The question about those images was, “What stays the same? What changes?” And people did not answer like seventh graders.
Instead, there was lots of discussion around proportionality, congruency, ratios, and other attributes of the shapes that are going to be one million miles from the minds of seventh graders in school right now.
But several teachers took me up on my offer and answered a little bit like children. I snapshotted them, paused the class, and presented them.
Things they told me that stay the same:
- The shape, the angles, the color, the orientation
- The color and the angle of the vertices
- The color and the paper size are the same
- The shape and the color
- Shape, color, orientation, centered on paper
“I love that you folks are finding patterns, noticing similarities, deciding what varies and doesn’t vary—including color!—using your eyes, your vision, your senses. That’s math!”
I read them an excerpt from Rochelle Gutierrez which is on my mind a lot these days.
A more rehumanized mathematics would depart from a purely logical perspective and invite students to draw upon other parts of themselves (e.g., voice, vision, touch, intuition).
By naming those responses “mathematics,” I turned them into money.
As a society, we decided long ago that certain pieces of paper had value—that they’re money. In much the same way, you are the central bank of your own classroom and you decide which student ideas are money. You decide which of them have value and, by extension, you influence a student’s sense of their own value.
I’m not hypothesizing here! Watch what happened with the teachers. On the very next screen in our lesson, we ask students to describe how this printer is broken.
Teachers clearly received my signal about what kind of mathematics was valuable.
They brought metaphors, imagery, and analogies that I don’t think they would have brought if I only praised deductive, formal, and precise definitions.
- My shape is drunk
- The lines do not stay straight…they are wobbly
- My pacman lines are no longer straight. The new figure looks droopy and sad.
- It got curvy, kind of sexy looking
The ability to decide what’s money is a lot of power! In this time of distance teaching, you have fewer ways to broadcast value to students than you would if you were in the same room together. But I’m so encouraged to see teachers using chat rooms, breakout groups, video responses, written feedback, snapshot summaries, whatever they can, to enrich as many students in their classes as possible.