maths lessons every seven days, two of which in the first three years were entirely devoted to formal Euclidean geometry, which I loved. Then the advent of calculators, and later, of computers – and I remember my thinking about teaching of graph-related concepts changed completely once I could access graphing software – which was so exciting. But in between, the whole SMP and ‘modern maths’ movement – that too was interesting because it challenged some assumptions, though again, was very liberating: you were learning lots of new ideas as a teacher, and then you could stand back and select from this wider range of possibilities. And then the move towards more inclusive maths education, leading to the advent of GCSE. Since my first job, which was in a boys’ grammar school, I’ve always taught in comprehensive schools. I do believe a good comprehensive can offer everything a selective system can, plus some – but only with really well-prepared and effective teachers.
I think, too, our theoretical understanding of mathematics teaching and learning has changed enormously over my career: Piaget was regarded as rather avant-garde when I trained, and Vygotsky was unknown in the west. I remember when Richard Skemp’s article was published in Mathematics Teaching, and being rather excited by it. So curriculum, tools, theoretical developments... then the policy context has also changed substantially. In my first job I was just given a textbook and expected to get on with covering the material in it. How I did that was up to me, so I was able to try out all sorts of approaches – only some of which appeared to work!
3. Tell me about a time in your career when something totally flabbergasted you.
‘Flabbergasted’ I can’t remember; surprised, delighted I can – for instance, when a student has come up with a better solution to a problem, or has asked a question to which I have no idea of the answer, or has shown me something surprising, or the penny drops for a student who’s struggled, or my whole class has opted for A Level Mathematics!
4. Do you practise mathematics differently in company?
Oh yes, and differently depending on the company too. With young children, for instance, our granddaughter, it’s about coming to enjoy the world, and the imagination, in a mathematical way; with older students I’m more conscious of doing that while simultaneously supporting the expansion of their already-in-place mathematical worlds; with beginner teachers it’s about coming to see mathematics in new ways, and from others’ point of view; with colleagues or other maths education junkies it’s sometimes just immersion in abstract mathematics, or perhaps just playing with it, or dabbling in geometry… I’m just spoiled I have had all those opportunities.
5. Do you think a brilliant maths teacher is born or made?
Oh, both, definitely – if such things exist. I do think I’ve come across some inspirational creative teachers, and have been privileged to work with some, and some of those have been near the beginning of their career, but they’ve always invested time and effort, and substantial knowledge, in their teaching, and have continued to learn and to reflect – and to nurture their own mathematical enthusiasm and experience, at whatever level.
6. What’s the most fun a mathematician can have?
Well, for me some of the best times have been when I’ve watched someone else cracking a problem they’ve been stuck on, whatever level that is, or coming to understand the elegance of an unexpected argument – that’s just magic, and the amazing thing is that sort of experience is accessible to anyone. For me, I think the vicarious experience even beats having that experience for myself – it’s about other people coming to appreciate this wonderful discipline.
7. Do you have a favourite maths joke?
It depends who I’m with: with primary children it’s the one about zero saying to 8 ‘I like your belt’, whereas with sixth formers it’s probably ‘the ‘B.’ in Benoit B. Mandelbrot stands for Benoit B. Mandelbrot…’