When I start a new academic year, I like to revisit sources that help me re-center as I plan. It's like being an athlete and doing drills and base training to get the body ready for an upcoming season. I revisit why we teach as a check to keep me from straying from the real reasons why we love our jobs as teachers. We are also privileged as math experts to have the capacity to see the wonder and beauty that lies far beneath what nearly everyone else considers mathematics.
What we are presented with every academic year are opportunities. Opportunities to use Mathematics (or whatever subject you teach) as a vehicle to provide transformative experiences for students. We very easily can get bogged down in the details of covering chapters 1-8, making sure all the t's are crossed and techniques are sharply executed. But what we are really after is, if you think for a moment, is helping students become powerful, creative learners.
Ten or fifteen years later, what do you want your students to have retained from your class? My guess is that knowing how to compute $\frac{d}{dx}\arctan(x)$ isn't highest on the list.
