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Eirini is an Associate Professor of Mathematics Education at the UCL Institute of Education, in London, UK. She has worked in teacher training programmes and one of her academic passions is doing research on the use of technology in mathematics education.
1. What’s your earliest memory of doing mathematics?
I vaguely remember myself doing mathematics at primary school. What I remember vividly though is that I was always “good at” maths throughout my education and loved it more than any other subject. When we were introduced to Euclidean Geometry at high school while I was still living in Greece, I remember looking at the diagrams and visualising the proof almost instantly. And with worded problems, I always sketched a diagram to “see” the problem and was able to “see” the solution.
An incident that I remember very clearly however is from the 7th grade. One day, the teacher taught us a method, including multiple steps, for solving certain types of mathematical questions. The method did not make much sense to me, and I must admit I lost interest while the teacher was modelling how to solve these types of questions. At the next lesson, when the teacher unexpectedly decided to give us an unplanned mini-test, I remember my heart racing as I knew the teacher wanted to assess us on the method she taught us; I could only remember two of the steps, not all of them, so it was impossible for me to apply it. I told myself to calm down and try to solve the problem in any way I could think of, not worrying about following the steps she had taught us. And I did solve it, but in my own way. At the end of the test, my classmate with whom I always discussed our responses to any maths tests, asked me what the answers I got in every step of the method were and I just told her I did not follow the method, so I could not answer her question. At the next lesson, the teacher handed back the marked tests and when she reached my desk, she looked at me, smiled, winked and said “Still, well done you!” I looked at my test and she had given me an A* and a smiley next to it. It was such a relief. It may be worth mentioning that my solution was presented in 5 lines, whereas the solution following the taught method, as presented by most of my classmates, took up almost a whole page. It doesn’t matter how you get to the right solution, as long as you get to it. But of course, being efficient is also important sometimes. Maths can be beautiful like this, can it not?
2. How has mathematics education changed in the time you have been involved in it?
Certain things have changed, while others have remained the same. For example, the invasion of technology into our everyday lives has led to some changes in the way we teach and in the way students learn, and has brought forward the use of digital resources in maths education. There is research that evidences the benefits of technology and how it can enrich mathematics teaching and learning, but its use in mathematics lessons varies from teacher to teacher, from school to school, from culture to culture, from educational system to educational system, etc. Also, up to a certain level, technology has made us impatient and encourages some of us to look for quick solutions, which makes me worry – while students can still see the beauty of maths when solving mathematical problems with the support of technology, they cannot always see it when letting technology solve the problem for them.
Maths education has been a research field for over 55 years and in the time that I have been involved in it, I am aware of a lot of research being carried out, but mathematics teaching practice, for example, is not always research informed. Looking ahead, if I were asked what some of the changes are which I would like to see in the next 20 years or so in this field, I would say a successful, efficient and fruitful integration of technology into mathematics education, but also a more research-informed (and technology-enriched) mathematics teaching practice.
3. Tell me about a time in your career when something totally flabbergasted you.
I once had a mathematics teacher trainee, who was an ex-marine who had decided to change his career and become a mathematics teacher. He was placed for his training at a school with students from a socially disadvantaged background and who did not always behave well during lessons. In the time I tutored him, there were times that he really struggled to “survive” the days he was teaching at that school. He found it very difficult to accept that students would answer back, be rude and refuse to follow simple instructions, but above all that they did not realise how important education is. Initially, his own upbringing and his experience from his previous job in the army conflicted with his expectations of what being a maths teacher involved and with his dream to help kids gain a solid maths education and achieve in life. There were successes, but there were failures as well in his training years, but I always remained proud of how hard he worked for his students, never losing faith in their abilities. When I got to meet with him years after he became a qualified teacher, he told me how grateful he was for my support and how proud he was of himself for persevering, and that nowadays he was having the best time teaching maths. 😊
4. Do you practise mathematics differently in company?
I do not think I practise mathematics differently in company. When I first see a mathematical problem, I always like to draw a diagram, note down what I know and what I am looking for, and to think about the problem and its solution. I would do this even if I was with others around me. The benefit though of practising mathematics in the company of others is the opportunity to discuss the problem and bounce ideas between us, reflect upon what others may suggest, think of an argument to support or challenge others’ suggestions and/or ideas, and as a result learn from others. There are times when I want and need to think through the mathematics on my own, but I never doubt the importance of collaboration and learning from other people’s ideas, suggestions, arguments, mathematical knowledge and ways of thinking.
5. Do you think a brilliant maths teacher is born or made?
Both. I think some people are born with a gift to be amazing teachers and have great pedagogical skills and teacher presence in the classroom, while others get to learn and with experience identify what strategies work for them to become brilliant maths teachers. Of course, in both cases having a strong background of mathematical knowledge is a must.
6. What’s the most fun a mathematician can have?
There are quite a few things I could mention here. For example (a) challenging oneself with a difficult problem; (b) trying different strategies to solve a challenging problem; or (c) discussing a challenging problem with fellow mathematicians. If I were forced to choose one, I would go with the last one, as I love discussing and learning maths with others.
7. Do you have a favourite maths joke?
In the past I did a lot of research on algebra and algebraic thinking, and I happened to come across a picture with two cartoon characters, a teacher and a student, having a dialogue in a maths lesson. The teacher was solving an equation on the board, finding out that the solution was x=2. Then, the student replied, “Just a darn minute. Yesterday you said x equals three.” This really made me laugh out loud, and definitely resonated with my own experiences as a schoolteacher and also as a mathematics educator researching students’ struggles with algebra.
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