In Conversation with: Dr. Aisling Twohill

We often hear about the continued challenges with students disengaging with mathematics. What first inspired you to really take an interest in the subject and to then pursue mathematics at third level?

Both of my parents loved maths and it never occurred to me to dislike maths when I was growing up. Even in school, most of my friends also liked maths, and I remember having great fun in secondary school competing with other girls to get the highest mark on quizzes and tests. We were encouraged to enjoy the competition in maths in the same way as we were in sport or other activities.

I also enjoyed puzzles and solving problems, and in a maths-y family, I had lots of opportunities to do this in discussion with others. To me, maths is not something you do by yourself with a paper and pencil – we all think better when we share ideas and challenge each other.

When I studied as a trainee actuary I found it difficult to engage with the highly applied mathematics – there was a lot less space for creativity, and finding my own individual way to figure something out. I think that I could have lost interest in maths at that time except that I started to engage with recreational maths through books by Martin Gardner and Ian Stewart. They reminded me that mathematics is a broad and diverse field that is far more than rote-learned procedures or mechanistic systems for crunching numbers!

When completing your PhD in DCU, what was the main focus of your research?

My PhD focused on the algebraic thinking of 10-year-old children attending Irish primary schools. Typically, when people hear the word algebra they think of x’s and y’s, but really algebra is a way of describing relationships between quantities, constant and changing. Focusing on the x’s and y’s is similar to learning music by only reading the sheet music and never hearing it played.

In my PhD research, I asked children, working in groups, to figure out how to predict future terms in shape patterns by describing how many elements were needed. For example, I presented stairs built from blocks and asked the children to tell me how many blocks would be needed to build a stairs with 100 steps. The first few are easy, 1 block, 3 blocks, 6 blocks, but after a while you need to find a sentence that will describe any term, or the pattern in general. In primary school, children can use words to describe a general term and still find the correct number of blocks.

Some examples I heard from children were long, clumsy and complicated but worked perfectly. Others were neat and precise, for example “in each term the number of blocks is half of the term number multiplied by one more than the term number”. Using natural language to describe the pattern keeps the focus on the relationships and the structure. When children understand this process, symbols can be introduced to help them communicate their descriptions in a neat and efficient way. This makes sense of the symbols and allows children to see their purpose. The children who were involved in my PhD research succeeded incredibly well in the mathematics I presented to them and thoroughly enjoyed the experience (or so they told me!).

What has been the most interesting aspect of your career so far?

I’m involved in an international collaboration where we are looking at the algebraic thinking of student teachers and how this impacts their teaching in classrooms. Our participants all took part in a preparation programme and then taught algebra lessons based on patterns in 3rd or 4th class in Ireland, Germany and South Africa.

I’ve loved working on this project because I get to work with student-teachers, with children and with my colleagues in teacher education. I also got to visit universities and schools in Germant and South Africa, and my colleagues visited DCU and my local school in Durrow, Co. Offaly. We are still analysing all of the data we collected from the student-teachers and the children but some of the interesting things we have found are that shaky understandings of algebra before participating didn’t result in poor outcomes for the student-teachers who participated well in the preparation. It was possible for our focused student-teachers to understand algebraic ideas that they thought would be very tricky, and then for them to successfully teach them in classrooms.

We were delighted with this and it reflects all of the cutting edge research about the brain’s ability to learn and develop at every stage. Just because something hadn’t made sense to our student-teachers when it was taught to them as pupils in schools didn’t mean they couldn’t figure it out in college. It might just mean that they needed a chance to see it in a different context, or without the pressure of exams.

Every year in October, Maths Week takes place to promote an appreciation and an understanding of mathematics in a fun and interesting way but what else can we be doing more of to encourage more young people to study maths beyond secondary school?

I think that a lot of the content that makes maths boring could be removed and nobody would learn any less. Some of the textbooks have 50 questions to practice one idea. This seems crazy! If you can do something, why would you need to do it over and over even 20 times. If you can’t already do it, then what is the point of doing it repeatedly?? I also think that a lot of what we do in schools, especially senior primary school and lower secondary school is meaningless.

Maths comes from human needs to communicate ideas about measurement, about finance, etc. We should be seeking meaningful contexts to engage children in mindful practice of important concepts, not mindless drill of the mechanics. Lastly, maths shouldn’t be silent and solitary. Most mathematicians talk about how mathematics is best developed as part of a team, but still in schools a lot of children don’t have a chance to work on maths problems with others.

I visit a lot of schools as part of my job, and a noisy, busy classroom is a wonderful place to be. Silent children are not happy children, and they are definitely not children who are loving their study!

What advice would you give to a young student who is considering a future in science or maths?

Take the time to make sure that maths and science remain fun and exciting for you. This might be particularly tricky around exam times, but it will keep you energised. Find books, youtube channels, podcasts and websites where mathematicians present ideas in funny and engaging ways. Also, never be afraid to figure out your own way to do something. You’ll learn far more by working something out for yourself, than by following a solution that worked for someone else.