#
Mathematical

Salad

## Seven questions with Professor Brent Davis

13 April 2018

*Professor Brent Davis currently works at the University of Calgary as Distinguished Research Chair in Mathematics Education and also currently holds a Werklund Professorship. *

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

I grew up in a smallish community, where my mother taught first grade. She was a profoundly caring educator who made herself available to any and all seeking assistance with their studies, and so our home often felt like a hub for people struggling with their homework or prepping for an exam. When I was about 10 years old, my mother started to involve me in helping my peers with their arithmetic, which means my first really vivid memories of being consciously aware of "doing mathematics" have to do with teaching mathematics – in particular, working with my neighbour on figuring out exactly what was going on with multi-digit multiplication.

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

Growing up in northern Alberta, in western Canada, I lived beside vast forests. I spent hours and days hiking them. But, as vast as they seemed and as far as I hiked, it turned out that it didn't matter how far from the rest of humanity I thought I'd wandered, I ALWAYS came across a beer bottle. I never managed to find a place where no one had been. And so, regarding the question, I would love to be able to point to wild and wonderful insights that have gripped and moved the field over the past 25 years. If they've happened, I've missed them. When I visit schools, the same questions seem to be occupying teachers' attentions. When I read journals or attend conferences, I routinely come across insights that excite me, but that, on further exploration, were at least anticipated by mathematics educators and researchers decades ago. No matter how fresh the idea, it never seems to be far from a beer bottle – metaphorically speaking.

All that said, I can point to two aspects of mathematics education that have changed dramatically in the last 25 years. Firstly, there's been a broad embrace of complexity thinking. When I started, the field was still dominated by what I'd describe as quests for "simple" answers – the best way to teach something, the most efficient explanation, the most accurate test, and so on. When topics of "complexity theory" came up, they tended to be met with ‘What's that?’ Secondly, while it hasn't had much of an impact on classroom practice, researchers are spending much more time attending to upcoming impacts of emergent technologies. That's always been a topic of discussion, but the questions are shifting from "How might we use technology to improve what we're doing?" to "How are things going to change?" That's a dramatic evolution.

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

Just one incident? I have to go with two – a happy one, and one less so.

The happy one was in my first year of teaching, in the early 1980s, working with 8th graders (early teens). In a lesson on subtraction of integers, one typically quiet-but-competent student noted in a tone that I interpreted as a mix of surprise and pleasure that "subtracting integers is exactly the same as dividing fractions." I heard it at first as nonsense – and some seconds later I re-heard it as a brilliant insight, one that triggered a complete reformatting of the unit.

A less-happy one happened a few years ago, when an experienced high-school teacher asked me, "How can we multiply by pi when we can't multiply by other infinite numbers?" At first I was amused, thinking he was joking – perhaps relaying something a student had asked. And then, realizing he was serious, I found myself as flabbergasted as I've ever been. It took me a while to find appropriate words of response.

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

If I were completely honest, I'd have to confess that I MUCH prefer to be on my own in my initial stages of engaging with new mathematics (i.e. working on an unfamiliar problem, or grappling with new concepts). Like many, I can permit myself to be totally absorbed when doing mathematics, and I love the feeling. It's rare that the same immersion-in-thinking can happen when engaged with others. But, that said, after my selfish initial stages, I tend to move fairly quickly to playing with others who are working on similar topics – and the modes and manners of engagement are usually very, very different.

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

To me this question is a little like, "Is intuition innate or learned?", and I fall squarely on the side that it is learned. At the risk of being interpreted as recommending something like social engineering, I wish eventual-teachers could be immersed in situations of making sense of the sense others are making from a very early age, and that they could be involved in activities of deconstructing their own mathematical understandings (I call it "concept study") throughout their careers. I believe that every instance of "brilliant mathematics teaching" that I have been blessed to witness can be properly interpreted as a blend of those two elements: firstly, insightful readings of learners' emerging understandings and secondly, nuanced structuring of those aspects of a concept that fall within "noticing range" of those emerging understandings. It can be so subtle and complex that it looks inborn, but it all sits atop experience.

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

I'm pretty certain I'm not qualified to answer this question.

While not an answer to the question, I often experience very similar "emotional sets" across wildly divergent activities, including skiing a difficult slope, riding my bicycle across impossible terrain, doing mathematics, and trying to make sense of the cognitive and interpersonal dynamics in a mathematics classroom. Among many elements, these emotional sets typically include frustration, amusement, surprise, joy, boredom – which, when encountered together, is what I experience as "fun".

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

A visitor to a museum of palaeontology wondered aloud about the age of a brontosaurus skeleton, inviting an immediate response from a passing custodian: "One hundred fifty million and thirty-two years." Surprised by the precision of the number, the visitor queried how the age was known with such accuracy. The custodian responded, "On the day I was hired to work here, I was informed that it was 150 million years old. That was 32 years ago."

(My father told me this joke when I was in Grade 3 – age 8 or so – and I understood it. I think that may be the reason it's my favourite. I delighted in the juxtaposition of the absurdity of thinking that way and the real possibility of thinking that way – plus it helped that my oldest brother, then 11, didn't get it. And now that I've answered this question, I think that I might want to change my answer for question one…)