On a mediocre day, teaching math is about showing students how to solve problems. If it's a decent problem, the students might care, but mostly they'd like me to teach them a rubric so that they can easily do the homework.
On a good day, I manage to not only teach students how to solve a problem, but also why a particular technique works so that they might have a tool to solve a different, but conceptually similar problem later.
On a great day, we have a problem and they figure out the how and why for themselves.
This week we are working on figuring out how to graph complex functions using calculus techniques. This lesson was on how we might find the concavity of a graph along with a review on the procedures for finding asymptotes.
My lecture was perfect. It started with a good question. I remembered to emphasize the big ideas. I modeled the correct techniques and justifications. I asked them a few questions to be sure they were with me and they answered each one correctly. And I ended just in time without rushing. They asked me nothing. As I was saving the day's notes to post online, I thought, maybe I should use them again later in the day because they were just right.
The hard thing is, because class was perfect for me means it wasn't that great for the students. The best learning doesn't happen when I do everything right. It happens when things go a little wrong. The act of wrestling with the material, struggling to understand, solidifies the learning. Asking questions about things they don't understand means they are thinking about the ideas, poking holes in the explanation.
When I deliver a perfect lecture, it means they didn't do any intellectual work. It means they didn't process. It means they are going to struggle with the homework. And it's better to struggle together in class than alone at home.
I had, at best, a mediocre day.