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Athina Thoma is a lecturer in Mathematics Education at the Southampton Education School of the University of Southampton where she teaches on the BSc, MSc and PGCE Secondary Mathematics programmes. She has a BSc in Mathematics from the University of Ioannina (Greece) and an MA and PhD in Mathematics Education from the University of East Anglia. In the past, she has also worked as a Mathematics and Statistics tutor supporting undergraduate and postgraduate students with Mathematics and Statistics in their courses and as a researcher at Imperial College London and the University of East Anglia. Her research interests include students’ transition from secondary to university mathematics and the use of Interactive Theorem Provers in the teaching and learning of proof at university level.
1. What’s your earliest memory of doing mathematics?
My earliest memory of doing mathematics was with my grandfather, a secondary mathematics teacher, when I was a toddler. We would be sitting in their garden, and he would say the following while performing the corresponding actions:
“One (extending one finger from the right hand),
Two (extending the same finger from the left hand),
Many (extending all the fingers from the right hand with the palm facing upwards),
Many more (extending all the fingers from the left hand with the palm facing upwards)
This is my earliest memory from our many mathematical activities and discussions. Our mathematical exchanges continued during my kindergarten (focusing mainly on counting), primary (practising times tables while walking to school) and secondary school years (discussing the importance of proof). Even now, we continue our mathematical discussions every time we meet, focusing on the different ways of doing the same problem, discussing the efficiency, and reflecting on the affordances and challenges of the different solutions.
2. How has mathematics education changed in the time you have been involved in it?
This is a very interesting question. I would like to highlight here that I had the pleasure of being taught in two different educational contexts while growing up (I went to school both in Greece and in the US), and I now work and teach in a different educational context (in the UK). Many changes have taken place in the Greek and the UK system. For me, it is very interesting to see the differences within the educational contexts but also across the different contexts and reflect on the decisions, policies, etc., and the flexibility, resources, and background that teachers have when teaching mathematics.
Additionally, it is interesting to see current developments in teaching mathematics at the university level. I am currently involved in research projects exploring how students engage with Interactive Theorem Provers (e.g., Lean). It is wonderful to see students being exposed to tools used by researchers in pure mathematics. I am interested in further exploring how students engage with Interactive Theorem Provers and examining the benefits and challenges when using them.
3. Tell me about a time in your career when something totally flabbergasted you.
I am always amazed at students’ interactions with mathematics. I will focus, though, on one particular time I vividly recall when I worked as a mathematics and statistics tutor with the Learning Enhancement Team at the University of East Anglia. I had a one-hour tutorial with a first-year student from the School of Engineering who wanted support with integration. We spent some time together at the beginning of the hour, both of us writing on the whiteboard, discussing the basics of differentiation and integration, examining the objects (derivatives, integrals), the processes and the links between them. After ten minutes, the student had an “Aha” moment and spent the rest of the time on his own on the whiteboard, solving the different questions and realising the links between differentiation and integration. I was no longer needed, and I was able to observe these links being created and/or strengthened and the multiple “lightbulbs” the student experienced. I always love that moment(s) when students realise the connections and take ownership of their learning.
4. Do you practise mathematics differently in company?
I think so. One of the most beautiful things in mathematics is that you can have many different ways of solving the same problem. And although I might be able to come up with a few different paths myself, having the ability to communicate with others makes me reflect on my solution, aiming to clarify it, make it more transparent and also be ready to be questioned on the correctness of it, the efficiency and the potential of the method. This communication also allows me to observe how others communicate, how they approach the problem, and which aspects they choose to highlight when discussing their process and solution. I always love to hear how people discuss mathematics and reflect on their solutions or how they view and describe mathematical objects.
In one of my Secondary Mathematics PGCE sessions this year, I shared with my students Maryam Mirzakhani’s quote, “I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.” Afterwards, we had a lengthy conversation with the trainees about the social aspects of doing mathematics, the importance of mathematical communication and discussion in the classroom.
5. Do you think a brilliant maths teacher is born or made?
Definitely made. I think that everyone can do mathematics, and everyone can learn to teach mathematics and teach it brilliantly, providing that they want to and of course that they are given the appropriate support and opportunities. Past and current research in mathematics teacher training (either pre-service or in-service) is providing further insight, different theoretical lenses through which to view the development of teachers, and of course tools that teacher educators can use with their pre-service and in-service mathematics teachers to support their development.
6. What’s the most fun a mathematician can have?
Finding a solution to a problem or an insight towards understanding a mathematical object and sharing it with others! As mentioned earlier, discussing mathematics with others – sharing the joy of the discovery (of a solution or a new way of seeing something) and engaging in mathematical discussions about the discovery aiming to clarify and further define the discovery – is a rewarding process. It also allows you to view the discovery through the eyes of others. When you see research mathematicians talk about their work and discoveries, you can get a glimpse of the fun and joy they experience. I enjoy sharing these celebratory moments from researchers, through written quotes or documentaries, with my students, as these moments also highlight the effort, time, perseverance, and problem-solving process needed to achieve the discovery.
7. Do you have a favourite maths joke?
It might be a cliché, but my favourite maths joke is the following:
A mathematician says the following statement in company: “There are three kinds of mathematicians, those who can count and those who can’t.”
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