
I may need to post this in a place where I can see it daily: Get out of your students’ way.
Neil Degrasse Tyson summed this up very well:

Children are born scientists They’re curious about everything around them. Imagine what kind of kids we’d have if we had scientifically literate adults.
Today, my volunteer shift at Math on a Stick was a bold reminder of that. Sarah Stengle , the visiting mathematical artist, brought Kaleidocycles. She cleverly created cardstock that was pre-scored with the template for easier folding by little hands.
The problem: this project had a specific directions for a specified outcome. We could fold in a different order and decorate differently but ultimately, the process for each kid needed to be very much the same so that they each ended up with a working kaleidocycle.
Because this craft was three-dimensional, we recommended that they decorate the paper before folding.[Side note: observing the differing levels of precision the children used while coloring was interesting].
When children know that the outcome is going to be really cool, they are very willing to let the adult do the work for them. To be fair, this was a tough project for the littler ones to do independently.
And then in walks an adorable blonde girl about five years old. She might as well have been Maria.
Child: I’m going to make one.
Me: Awesome, let’s grab some markers so we can decorate it.
Child: I want to decorate it AFTER I fold it.
Me: Well, because it’s…nevermind, you can do that.
Child: I’m going to draw pictures of my family on the triangles.
When we finished, she had come up with the most beautiful piece of math paper art I had ever seen in my life. The reason: She fought my insisting that the paper needed to be colored pre-folding.
When she played around with the kaleidocycle, she could hide and unhide her family. And then the heart in the middle…exploded. And so did my brain. This was so…incredibly…awesome. Take a second and watch her awesomeness.
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