As I general rule I find thinking about math pedagogy deeply rewarding. Teaching a technical and beautiful discipline like math is difficult to do well. Students come from all sorts of backgrounds, the material can be challenging, and there are tons of moving parts in a course. It’s a challenge that I find exhilarating.
On the other hand, I find the act of reading the scholarship of math education to be dreadful and unpleasant. It is filled with jargon and hero-worship.
That being said, I’ve been extremely lucky to have great mentors and colleagues to bounce ideas off of. I’ve collected some of this advice in a Reddit post, which I’ll recreate here.
Undergraduate students often ask me for advice for how to improve themselves as mathematicians. There are many answers to this question: you can focus on learning new mathematics, you can work on your programming skills, you can improve your career prospects by working on professional development, …
This post is the result of many conversations and coffees with undergrads; It is the advice that I would have given myself as a second-year undergrad at the University of Winnipeg. These 35 projects will also provide necessary skills for completing a Ph.D. in Mathematics and will increase your employability.
Some of these projects will take an afternoon (“Learn how to make a bibliography in LaTeX”) and some might take a month (“Make a Predator-Prey Visualizer”). There is no time limit and no test, so take your time and make it your own.
Table of Contents
Some projects are marked with a [B]. These are especially well-suited for beginners.
In my second year of undergrad I had a formative experience with Delta-Epsilon proofs that stuck with me for a long time. Last week I was able to provide a similar experience for some first year calculus students.
(This talk was given as part of the Adventures in the Classroom lecture series at the University of Toronto on August 7, 2014. It aims to connect math educators with researchers in the academic math community. A video of this talk will be available later.)
We will introduce two fun projects involving Geodesy, which is devoted to measuring things to do with the Earth.
“Without doing anything dangerous, measure the height of your school”
I love this question. It is a bit affronting (how could I possibly do that?!), but there’s something magical about it that draws you in and gets you using your imagination. If you have never thought about this question before, please take the time now. (Seriously, go for a walk and think about it.)
I have posed this question to many people and have received many different solutions. When I talk to people about this problem I am struck by what solution they think is the most “obvious” or “natural” solution. Think about that as we examine this problem.
(This talk was given on March 31, 2014, at the University of Toronto to a class of mostly MAT 137 students. It was standing room only!)
In my first year of undergrad I was bad at proofs. In my second year of undergrad I was terrible at proofs. In my third year I was okay at proofs, but I was terrible at studying proofs.
The way I used to learn proofs was by memorizing the words in the textbook’s proof, word by word, with almost no understanding. I knew math, and I was fairly good at problems, but I just couldn’t get any purchase when it came to learning proofs.
Eventually I started to pick up various “tricks” and strategies for learning proofs. This talk is aimed at me in first year, and what I needed to hear so that I could have studied proofs better. (“I no proof good.”)
We’ll look at the basics of proof reading, the idea of definition unwinding and clever ideas, and finally we’ll present a general method for reading proofs.