Prologue
My first advice on teaching, when I first became a TA in my Master's program, was a 2-page list of Do's and Don'ts. I don't remember most of them, or even how many they were but I do remember the first three.- Know more than your students
- Know a lot more than your students
- Never tell your students everything you know.
This advice comes back to me approximately once a month, and its meaning always has subtle differences from the last time. I think it's extremely important advice. It's probably my most used benchmark for deciding how to participate in all sorts of discussions. The first point is a little "duh," but the second point makes you stop and meditate a little on the importance of the first. For anyone who has taught for more than 10 years, you get a sense of why 1 and 2 are important. But then, there's the importance of 3. I thought 3 was a little silly and perhaps just a tad elitist for the first few years of teaching. But then, little by little, the power of 3 has crept up. I feel like, for me at least, there is a lot of wisdom in 3. Especially when it follows 1 and 2.
Here's an example.
Subtraction has been bothering me for some time now, and I've only recently started paying attention to this bother. I have been evolving the ways I've guided conversations around subtraction for the past few years, and I generally feel good about how the conversations go. However, I am always keenly aware of what parts of the conversation I'm leaving out (à la 3), and I'm wondering what parts I should start adding in (yes, I note the pun of this sentence).
