I'm convinced the work of teaching starts with a successful invitation. Ideally, you're inviting early student thinking and helping students develop and mature it in mathematically useful ways. But it's hard to help students develop or mature thinking they haven't offered yet!
One of my favorite ways to invite that early student thinking is by starting with student senses.
Start with their senses.
In Turtles All the Way, we eventually ask students to calculate and write equations, but first, we just ask them to describe. Describe what's happening. Describe what happens to a variable of their choice over time.
In these early moments, I hope you'll find the students who are stuck or struggling or perhaps just worried that their thoughts aren't invited. Consider making your invitation explicit by letting them know, "Hey—right here, I'm just wondering what your eyes are telling your brain right now. Nothing's off the table. Let us all know."
As more students offer you more of their earliest ideas, ideas they might not even consider mathematical yet, I hope you'll find that their job of learning and your job of teaching becomes easier and easier.
Dan & the Desmos Classroom Team
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