Since I started, I've always been forcing myself to push students further. Around Year 3 or 4 I realized that for all the kids I taught in Year 1 meant, they will forever be my worst, in a manner of speaking. I had no expectations and generally no idea what I was doing. I resisted intense instruction or tasks because I thought the kids "couldn't handle it" or would resist or because I doubted my ability to persevere when they were uncomfortable.
It took a while to silence those concerns. I spend a lot of time rethinking instruction and take my sweet time making changes, but over time I see dramatic differences.
Let's flash back to November 2012, here's a project on graphing sin/cos:
At the time I was patting myself on the back for this. Super colorful, but the demands were so simple. Take a trig function (that I made), do a 5 second frequency calculation and then graph it. No sense of scale, no comparison with the parent function, and no explanation of what the heck is going on if you're casually looking at these.
Flash forward four years to the same project:
I made nothing here. Students were required to design functions that met certain requirements in terms of frequency, amplitude, and translation. Then they had to write about everything they did. We spent some time learning Desmos and how to print, and they were off. I even required a complimentary task on the reciprocal functions:
Unthinkable in 2012 both in terms of technology available and determination on my part.
The question I want to you to answer, how do you push? What are you doing to make previous activities, concepts, and topics more demanding of your students? What would happen if a Pre-Cal student of mine from 5 years ago walked into my room today? Would they be able to hang with the young ones?
I overhear a lot of negative chatter about what kids can't do. That they're behind, or incapable of [blank] mechanic. That teaching had to slow down because the group felt like it was going by so fast. How are you pushing to fix these problems? What tiny routine or change could you incorporate to make it better?
Who's really scared of going too fast?