May 2017

Math Central (MC):

It's been quite a while since we have been in contact. I am looking forward to this interview and really appreciate your agreeing to it.

Can you tell us your job title and who is your employer?

JOY :

I am a professor at the University of Lethbridge.

MC:

How would you describe your job?

JOY:

I work half-time at the university. This involves teaching two courses every Fall, supervising a graduate student, pursuing my research, and service work.

To a mathematician, I would say that my research is about automorphisms of Cayley graphs. That’s very specialised and technical language; usually when I’m asked, I tell people that my research is about symmetries of networks. This can be any kind of network: roads, computers, communications, inter-personal… anything you can model as a bunch of points, with lines that connect some of those points. When a network is being designed, two important but competing factors are cost and reliability. If you connect every point to every other point, then it’s very hard for any part of the network to become disconnected from the rest; but it’s very expensive to create that many connections. Network designers try to balance these competing factors. Research has shown that when a network has symmetry (for example, when all of the points are connected in a loop that could be rotated without changing our picture of the network) it tends to do a good job of balancing these factors. I study some of the less-obvious ways that a network can have symmetries. My work is definitely theoretical, because despite the application I’ve described, for practical sizes of networks a computer could fully analyse the symmetries. My work would apply to any size of network

Service work can mean a lot of different things. It can mean sitting on committees; organising events; and many other items. However, one thing I’ve been focusing on more recently is outreach work: bringing my math skills into the community.

MC:

Can you expand on your work in the community?

JOY:

I have a daughter in grade 6. One of my outreach activities involves doing weekly interesting math activities with two of the classes at my daughter’s school. Doing volunteer work as a parent has created good connections for me with the schools in Lethbridge and with other parents.

For years, I’ve been hearing frustrations from parents around math. They worry about the math curriculum, about whether or not their kids know their multiplication tables or understand the value of money. Probably anyone who likes math has heard people say, “That’s hard!” or “I hated math.” One of the more interesting things I started hearing from parents recently was a sense of helplessness: that they did not have access to the skills or resources they needed to help their children when their children needed help with math homework. Even parents who were willing to try, or who thought they knew what they were doing, were often scared off when their kids told them, “That’s not how my teacher does it,” or in some cases when the child received a poor mark for not having done the homework the way the teacher wanted it done. When these concerns were expressed by people I knew, I would sometimes offer to help, but they rarely took me up on it. I had the strong sense that they were intimidated or reluctant about what they saw as imposing on me.

I realised one day that I could do something about this. As a math professor, I have the skills to help these parents. I have connections now with the local school district, so I approached the superintendent with the idea that I could run a drop-in program for parents who wanted to be able to help their kids with math homework, but needed some help.

Our district has been trying to focus on improving numeracy skills in middle school, because over the past decade or so, our kids have shown a significant drop in achievement levels from their performances on the grade 6 provincial achievement tests to their performances on the grade 9 tests. So they suggested I focus on middle school math. This made a lot of sense, as most parents don’t struggle too badly with elementary school math, and high school math can require significantly more time to introduce and get someone up to speed on. We agreed that they would host and I would run a drop-in program at one of the middle schools. It ran once a week for 8 weeks, for about 1 to 1.5 hours.

The middle schools sent emails and did phone-outs to all parents, and I grew worried that I might have more parents than I could handle. So I reached out to our Math Education program, and ended up with about 15 volunteer Math Education students who were getting ready to start their second placement in schools. These students were amazing, and helped me plan activities as well as coming out and working with the parents and kids. The Math Education program also provided me with two big boxes of games and activities that relate to the middle school math curriculum.

The sessions were very successful. Each week we talked about two of the math curriculum outcomes for middle school, and ran activities that related to those two outcomes for anyone who hadn’t come with their own questions. Almost all parents brought their kids, and we had anywhere from 2 to 30 participants in various weeks. We received a lot of feedback from parents saying that they had found it very useful, and would like to see it continue, so we are planning to do it again this year.

