I am currently (spring, 2020) teaching an undergraduate course entitled "Calculus A(2)(Eng)" - it's an English stream of a first year multivariate calculus class. The novel coronavirus epidemic (predominantly in China as of now) has resulted in us needing to teach classes online. This is a bit of a challenge, but we'll see how it goes. And last semester I taught a graduate level course entitled "Riemann Surfaces: a hyperbolic approach".
I was a departmental tutor in the Mathematics and Statistics department at the University of Melbourne during my PhD. I've tutored subjects at every level:
- Calculus 2 (first year),
- Accelerated Mathematics 1 (first year),
- Group Theory and Linear Algebra (second year),
- Real Analysis (second year),
- Complex Analysis (third year),
- A few replacement Differential Geometry (Masters level) and Complex Analysis (Masters level) tutorial sessions.
Things that I've learned from teaching:
- The single most effective teaching technique that I've implemented, has been to get students to write their names on the board when they're in their small groups.
- I've been told by the Melbourne Uni education gurus that students learn more from their peers than from their teachers (including me). And I very much suspect this to be true.
- Blogging for students is a lot of effort, but it very rewarding when it works. Plus, I find that having a semi-regular audience is really good motivation to keep blogging.
- Epsilon-delta proofs (probably) aren't as hard as they are scary, it's more just that the formal language of analysis is a bit foreign.
- No matter what problem your students are working on (it could be the Goldbach conjecture for all I know), it invariably helps to first convince them that it's easy. Even just saying that something is easy somehow makes it way easier. Plus, everything is totally easy...right?