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Tony is Senior Lecturer in Educational Technology and Deputy Head of the School of Education at the National University of Ireland (NUI) in Galway, designing and contributing to various programmes including joint Maths and Education, and Computing and Education degrees. An elected Fellow of the International Society for Design and Development in Education (ISDDE), and General Editor of Ireland’s educational research journal Irish Educational Studies, he has a particular interest in innovative approaches to teaching mathematics, including through the use of educational design, technology-enhanced learning and cross-curricular methods.
1. What’s your earliest memory of doing mathematics?
I specifically remember having a brilliant maths teacher in primary school when I was about 7 or 8. He used lots of visuals and creative approaches to make our initial learning of maths fun and meaningful for us. The teachers I had in primary and secondary school were similarly superb – they used the history of mathematical ideas to contextualise our learning. These stories still fascinate me today - things like the Calculus Wars. So, in a way my earliest memory of doing mathematics is strongly connected to concepts of good educational design in context.
2. How has mathematics education changed in the time you have been involved in it?
It has changed of course, but in important ways it hasn’t. Mathematics is a very ancient discipline of learning and language for understanding the world, so while the content may remain somewhat consistent, particularly the concepts studied in school curricula (which in Ireland still owes its provenance to foundational works such as Russell & Whitehead’s Principia Mathematica, published in 1910) new approaches, methods and technologies have emerged to potentially fundamentally change the ways in which mathematics can be taught and learnt.
A really important change in mathematics education is that design has become ever more important. Design – with a capital D – is front and centre now in mathematics education, and this can be seen in the power of beautiful, well-designed resources for teaching mathematics, e.g. the designs created by Cambridge Mathematics, including the Espressos to support teachers’ innovative practice in schools.
The potential of new and emerging technologies is also fundamentally changing how mathematics can be taught. The capacity to virtualise and visualise mathematical phenomena dynamically is opening up new possibilities for mathematical interpretation and numeracy in classrooms. Bertrand Russell wrote that the way we see the world significantly shapes our understanding of it. Technology is affording us whole new ways to “see” – to comprehend and understand – the natural and physical world all around us.
This is exciting – not only for scientific and mathematical advancement but also for teaching, where new dynamic software can enable pupils to interact with and experience mathematics in a much richer, embodied and potentially more informative and instructive way. They can explore mathematical phenomena interactively in real-time, which augments the potential for deeper learning.
3. Tell me about a time in your career when something totally flabbergasted you.
There have been many! Seeing our pre-service maths teachers develop in the school practice context never ceases to amaze me – witnessing their emerging professionalism and the innovative approaches and methods they deploy to make mathematics fun and meaningful for their pupils. I have also been flabbergasted at the tremendous action research projects that practising teachers have developed in the context of their studies in the Professional Diploma in Mathematics for Teaching qualification, and the impact of their work on their pupils’ mathematical learning in their classrooms and schools.
As a maths teacher, it is always a joyous moment when you see a student experience an Archimedean “Eureka!” in class – when they figure something out and solve it for themselves.
It’s been a privilege to see our pre-service student teachers create many of these moments over the last twelve years as we’ve travelled up and down the country on school placement visits for our BA Mathematics and Education programme.
4. Do you practise mathematics differently in company?
There can be many solutions to a maths problem so when discussing mathematics in company, I think you are especially open to others’ views, ideas and solutions. Even when practising on one’s own, I think you’re still “in company” so to speak – particularly when you look at a resource or textbook and consider how others approached a problem and solved it.
5. Do you think a brilliant maths teacher is born or made?
A great question, and I believe it is both. I think great teachers are born, to some extent, but as a teacher educator I truly believe teachers are also formed. Even for those with an innate ability, passion for, and interest in mathematics and teaching mathematics, teacher education can have a significant impact in developing their capacity to use new technologies and creative and innovative mathematics teaching methodologies, exposing them to challenging and thought-provoking educational ideas in the disciplines of history, psychology, sociology and philosophy of education. Education is such a complex and constantly evolving domain, and the challenges of learning and teaching today are not inconsiderable. Therefore, great teachers must be great learners – for me teacher education is a sine qua non (essential) of brilliant teaching. Drawing inspiration from John Dewey, we might say that brilliant maths teachers are always in a process of becoming/of being made.
6. What’s the most fun a mathematician can have?
Solving problems – it is always great fun to systematically work through and solve a mathematical problem. Maths is truly the language of the universe, ubiquitous across all fields of human endeavour; e.g., music, sports, computing, engineering, technology design, data analysis, and even poetry (metre and rhyme). For me, Pythagoras’ view of the relationship between maths and music captures the intrinsic, profound importance and tangible joy of mathematics – how appreciating music or playing an instrument is a way of sensuously experiencing the mathematical order of the natural and physical world all around us.
7. Do you have a favourite maths joke?
One of my favourite, humorous maths stories is in John Allen Paulos’ highly entertaining book I Think, Therefore I Laugh: The Flip Side of Philosophy, and the exchange the author imagines taking place between the great mathematician-philosopher Bertrand Russell and the comedy genius Groucho Marx, and the absurdly funny dialogue that ensues when they find themselves stuck in a lift together: https://math.temple.edu/~paulos/oldsite/groucho.html.
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