It’s probably not a far stretch to say that the majority of us have had, or at least know of friends who have had, Professor Andrew Beltaos as our Calculus or Linear Algebra lecturer. Completing his Bachelors degree in Honours Mathematical Physics and a Masters degree in Mathematical Biology at the University of Alberta, Professor Beltaos then came to the University of Waterloo in 2009 to begin his lecturing position. Since then, he has shared his undeniable love and excitement for teaching with countless students from the Civil, Chemical, Mechanical, Electrical and Computer, Systems Design, Mechatronics, Management, and Environmental and Geological Engineering Programs.
This issue, the Iron Warrior had the pleasure of getting to know this amazing professor a little more personally.
Which courses do you teach?
These days I’m teaching a lot of the engineering calculus courses and in the past I’ve also taught linear algebra for the math, engineering and science faculties. Specifically, I’ve taught SYDE 111 (Fundamental Engineering Math 1), Math 116 (Calculus 1 for Engineering), Math 118 (Calculus 2 for Engineering) and Math 215 (Linear Algebra for Electrical and Computer Engineers).
Why did you choose to become a math lecturer?
I would say it chose me. When I was doing my Masters, I realized that teaching was really fun and really awesome. So I heard that what you need to be able to lecture at the university level is a Masters, and I had that, so I asked them if I could teach courses and they said yes. It was harder than I thought but it was still really fun and I kept doing it, and getting better at it, and that was nine years ago.
What is your favourite part about being a lecturer?
The best part is honestly being able to pass on knowledge of really cool things. There’s certain things when I was a student that I found really exciting to learn about them, and now as I teach them, I hope that I can pass on that excitement and give a lot of people the same insight as to what is so interesting about this material. In my classes that I teach, which is typically first year calculus and linear algebra, there’s a handful of days of specific topics which I’m always excited to cover. I’m like, I can’t wait to teach about, the definition of the definite integral for example, where we do the limit of the sum of the rectangles. I think it’s just such an interesting idea and I always look forward to that. I always feel honoured that I get to be the one, in so many peoples’ lives, to let them know about these really cool things. So that’s what one of the best things. When students respond to that and they are like, wow that is awesome, it just makes me feel so happy. That’s the best part I think.
What is the most challenging part of being a lecturer?
I don’t know, I’ve been really lucky that I haven’t had any crazy situations with my teaching. Students are always pretty respectful, so I don’t have to worry about discipline or anything like that. That’s what I would fear having to deal with, because that’s not what I like to do, it’s not what I want to do.
I think the biggest challenge I ever had was during the first year that I taught. I made a rookie mistake of not bringing enough copies of the midterm to the exam. It was a bit of a fiasco, and I got really panicked. There were 100 students, and I picked up the big pile of papers and didn’t look carefully at the numbers since someone else printed it and it turned out I only had 50 exams. So I got half way through the room and I ran out of exams! It was kind of crazy, but the resolution was that this was a large course and there were many sections. So a student, it was like a funny dream basically, he came up to me, dressed in gym shorts and stuff and he’s like, “I’m a runner, I could run to the other classrooms and see if they have spare copies. And so he ran to the different classrooms that were writing the same midterm and he collected about 50, because he went to about five or ten different rooms, and brought them back. We ended up starting the exam late and it was really terrible, but it was a long time ago and I learned a lesson to always count your exams before you come to the exam. So that was the most embarrassing, challenging thing so far. But it’s actually not so bad, like it was bad but I feel like I’m lucky that there haven’t been worse things.
What is your teaching philosophy?
I definitely have a way of teaching, and it has evolved a lot over the years. When I first started teaching my philosophy was, “when I learned this topic I found this difficult, so I’m going to make sure students don’t find that thing difficult, because I know I found it hard.” But over the years, I realized that there’s so many types of people out there and they are not all like me, they don’t all think like me, not even a little bit. Now I’ve adapted my explanations to target what students find tricky and not what I used to think was hard. So every time a student asks a question, it adds to my inventory of possible ways of looking at a topic. Now I have like dozens of different perspectives on any one given topic so that when I start teaching it I can portray it from different angles. Presumably after enough years, I’ll have a way of explaining it that will make sense to everybody.
When I teach, I really like to teach to the students that are in the room. For example, right now I’m teaching two different sections of Math 118, and the lectures are different because it really depends on what the students need or what they ask. When they stop and ask a question, that’s when I’ll go and do an example on the spot that explains the question they have, but in the other class they might ask about something different, so I’ll go and do a different example. So it’s very customizable, my lectures are like a conversation between myself and the students in the class.
