Dr Luigi D'Antonio is an avid walker, with a passion for late antiquity and problem solving. He is the Head of Mathematics at the International School of London and a trainer, setter, and senior examiner for Cambridge University Press & Assessment. Prior to teaching he worked for Ericsson Research in the field of mobile communication in the Netherlands, Sweden and Italy.
1. What’s your earliest memory of doing mathematics?
I was probably seven or eight years old, and I remember spending a whole afternoon on a problem involving people / time / task, something like if one man takes one day to dig four holes, how long does it take three men working at the same rate to dig sixteen holes? I do not really remember the details of the problem, but I do remember the sense of achievement after solving it.
To me doing mathematics is the same as solving problems, and as a child I loved a game called Mastermind, where the goal is to guess a hidden sequence of coloured pegs, created by your opponent, as quickly as possible. What I liked about it was the fact that it was mainly based on logic, and at the same time the most effective long-term strategy was to exploit patterns in the way the sequence was created. When I look at a number, what I see is a set of colours (e.g. 1296 is red – yellow – dark blue – blue), and this might be another reason why I loved Mastermind, which is mathematics in colours.
2. How has mathematics education changed in the time you have been involved in it?
I started teaching in 2008 after moving to the UK from Italy. What struck me was the fact that in the UK both statistics and mechanics were part of the mathematics curriculum; in Italy statistics and mathematics are two completely different degrees, and mechanics is only taught as part of physics. Apart from this, the teaching approach was basically lecture-based in both countries. Since 2008 some changes I have noticed are an emphasis on conceptual understanding, as opposed to rote practice, an attempt to apply mathematics in real-life situations, and the integration of technology in teaching and learning. The most important change is that the student is increasingly at the centre of teaching and learning, so that personalised learning and student agency become seamlessly embedded in every lesson.
3. Tell me about a time in your career when something totally flabbergasted you.
The first picture that springs to my mind is the reaction of two Year 8 students, when they realised the implications of the investigations they were carrying out. The activity was about calculating the number of ancestors each of us has, generation after generation (two parents, four grandparents, and so on). After many generations the number grew so big that it was much larger than the number of living people. When I asked the class how we make sense of it, one student realised that it meant that most of us have common ancestors, and as soon as she said it, two students started shouting, jumping for joy and embracing, as they realised that they were related to each other.
4. Do you practise mathematics differently in company?
Unfortunately, I do not have the opportunity to practise mathematics in company often, but when I do it is usually rather exhilarating, as the degree of initial divergence and the speed of later convergence are much faster than when I work on a problem on my own.
5. Do you think a brilliant maths teacher is born or made?
In my experience I have met many teachers who seem to have a natural inclination or intuition about what to do in different situations, and their call is often the right one. When I talk to them, they often tell me that what seems natural and spontaneous is the result of many failed attempts, and lessons learned. I am not sure whether natural talent is a necessary condition for a brilliant maths teacher (I am inclined to say no, but the jury is still out), but I am very confident (say 5σ, like the existence of the Higgs boson 😊) that it is not sufficient.
6. What’s the most fun a mathematician can have?
I am an engineer, so my answer is biased, but I had great fun designing and building an optical illusion room (a.k.a. Ames room) and then touring it to local Primary schools with the help of a group of my students – who talked about it and organised fun mathematical activities in the host schools – and their parents, who helped me assemble / disassemble the room on the weekends.
7. Do you have a favourite maths joke?
An engineer, a physicist and a mathematician are observing an empty house. Two people go in.
Three people come out.
The engineer says, 'Our initial measurements were faulty.'
The physicist says, 'It’s an optical illusion caused by wave-particle duality.'
The mathematician says, 'If exactly one person goes back into the house, it will be perfectly empty again.'
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