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Cristina Mio is a lecturer in Maths Education at the University of Glasgow, where she teaches Initial Teacher Education. She is interested in student teachers’ attitudes and beliefs towards mathematics and its teaching and learning.
1. What’s your earliest memory of doing mathematics?
I think I was little, possibly five or six, and I remember being on the floor of a tiny third bedroom box room in our flat. I was cutting out a paperchain of dolls; I just remember spending ages like that and of course I would make a mess. For that, you just fold a piece of paper a few times and you cut out a silhouette along one side and then you open it up and you see these little dolls that are holding hands and their feet touch. At that time, I didn’t realise I was doing maths otherwise I wouldn’t have done it, possibly. But now I can see so much maths in it – and symmetry – and actually it was quite tricky because if you don’t cut properly, then the dolls don’t hold hands, so they just fall apart. Or if you cut too wide then their heads are too squashed, so they don’t look right. So, there was actually quite a bit of planning and thinking involved. Another thing I had was Cuisenaire rods which are such a powerful tool for learning maths. I remember we were careful with our money, but my mum always bought us anything she thought was helpful in school. The teacher said these Cuisenaire rods could help with maths and I have to say I never used them properly. I used them for imaginative play so I would create a classroom by making a desk for the teacher using the rods as well as the pupils’ desks in rows and I would use a tall rod for the teacher and smaller rods for the children.
2. How has mathematics education changed in the time you have been involved in it?
For me, I did most of my schooling in Italy and then spent some time in America, although I was not involved in maths education at that point. Then, for a few years I lived in England, where I got my PGCE, and then I moved to Scotland – so not only has time changed for me but country as well, so I don’t know if the changes I experienced were due to time or place. Also, I don’t know if I’m picking up on certain changes in maths education because I’m more interested in that aspect of maths so there is some confirmation bias in my perceptions. However, I see that there is a willingness now to make maths more “human.” Now it's not just for an elite of highly intelligent people, it’s for everybody; you don’t have to be the best at maths to enjoy it, you just do it, and I really like that. I highly recommend reading Francis Su’s Mathematics for Human Flourishing and Anne Watson’s Care in Mathematics Education.
3. Tell me about a time in your career when something totally flabbergasted you.
I’m very often surprised about maths-related things. But when I had just started my PGCE, I was totally confused one day. I am still not sure if I got this right. At that time (15 or 20 years ago in England) they were using something called tracking, I think, where they were predicting the academic outcome of children at GCSE level (when they are aged 15 or 16) from the child’s academic achievement at the end of primary school. To me it didn’t make any sense because it implied that whatever’s in between those two points in time didn’t matter. Another thing that really surprised me when I did my first placement in schools was that children were split into bottom, top and middle sets. I think this practice is changing now, but at that time it was very common. I went to school in Italy, where there is no ability grouping or setting, so this was so alien to me. Different countries do things differently. It’s really good to come from a different country because you question things rather than just accepting them.
4. Do you practise mathematics differently in company?
It depends on who the company is, and what the goal is. If it is to achieve something together, I think I’m ok working with other people. Otherwise, I’m actually quite selfish if it comes to something I have to learn or figure out. I tend to listen to other people only until I get enough clues; then I stop listening and I carry on by myself. I don’t want others to spoil it for me. I also don’t want them to tell me where I made a mistake, because I prefer to figure out what I got wrong by myself and understand where I made some wrong assumptions. But of course, if I am stuck I don’t mind asking, but I don’t want to glean too much from others.
5. Do you think a brilliant maths teacher is born or made?
Made! However, I don’t think that just anybody can be a brilliant maths teacher; I think there are some necessary conditions. You have to be humble; humility is very important and you have to be willing to listen to other people about how they do things, really letting go of your ego or of your point of view and really paying attention. I think also to maintain this brilliancy (brilliancy is not steady, you have to maintain it), you need to learn new things – not just because you want to learn these things but just to remind yourself how difficult it is to be a learner and how difficult it is to make sense of something that is unfamiliar to you. Then you realise that nothing is obvious, and that learning takes a long time, and even when you think you understand something, if you spend more time thinking about it, you will see things differently and find new meanings and connections.
6. What’s the most fun a mathematician can have?
When mathematicians discuss maths concepts that interest them with someone else and they get a connection and response; if they can share their feelings of wonder and happiness, or an appreciation of something – it can be something tiny. Even talking about something – for example, “Oh, I just found out this…” and somebody else says, “Ah yes, that’s interesting” – I think that’s the joy. But I think it’s the same in anything; e.g., if somebody is interested in fashion, they will get a lot of joy out of it when they can meet with somebody else and discuss what they like in that topic.
7. Do you have a favourite maths joke?
I really like jokes, but I’m really bad at remembering them because I usually just remember the main idea and so I don’t tell them properly and ruin all jokes! I remember this joke about a black sheep (I looked it up as I wouldn’t be able to recall it properly):
Apparently, there is a mathematician, a physicist and an engineer and they are riding on a train through Scotland. The engineer looks out of the window, sees a black sheep and exclaims, “Hey, they’ve got black sheep in Scotland.” The physicist then looks out and says, “Well, actually all we can say is that there is at least one black sheep in Scotland.” Then the mathematician of course says, “Well, actually, all we can say is that at least one side of one sheep is black in Scotland.”
My background is in engineering so I can see it from both points of view!
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