Name: Geoff Wake
About you: I started working as a flight simulation engineer after university and must have been among the first people to have flown a computer-controlled flight simulator - it’s strange to think that there are now better versions for use on your phone! However, I didn’t find that work very interesting and decided that teaching could allow me to work both with people (much more fun than machines) and maths!
After five years teaching in a South London comprehensive I had a stressful summer holiday, during which I got married, moved to Derbyshire to teach in a tertiary college, and bought a house in which we have lived ever since. I taught a lot of A-level maths, started using computers (with David Tall’s calculus software and Mechanics in Action kits). When I had an opportunity to work with the Mechanics in Action Project team at the University of Manchester, I jumped at the chance – and I’ve been working at Manchester University ever since on a range of research and curriculum development projects, such as the PRIMAS and COMPASS projects. For a time, until recently, I also looked after our PGCE in Secondary Mathematics.
The most recent use of mathematics in your job was…
I write the comprehension papers for AS Use of Mathematics and the pilot A Level Use of Mathematics – that is where I do most of my mathematics these days. This summer, therefore, I’ve been working on exam papers that look at radioactive decay and using calculus to calculate where to fill wine and cocktail glasses so that they are half full. Day-to-day, I approximate how much I’ll be charged in shops and I’m amazed at how often mistakes are made: not long ago I was charged for grapes rather than potatoes, and I think the check-out assistant was surprised that when she told me the total I immediately suggested there must be some mistake.
Some mathematics that amazed you is...
I’m constantly amazed by mathematics in art and art in mathematics. I’ll give just two examples.
Art in mathematics: I have been very impressed by Japanese Sangaku. These wooden tablets, which were hung at the entrance to Buddhist and Shinto temples, presented geometrical problems for the congregation. I love the nested circle problems – which are so visually pleasing – and have tried constructing some using dynamic geometry software.
Mathematics in art: I was intrigued by the account in Judith Field’s book The Invention of Infinity: Mathematics and Art in the Renaissance of how artists in the renaissance painted with a true sense of perspective using geometry – again I tried building a dynamic geometry file to explore this and had more success this time!
I suppose these examples hint at my general appreciation of visual representation in mathematics.
At school I just found that somehow I was in tune with the logical structure of the subject. When I was 12 years old I had a teacher who taught us differentiation from first principles using many diagrams with coloured chalk. I’m sure most of the class were lost, possibly forever, but I was intrigued! When I got to mechanics A-level I found connecting mathematics to reality a real challenge, and had to draw on the persistence I first encountered when making sense of algebra. I suppose, overall, I enjoy a sense of achievement in constructing mathematical arguments and solving problems.
A significant mathematics-related incident in your life was...
A number of years ago I was developing some mathematics for science resources and one day in a college was interviewing a chemistry student about her work in chemistry. This was tricky for me as I really know very little chemistry, but when we looked through the graphs in her report of an experiment she had done I found I could use my mathematics to interpret what had happened in the experiment. It struck me then how empowering maths can be and how everyone should have access to that. That moment was very influential in my vision for Freestanding Mathematics Qualifications that I went on to develop.
A mathematics joke that makes you laugh is...
A mathematician and an engineer are on a desert island. They find two palm trees each with one coconut on it. The engineer climbs up the first tree, gets the coconut and eats it. The mathematician climbs up the second tree, gets the coconut, climbs up the first tree and puts it there. "Now we've reduced it to a problem that we know how to solve."
The best book you have ever read is...
Almost always the book I have just finished. I guess I’m the sort of person who becomes completely immersed in the author’s world, which I suppose is what they try to achieve. I rarely go back to a book, but recently I have re-read Nineteen Eighty-Four, and although in reality 1984 was nothing like the world Orwell envisaged, I somehow think we are very slowly creeping towards it!
A mathematics book that I like using if I have the opportunity to teach something interesting is The Heart of Mathematics: An invitation to effective thinking, by Edward Burger and Michael Starbird. It’s full of interesting mathematics with many illustrations and can provide inspiration for many lessons.
Who inspired you?
The people that I first worked with in Crown Woods School in Eltham gave me the confidence to try things out in the classroom. In particular Trevor Weight, the Head of Department, who supported both staff and pupils (sadly Trevor passed away a few years ago but, as he would have liked, it was while he was refereeing a school hockey match). And more lately, my colleagues in Manchester, and of these of course Julian Williams, who inevitably has been a great influence and has supported all aspects of my work.
If you weren't doing this job you would...
be a journalist or maybe an architect. One of our sons is working towards becoming an architect and the interdisciplinary nature of it is really appealing!
What do you see in your crystal ball for mathematics education?
Well, as all good mystics say: “It’s very cloudy but I see emerging...a time when mathematics in schools is re-energised, and better connects with the world in which young people operate. New technologies are harnessed so that we have classrooms where pupils enquire, explore, model, investigate…, there is excitement and intrigue and, as well as there being a new mathematical world, we also make connections to other subjects and disciplines.” Of course, this is all possible now, but we are too restricted in schools through having to comply with testing and inspection that lacks vision and imagination. There’s a lot for us all to do!