# Seven questions with... Dr Catherine Gripton

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- Seven questions with... Dr Catherine Gripton

## Seven questions with... Dr Catherine Gripton

Cath Gripton is an Associate Professor in Mathematics Education at the University of Nottingham, England. She researches pre-school and primary mathematics policy and practice, and is currently a Principal Investigator on studies of early counting as well as a project focussing on the mathematics in play.

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

I have a clear memory of watching my dad build a stone wall when my brother and I were young. Despite leaving school at 15, my dad was good at mathematics. He was a car mechanic and able to do all kinds of practical things, quickly calculating measurements, sketching rough diagrams and visualising the internal workings of machines. My brother and I watched him chip and chisel away at stones to make them the shape he wanted, rotating stones to fit and building patterned rows. My brother asked if we could have a go and Dad gave us the bits that he had chipped off the larger stones and a board with a dollop of cement. We each set about building our own wall on offcuts of wood. It was much more difficult than it had appeared. I had to do a fair amount of doing and undoing, trying to fit the stones together so that each row was the same width and had approximately consistent depth. I remember getting quite tired from the hard thinking I was doing. It has stuck with me how much mathematics is involved in so many occupations. I was really pleased when we decided to include “my mathematics” interviews in the *Mathematics Teaching* journal as these showcase the mathematics in a range of professional lives.

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

When I began primary teaching with a mathematics specialism in 1999, mathematics education in England was changing. The National Numeracy Strategy was being rolled out but I worked in a school that used it flexibly (drawing upon the subject knowledge, vocabulary and questioning more than the sequencing and lesson structure). Working with younger children, we taught mathematics successfully through play and routines. The mathematics in morning registration was rich and took around 30 minutes, I recall. The children, from a socio-economically disadvantaged community, achieved very well and we had a real focus on problem solving and reasoning. Whilst we have gained in many other ways, I feel that we have lost some of the rich and extended problem solving and reasoning since that time. I think this is partially due to the amount of curriculum content which we try to include. My feeling is that if we taught less, in more depth and over longer periods, then we might strengthen mathematical behaviours and connection-making, preparing generations of mathematicians who persevere and enjoy challenge. It is not about comparing mathematics education then and now, as better or worse, and wanting to take retrograde steps. It is a matter of acknowledging changing contexts and taking the best practices from different education periods to forge new practices incorporating these ingredients.

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

In a university seminar, our lecturer encouraged the class to visualise a number and point to it with our eyes closed. They then gave us further numbers and we continued pointing to each. Afterwards, we discussed how and where we had seen each number. I was amazed by the range of responses and that none were the same as mine (a dynamic size and distance model where larger numbers were physically bigger and travelled towards me from further away). Previously, I had believed that we all saw number in the same way and had similar mathematical skills, that were relatively more or less advanced, so it was this that accounted for differences in mathematics achievement. I have repeated the exercise with groups of adults many times over the years and it continues to remind me that we internalise models and representations differently and use these to work flexibly as mathematicians.

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

I think I have my own mathematics personality – my own ways of working and thinking – but then work differently with different people. I do like to work with others, talking through ideas and jotting or drawing as we go. I need to feel comfortable to conjecture and use approximate language and loose methods to begin with. This helps me to get a feel for a problem before working with more precision. Consequently, I tend not to work so well with people who want to move quickly to calculating. If they do, then I like to pause every so often to do some oral sense-making, often asking a lot of questions and checking our agreed assumptions.

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

Definitely made. Mathematics is learned in the cultural and social contexts of the individual. We learn mathematics in a number of changing contexts over time, so we really are an amalgam of our contextualised experiences of mathematics. Great mathematics teachers draw upon all of their lived experiences of mathematics and channel this into their teaching. They are driven to create positive learning environments where students experience success and connect emotionally with what they are learning. Here, success comes in a range of forms. It can be getting correct answers and high grades, but it can also be learning something new, making a connection for the first time, making efficiencies, overcoming a persistent difficulty, teaching somebody else something or finally getting something right that they have been getting wrong for months. Great mathematics teachers aim to create the environment where these things are possible and persevere until they do.

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

There is nothing quite like the satisfaction and reassurance of making connections and noticing patterns when being mathematical. This is when mathematics nourishes you. The abstract nature of mathematics is sometimes talked about in a way that suggests it is somehow quite clinical or a step removed from the messiness of the real world (unless it is bridged to it through being “applied” or through modelling). But I think that mathematics is innately human, whether pure or applied. To make connections and notice patterns, including those magic moments of clarity or revelation, is a deeply human sensation and can be quite cathartic. Maybe this isn’t “fun” but it is immensely satisfying.

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

Parallel lines have so much in common. It’s a shame they’ll never meet!

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