It's true: practice and time really do help. Every day I feel like I improve my lesson planning and teaching skills, and it's always enlightening to go back and see my previous work and compare it to the work I feel like I can do now. Looking back at my lesson objectives from a week ago, even, I can pull out some things I really like, and some things I want to change. For example, I said: "I aim for students to be able, at the end of my lesson, to extend their understanding of function dilations in a positive direction (leading coefficient > 1) to a fractional direction (leading coefficient between 0 and 1). This is a big jump for students, and something that they often struggle to understand when they first see it." That's true, though my students did a lot better with establishing that understanding than I expected. And now, reflecting back on how I taught the lesson, I wonder if I could have helped them get even farther by talking about gravity at the beginning of the lesson, instead of at the end.
Here's what I mean: I hoped for students to understand how a leading coefficient can cause a function to stretch or shrink, and I wanted them to come up with criteria for a shrinking function on their own. They got there, for sure, but only through a numerical understanding ("when my leading coefficient is 1/2, all my y values are 1/2 of what they would have been without the leading coefficient, meaning the graph is more flat"). I can't help but wonder: if we had started the lesson by talking about jumping off a diving board on the moon, how would student understanding differ? Would even more students make the connection between a leading coefficient and a graph's shape? Or, would it confuse them?
I ask myself these sorts of questions all the time and I find they inform what I focus on when I teach. I want my teaching to be intuitive and relatable to my students, and asking myself these questions about who my students are, how their understanding works, and how I contribute to it really helps me see my role in lesson planning clearly.
I guess that's the beauty of it all - I feel like I'm constantly digging, getting closer and closer to connecting with the root of my students' ability to make sense of things, and the more I learn about them as people and as students the closer I can get and the more effective I can make my teaching. Of course this is a pretty never-ending process, but it feels good to be able to get closer.
My students, for example, absolutely love Gimkit. I guess I'm not surprised, kids love games, but the extent to which they're willing to step out and actively show their learning in Gimkit games really surprises me. They also love (and love to hate) "Brain Break" videos and activities, which usually have something to do with moving their bodies and pushing their brains in weird ways (one asks students to say a number out loud and simultaneously write a letter in the air, counting each of the letters from 1-26). Students always complain about getting out of their desks, but it really does help them stay fresh and focused in class. Never underestimate the power of breaking up learning!