What would you have pursued as a career if money didn’t matter at all?
If money didn’t matter, and I could just fill my time with whatever I wanted, I would still really enjoy teaching. When I was back in my old town and met with my old high school teacher from 17 years ago, we were talking and he was asking me, since I was in a similar career as him, if I liked marking. He said, “I hate it. The teaching, you know, I do that for free. The marking is what I get paid for.” So I kind of agree with him; there’s certain aspects that go along with teaching that are a lot of work, like marking, or even creating exams which can sometimes be a little stressful since you have to make sure it’s good and that all the numbers work out nicely. If I wasn’t getting any money, I wouldn’t want to be doing those things. But being in a classroom, explaining concepts to people, I would still love to do that even if money was not a factor. The other thing I would do in my time is music, because I’m very into music.
Leading to the next question, do you have any hobbies?
I play a number of instruments. Guitar is my main one, it’s the one I’ve been playing since I was 11. I’ve learned a couple of other ones, I don’t play any of them very well, I just have a basic level that I’m competent at and it’s what works for me, and it’s really fun. So I also piano, accordion, harmonica, drums, and just last year I started playing the gamelan, because the university has a group for Balinese music, and I’ve been playing for a year and a half and it’s so fun. I pretty much all my free time on music. If it’s not basic necessities or social things, I’m just focusing on music, either playing or listening or going to concerts or writing music.
What was your most memorable experience as an undergraduate student?
I think I have two very memorable experiences from undergrad. One is memorable just because it was the first time I pulled an all-nighter. It was third year quantum mechanics, and I had gotten into this bad habit of starting an assignment the day before it was due. So me and my friends were working on it, and I ended up staying up all night. It was actually kind of exciting and fun, like it was the first time I did that for working on school. I went home after handing it in at 1pm in the afternoon, and then I went to sleep for I think 19 hours. So that was memorable for that reason.
But the most interesting thing in a really positive sense, was the first day of university, when I went to an astronomy class which I was taking as an elective, and the professor explained how gravity behaves. Before that I didn’t really understand it, like I thought, you’re in space, you float; you’re on the earth, you’re stuck to the ground. But it’s not even remotely like that. Gravity works the same way whether you are within the earth’s atmosphere or in space, and it’s just that there is a force pulling directly towards the centre of the earth. If you have a little bit of tangential velocity, you are going to go in that direction of the tangential velocity, as you are still being pulled down, so the vector addition causes you to orbit. If you are standing on a mountain and you throw a rock, it will start to orbit the earth. If you didn’t throw it fast enough though, it will hit the surface of the earth before it has an opportunity to continue its orbit. And that just blew my mind. It was 16 years ago and still to this day it amazes me, like every time I watch a soccer game and there’s a big kick I think, wow, this object is in orbit, just for this brief moment, and then it gets interrupted by the foot of another player.
Do you have any advice for your students?
One advice I have is just don’t stress about exams. When I was in undergrad, it was probably in third year or so that I started to see exams more as just an opportunity to sit down in a quiet location and work on some math problems for two and a half hours or whatever the course was, rather than, oh no this is a thing that my grade is riding on. If you’ve been putting in the work, if you are a reasonable student with a good work ethic and reasonable competency, then it’s no different from if your friend is like, “Hey you like crossword puzzles? On Friday I’m going to have a crossword puzzle party, you can come over to my house, it’s between 2pm and 4:30pm, bring a pen and I’ll give you a crossword puzzle and you can work on it, and it will be quiet and nice.” So there’s no stress there. You just think, sure, I like doing this, why wouldn’t I want to go and sit there and do that. Most of the learning you do at school is pretty fun, sometimes you get a little bit overwhelmed with the sheer load of it of course, but overall the learning is fun. Plus, the material you are working on, if you’ve chosen the right field of study, is something that you enjoy doing and are probably reasonably good at after putting in the work, so when it’s time for the exam, it’s not a stressful thing. So the exam anxiety is something I don’t think students need to have. Of course, there are some who have different levels of anxiety, I’m only talking from my own experience right now, but having that perspective reduced my exam anxiety significantly.
The other thing I would say on a similar note about if you are in the right program, is that you have to look towards what you are enjoying. What I did with my undergrad, and Masters, and career, is that I pick and choose the things I like, and then those are the things I’m motivated to do. That means those are the things that I will do well in, and then it’s like a positive cycle because I’m rewarded for doing things really well by being able to do more of it, which is fun. So just explore deeper the things that you enjoy the most, and you will find your path, in an ideal world. I’ve been lucky that I’ve had an ideal situation and I hope that everyone can have that kind of luck as well.
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