My History as a Math Learner

As I simultaneously reflect on the past and ponder the future, I can't help but draw parallels to the most recent movie I've seen: "Tenet" by Christopher Nolan. I highly recommend the quest to a silver screen to see the film. I write this blog post as I listen to the soundtrack at a reasonable volume. 

 

Past Teachers

I honestly can't remember much from my elementary school learning experiences, so I will reflect on my learning experiences in high school math. I'm fortunate that almost all of my math teachers were good so I will instead share my memories of one not-so-inspiring and one inspiring.

The not-so-inspiring: my grade 9 math teacher. It was a boring class. The lesson plans were clear, but the majority of the time was spent with dimmed lights and a squeaky marker shrieking y = mx + b on the sheet of an overhead projector. They taught well and I improved over the course of the semester, but I was far from interested in the material. To utilize vocabulary from the reading from Skemp (1976), this class felt entirely instrumental, which engineering students especially like to call "plug and chug". During class I was doing math, but I wasn't thinking about it. Perhaps these negative experiences are due to my 14-year-old self still getting used to high school, but I think there are better ways to get grade 9 students thinking about math.

The inspiring: my grade 12 functions teacher. On the contrary, there was less instrumental understanding in this class. We talked about more real world examples of the math we were learning and consequently these types of problems came up in word problems on tests. Class started with examples on the smart board, followed by independent work time on the homework problems. We could ask for help if we needed it, and sometimes these questions would lead to discussion involving the whole class to further clarify a concept. However, we were usually able to work at our own pace, which I liked because I could get into my own groove - meaning it was okay to rip through a handful of problems and then get pleasantly stuck on the next few. In addition to the class structure, they also utilized math puzzles. Each test, the bonus question was a different math puzzle which we could practice throughout the unit. My favorite was the KenKen.

(A close second place is my grade 10 math teacher. They wore a button on their dress shirt with a math pun Monday to Thursday, and on Fridays they dressed casually, usually with a t-shirt with a math pun. Some of the puns that come to mind include "math is the path" and "I can't get no satisfraction".)

Future Students

It's exciting and intimidating to think that we will be teaching as many as 6,000 students during our career. Here are two hypothetical emails from future students.

Hi Mr. Hamilton,

I'm in my final year at the University of Waterloo in mechanical engineering. The program has been a lot of work, but I know I made the right choice. The math classes we've taken have been tough, especially ODE's and PDE's. However, I felt prepared for these challenges thanks to your class in high school. You taught me to be patient with problems I can't solve and to ask for help when I need it. 

Do you have any new favorite math puzzles?

Sincerely,

A student who absolutely loved your class 

Hi.

Lots of my friends took your class and for some reason they really liked it, but I feel it's necessary to send this email to tell you that I thoroughly despised it. Even though got a decent grade, it was the lowest of my classes in grade 12. I don't think the applications to engineering and medicine were interesting because I was just in class to get through the math so I could go to business school.

Just wanted you to know.

And math puns aren't cool.

Cordially,

A student who didn't like your class

 

One of my motivations for becoming a math teacher is to provide an enriching learning experience like my grade 12 functions teacher did for me. I hope my future students will feel how I feel about this teacher. If that were the case, they would say things like my positive letter. However, my main concern is that after several years of undergraduate and graduate studies I am quite rusty with the material in secondary math and I am anxious about my abilities to teach as well as I have been taught.

This has been an interesting thought experiment and I will continue to think about what skills I need to develop during our time together over the next year.