One of my most vivid memories of childhood is carpooling with Brad's mom to a church group when I was ten. It was early fall and we were talking about the changing seasons when she quoted her husband, an amateur astronomer: "We're losing a minute of sunlight every day."
That remark was so traumatizing that even now, almost twenty years later, I can recall the exact cross-street we passed when she said it.
I pictured neverending darkness. Riots. I wondered if we should maybe skip church group and stock up on flashlight batteries before the rest of town found out. Even at that age, my sense of patterns (and what a math teacher years later would call "indirect variation") was developed enough to understand that we didn't have much time left.
This is what I used to know:
That was a perfect, teachable moment for someone to step in and show me that what I used to know wasn't good enough. "Not everything works like a line. Some things work like a cycle, getting bigger, getting smaller, getting bigger again. Can you think of anything else that works like a cycle?" Et cetera.
It has taken me six years to rewire my teaching to approach new knowledge as the solution to the limitations of what we used to know, rather than as an entry on a list of standards or "what we're learning today."