December Instructor of the Month Vincent Bouchard

It's hard to over-estimate the importance of mathematics, explains December Instructor of the Month, Vincent Bouchard.

News staff - 1 December 2016

What do you teach?

I teach in mathematics and physics. I have been teaching quite a few advanced level courses in mathematical physics, close to my research area-which is centering around the geometry of string theory. But recently I have been focusing on first-year calculus. I helped designed a new first-year stream of Calculus for the Physical Sciences I and II, where I teach using a blended learning and flipped classroom format. It is a super fun experience!

But beyond disciplines, my main objective with teaching is to help students learn how to learn by themselves, thus fostering intellectual independence and critical analysis. I see myself as a facilitator, whose role is to do everything he can to guide students through their own learning process.

Why should people learn about mathematics and physics?

Well, it's hard to over-estimate the importance of mathematics! It is used in almost every aspect of life. But perhaps more importantly, most people see mathematics as a tool to do calculations; they don't see the beauty of it. Mathematics is not really science; it's an art. It's music. Its sounds are ideas; its instrument is the language of logic. I think that we do not do a good enough job emphasizing how fun mathematics is. When students realize that it's not actually about calculating, but it's about playing with ideas, shapes and numbers, they start finding it a lot more interesting!

What are some of its real-world applications?

Mathematics is applied everywhere, from engineering to physics to biology to accounting to music. It's used to model brain tumours, it's used to build bridges, it's used to tune pianos, it's used to describe the universe. The list goes on and on. But while applications are certainly important and worth emphasizing, this is the easy side of mathematics, since it is so universal. It's like teaching English; of course English is applied everywhere. But English is still studied for its own sake, and mathematics should be as well. My own research however revolves about applying mathematics to physics, and vice-versa. On the one hand, I'm working on applying mathematical tools to understand better our universe, in particular to formulate a theory that unifies Einstein's gravitational theory with quantum physics. On the other hand, I'm actually using physics (more specifically string theory) to formulate new ideas and connections in pure mathematics. So while mathematics certainly has real-world applications in many areas, what's actually interesting as well is that science, such as physics, also has applications to pure mathematics!

What's the coolest thing about this subject area?

The coolest thing I think is that in mathematics we are free to study whatever we want! That's why it's not really science: in science, you are trying to describe nature, to model phenomena, to understand the universe. You are given something, and you are trying to understand it. In mathematics, we are just playing with ideas. We find ideas that we think are worth investigating, problems whose solutions we think may lead to a more beautiful and greater understanding of the mathematical system. And we study them. This is certainly one aspect of mathematics that I find really fascinating! Another thing that's cool is that in mathematics we can always, in principle, determine whether a statement is true or false. That's quite powerful. And very satisfying! We don't have to spend days, months, years, formulating opinions and arguing with each other! (although we certainly still do sometimes, since it's not always easy to say whether something really is true or false...

You are this year's winner of the Faculty of Science Innovation in Teaching Award - what are some of the innovations you use that you've found most successful and what inspired you to propose them?

The last few years I have decided to use technology a lot more inside and outside the classroom. I used to simply teach on the blackboard, which worked well for small, higher level classes. But I figured that with large, first-year classes, technology could be an invaluable asset. And I think that it worked well. I've been very much inspired by the whole idea of blended learning and flipped classroom. As instructors, we all want students to be prepared for lectures. For higher level classes, we asked them to do readings before coming to class; but for lower level classes, this rarely works. The blended and flipped approach however works really nicely in my experience. In my approach, students watch a pre-class video (and answer a very short pre-class quiz) before coming to class, so that in class we can work on problems. In this way, much of the learning actually occurs in class, where I am there to help and facilitate the process. And making videos is actually really fun!

Another thing that I've been experimenting with and that I found very successful is two-stage exams. In such an exam, students first answer a standard individual exam for two thirds of the allotted time. They then submit their copy, and I give them back a brand new copy of the same exam to be answered in groups of 2 to 4 for the rest of the exam period. This way, they realize right away what their mistakes are, and experience the power of peer learning and working in groups. I think that this instant feedback mechanism provides a much better learning experience for students than standard exams. And as far as marks are concerned, I give 80% for the individual part, 20% for the group part, and if they do better on the individual part than the group part, then they get 100% for the individual part. This way they can't lose!

As a former Science 100 instructor, what are some of the benefits of taking an interdisciplinary approach to teaching science?

There are certainly huge benefits. In fact, science is interdisciplinary. Research is interdisciplinary. Most jobs involve interdisciplinary science. So why teach it differently? Learning things as separate entities instead of seeing them as parts of a whole is quite far from how things really work. It only provides a fragmented understanding, while in my opinion understanding the "big picture" is what is perhaps most important. This is true for everything in fact, not just science. By taking facts out of context we can make them say whatever we want. By taking aspects of science out of context it certainly becomes much harder to understand why they are important and why we should care about them. That's a mistake that a lot of us do too often when we teach mathematics in fact.

What was your favourite learning experience as an undergrad, and how do you incorporate that experience into teaching your students?

It was probably learning how useful it is to collaborate with other people. In my physics undergrad most of the students ended up getting together to work on assignments. It was all group work, which was fantastic. I learned so much more this way than I would have working on my own. And I realized that collaborating with other people is much more useful and productive than competing. It's all about sharing knowledge. Even if you think that you understand something, by having to explain it to other people you get a much deeper understanding of the concepts than you would otherwise. And along the way we became really good friends; my undergraduate colleagues are still some of my best friends after all these years!

I've learned a lot from this experience, both for my research, my teaching and my life in general. As far as teaching is concerned, I certainly try to encourage students as much as possible to work together. I also like to emphasize collaboration vs competition; collaboration is what real-world research is about. Peer learning is another aspect that I try to incorporate in my teaching.

What is one thing that people would be surprised to know about you?

Maybe that I like to run very long distances in the mountains? The longest that I have run so far is a 161km race in the Rockies called Sinister 7 (in fact I even won it in 2014! I would have never taught that this would be possible when I started running 7 years ago...). I have run many other races of 100km+ in recent years. In fact last year attempted my longest race to date, which is Fat Dog 120: a 197km in the mountains with about 9000 vertical meters of elevation (higher than Everest!) Unfortunately I had to drop out of the race after 135km because of an injury, but I will certainly be back and finish strong soon enough.