I showed my geometry students how to bisect and copy angles and segments. I also showed them how to make an equilateral triangle. (and therefore a 60 degree angle)
I gave them this challenge:
“No, no, what is the answer?”
“But, thats not how to do it, I want to know how to do it.”
Statements like these. Students want the formula or the process. I want them to evolve. To think. To wrestle. They did.
It was pretty cool. With little to no instruction, (except to point them to the strategies of bisection and copying angles of the previous class) most were able to overcome their fear of “but you didn’t tell us how to do it” and challenge their brain to think about angles, constructions and problem solving.
It was kinda cool.