# Seven questions with... Alison Borthwick

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- Seven questions with... Alison Borthwick

## Seven questions with... Alison Borthwick

Alison has a wealth of UK and international experience in mathematics teaching and learning. Her career has spanned early years, primary, secondary, HEI and advisory roles. She is currently a freelance mathematics adviser working in the UK and abroad with a variety of organisations and schools. Alison is an active member of several mathematical organisations, is a member of BSRLM, chair of the primary ATM and MA group, a member of the Early Childhood Mathematics Group and is part of the Primary Contact Group for ACME, Royal Society.

After half a lifetime believing she was not mathematically minded, she gained her PhD in 2008 in mathematics education, researching children’s perceptions of, and attitudes towards, their mathematics lessons. Since then she has remained an active researcher, writer and co-author. She continues to write, edit and publish books, journals, academic papers and blogs

**1. What’s your earliest memory of doing mathematics? **

My first memory of doing mathematics is completing card after card from the SMP box, which is probably going to label me as a child of the 1980s! The SMP cards, along with my 1cm squared mathematics book, were my exposure to mathematics, which had a negative impact on me for many years.

The cards (which we would now recognise as worksheets) were all divided up into categories – such as addition, subtraction, multiplication, division, and the idea was that we worked through a card at a time. I would complete a card, and then queue at the teacher’s table to get it marked, before I was allowed to move on to the next card. The cards were all kept in different coloured boxes to denote levels of difficulty. At the time, all I could think about was getting on to the next box, which I rarely did, as I never quite managed to get all the answers right and so I would often have to repeat a card to try and improve my score.

Perhaps this is one of the reasons that I now react negatively to worksheets!!

**2. How has mathematics education changed in the time you have been involved in it?**

Both at primary and secondary school, I was the recipient of very formulaic, procedural teaching. I remember always thinking “But why …?” *But why do I have to add a zero when I multiply by 10?* I never seemed to be given an acceptable answer. I didn't know there was another way and so when I began teaching, I replicated this approach. However, I soon discovered (through PD opportunities mainly) that there was another way: that it was OK, even encouraged, not to reach an answer quickly; that there are often multiple solutions to solving problems; and that making mistakes is a powerful way of learning.

I now realise that mathematics education hasn’t changed that much in my lifetime, but the exposure and experience I had to it has. I still go back to the research of Polya, Bruner, Vygotsky and Piaget as some of my guiding principles. I positively encourage all students (young and old) to think and work mathematically and to use characteristics (John Mason might say “mathematical powers”) to conjecture and convince, and specialise and generalise

**3. Tell me about a time in your career when something totally flabbergasted you.**

In 2018 I was invited to be a keynote speaker at a Cambridge International conference. One of the conference organisers had come across my research around perceptions and attitudes of pupils and invited me to talk about this under the banner of “Mathematical Literacy.” I accepted before I had a chance to consider what I was agreeing to – and a persuading factor was that the conference was in Miami!

As I stood on the stage and looked out at an audience that surpassed 450 I thought I would never have considered this possible – me, the reluctant mathematician, who believed by the end of secondary school that I could not do mathematics, was standing on a stage telling my story and sharing my research! If there wasn't photographic evidence I still might think it was all a dream!

**4. Do you practise mathematics differently in company?**

No, I don't think so. But this goes back to having to re-learn how to do mathematics and not give in to the panic I felt at primary and secondary school. So, I now try to adopt a “What do I know?”, “How could I approach this problem?” and “What should I do next?” approach, whether I am alone or in company. I have almost over-learnt the formulaic procedures for calculations I was taught, so when I want to demonstrate why a number line is more powerful than a column method (for example), I have to really think how to do this.

**5. Do you think a brilliant maths teacher is born or made?**

I believe that we all have the ability and capability within us to be brilliant. Again, referencing John Mason’s *Mathematical Powers*, I love (and agree with) the idea that we are all born with such powers. So, in this way my answer is leaning towards “born.” However, I also think that the experiences and opportunities we are offered (and then recognise and make the most of) develop us and shape us in ways that allow this next part of the journey to be “made.”

It is also interesting to notice that the question is around being a brilliant maths *teacher*. We can all probably think of brilliant mathematicians that would need some guidance to becoming a brilliant teacher. While I believe we all have these capabilities within us, understanding how to teach is not the same as learning how to learn.

**6. What’s the most fun a mathematician can have?**

Being ambushed! This can happen either to yourself, as you work on a problem, or it can be a problem you are sharing with a class of students. Either way, you might have anticipated the route a problem is taking or you are quietly confident about the solution. Then something happens that surprises you! This might be something you have noticed that you hadn’t observed previously or perhaps a contribution from a peer or a student that causes you stop and think … and be ambushed. I love this happening! Always learning, always being surprised, being ambushed!

**7. Do you have a favourite maths joke?**

Just one, so apologies if you have heard this already!

Children are baking cakes. One of the children asks the teacher if they are allowed to decorate their cakes. “Of course,” comes the reply, “the more creative, the better!” “Great,” says the pupil, “please can I use the tens and ones?” The teacher looks confused. “Do you mean the hundreds and thousands?” “Well I would,” says the child, “but we haven’t got onto that level yet.”

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