they don’t need to be told how

I taught my classes the basics of using a compass: how to duplicate a segment and how to draw a circle.

I taught my classes the necessary vocabulary: bisect and perpendicular.

I gave them a page full of segments.
I told them to find the perpendicular bisector.
I provided a single hint: You’ll use two circles and a line.

They figured out the rest.

I had students come up and show their methods, and teach their classmates how to do it. All I did was help with the explanations and summarize their thinking.

THAT is the beauty of math, when it’s at its best.

When the students EMBRACE the exploration.
When the students WELCOME the failure.
When the students LIVE the scenic math.