Countdown to School: Interview with The Apprentice

What are you studying at university?

I am in a research-based science program, with a specialization in math. This will effectively give me a double degree in science and math. This program has a strong focus on conducting research, reading and analyzing papers, presentation and scientific writing, and pedagogy (teaching).

Do you think of yourself as a "math person?"  Do you see the world mathematically?

I don't actually see myself as that much of a math person. Although I was one of the stronger math students at my high school, I've met an awful lot of people at university who are more talented in math than I am. Not that I don't have good math skills, but when you talk to these people about a problem, or see their proofs, you realize that it's more than just algorithms, it's more like learning a language. You can memorize vocabulary lists and learn grammar, but constructing speech itself is more of an art. I know how to order a beer in French, but I certainly can't write poetry.

What got you interested in pursuing post-secondary mathematics?

My short answer is that I wanted to do physics but I'm better at math, so I decided to go at it from the maths side. The first two years of my program, regardless of your specialization, have mandatory full-year math courses. The program tried hard to show how this math could be applied to other branches of science, but to many of my classmates it didn't even feel like part of science, just an annoying course to get through. As I've taken more and more math courses, I've found them linking together and applying to other disciplines. I've always found math useful and relevant. I feel like my degree is really just in research science, but when I was able to pick a focus I wanted to have a tool that would be useful in any of my scientific aspirations.

Would you like to be a math teacher?  Why or why not?

I would absolutely love to be a math teacher. I spent a lot of time in high school acting as a math tutor at the school's math help centre, and I also peer tutored a math class. After physics lessons I often found myself surrounded by students wanting me to run over the problems (I loved doing that but it meant I never got my own homework done...). At this point I feel like I may end up in something similar to teaching or perhaps administration. Ontario teaching jobs are very hard to come by no matter how good you are. While I'd prefer to teach on the undergraduate level anyway, this generally requires a PhD. I'm not sure at this point that I would want to pursue that much school. However, I am keeping learning and pedagogy in my sights, this year I am taking a child development course and hope to focus an individual project on the effectiveness of various mathematics teaching methods.

What were some of your early math experiences?  Do you think they were important to your later interest in math?

The earliest math experience I can remember is learning addition and subtraction on a homemade scale constructed from string and yogurt cups. ("This piece weighs five. The piece on the other side weighs two. What do we need to add to make them balance?") Later achievements involved hopping back and forth on a number line, and learning fractions through cooking. I think these experiences were really important, especially watching my parents use things like fractions in everyday life. Learning things like the fact that you can fill the half-teaspoon measure halfway full to get a quarter-teaspoon without dirtying two spoons (or with my dad, if you pour out half a bottle of engine oil, that's 500 mL) have always reminded me how useful math is in real life. Learning that numbers and electricity could be connected in small electronics led to an interest in physics.

Was there a time you did not feel "good at math," or that you disliked it?

There are always times that I don't feel good at math. The problem is that until you get really really specialized, everything has to stay connected. It may not always be clear that eventually two concepts will merge together, so if something seems kind of pointless at the time and you just learn the bare minimum, it can come back to haunt you. I'm sure I disliked it at various times in elementary school. What I've found in tutoring others is if they're really not getting it, you need to take a step back and try a completely different direction or explanation. A lot of students I found just needed a reason for what they were doing to understand (e.g. trig gives you ratios between angles and sides of a triangle, so if you don't know one of them, you can find it). This really frustrated me at one point when I was tutoring students in the "lower" academic stream. Those students might have been there because English wasn't their first language, because they had a learning disability, or sometimes even because they just didn't like school. But none of them were stupid. I had a supervising teacher actually stop me mid-explanation and tell me that I couldn't give a student the logic behind a concept, I should just teach them the algorithm for doing it, because they weren't capable of understanding. No wonder they didn't think they were good at math.

What parts (types) of mathematics do you enjoy studying most, and which ones not so much?

I really like working with mathematical computer programs and understanding how they work. I did a research project on this last year looking at molecular electronics using several programs. Really the part of math I don't like is certain testable things that you only have to know for a course, but later you would just look up or use the computer to solve. I understand that you need to know the process, and I'm interested in knowing the process, but I tend to make computational errors by hand which can slow me down or give the wrong result.

If you were teaching your twelve-year-old self, what would you do do make math a good subject?

If I was teaching my younger self, I'd have lots of practice and worksheets because practice makes things much easier. But I'd also have experiments where you can collect real numerical data and apply the concepts to that, so you can see how they're used and they become relevant.

Any other thoughts?

One of the best math resources I've come across is Khan Academy.  I'd highly recommend it for high school level math (it has other grades too including some university). The conceptual teaching is excellent and there are lots of practice questions too. You can earn points for watching the videos and doing questions, which I loved when I was a kid and still enjoy.  (We didn't use Khan Academy; I just liked playing games and getting points.)

Thanks, Apprentice!