It was a great partnership, and a real win-win activity. The math education students don’t usually get to interact with parents during their studies, and got to add something interesting and unusual to their resumes. They were wonderful role-models, and shared their interest and enthusiasm with the parents and children. Research now shows that most kids’ attitude to math is set before they even begin school, so this was a chance to break the cycle of negative attitudes to math that a family can perpetuate. The school district was able to offer this assistance to parents at no real cost. The university received positive publicity and visibility in the community. A short film was made at one of our sessions, that was shown on local tv stations; it is available at https://youtu.be/jJ4QwvhbEww.

Some of the activities we ran included adjusting recipes for different numbers of people (working with fractions); doing currency conversions for a trip to Disneyland (working with decimals); a game that involved calculating sale prices and sales tax (working with percentages); algebra tic-tac-toe; and many more!

 

MC:

Tell us a little about your background and education.

JOY:

I grew up in Toronto as the youngest of 4 children. I have memories of my sister explaining algebraic equations to me when she first learned them - I would have been about 6 - and I was very confused by the idea that x was called a “variable” but you could solve the equations to work out a specific, determined value for it, with no variation. When I was in high school, she was studying computer science at the university of Waterloo, and marking for some of their math courses. Sometimes she would let me help with the marking; I was very proud of that.

I started at our neighbourhood school, but after grade 3 attended a series of alternative programs in the public school system: first the “Alternative Learning Program” from grade 4-7, which had K-8 sharing a classroom, with the older kids helping the younger kids and a lot of flexibility to work at different grade levels in different subjects; then the gifted program when it was founded, for grade 8-9; and then the “Alternative and Independent Study Program” for grades 10-13, which was set up along similar lines to a university, with only 1-3 hours of meeting time for each class each week, the expectation that students would work independently outside of that time to complete the curriculum, and lots of office hours by the teachers to provide extra help where needed.

I did my undergraduate degree at Trent University in Peterborough, Ontario. I started out as a joint math/English major: I loved creative writing and I had always found that math came easily to me. There was no creative writing in the Trent English department, and after completing a 3-year degree with a joint major, I had enough math credits to achieve a single-major honours degree in math after my 4th year of study. At the end of my third year at Trent, I saw advertisements from the University of Windsor and Simon Fraser University, for undergraduate students interested in doing math research with professors over the summer. I was offered either opportunity, and chose to spend my summer doing research with Brian Alspach at Simon Fraser University in Burnaby, BC. I published a paper and SFU used this evidence of research to offer me direct entry into the PhD program after I completed my 4th year at Trent.

I spent 7 years at SFU doing my graduate work; partly because I didn’t have a Master’s, but also because I was enjoying myself and getting active in student union work. I was on the provincial and national executives of the Canadian Federation of Students for some of these years, as well as the Senate and Board of Governors of SFU, made two presentations to the federal government’s Finance Committee, and met with Paul Martin when he was Finance Minister about the issue of student debt.

I have been a faculty member at the University of Lethbridge since 2000.

MC:

Why did you decide to study Mathematics?

JOY:

As I said earlier, I started studying mathematics at university mostly because it had always come easily to me. Both of my parents had PhDs, as does my sister, so continuing to graduate school was very natural to me. I had some professors as an undergraduate who really encouraged, challenged, and inspired me, but probably the biggest influence on my was one of my brothers. He was also at university when I was (although he was at York). He took many math courses and was active in their math society. He has the most inquiring mind I know. He was never able to learn things, as I often did, just by seeing that they worked and accepting that; he always had to understand the reasons for everything before he could learn it. He has the most inquiring mind I know, and is still constantly coming up with interesting questions about mathematics and physics and conducting his own research and experiments to figure out the answers, although his employment is in renovations and caretaking. He challenges and inspires me regularly.

MC:

What are your hobbies and other interests? What do you do when you are not doing mathematics?

JOY:

Outside of mathematics, I have a passion for social justice and devote significant volunteer time in particular to the education system, the issue of truth and reconciliation, and restorative justice. I am also a knitter, which keeps my hands occupied during many meetings. I enjoy travel and am delighted to have work that enables me to travel often to attend conferences and visit colleagues. I love to play games, and to read.