Each year, as part of a bookmaking project with sixth graders, I bring in my impressive assortment of paper punches, and let the students decorate their handmade books with a colorful array of items which include stars, crescents, hearts and creatures. It can be a wild free-for-all, with some students slapping on their paper-punched creations willy-nilly, and others making carefully thought out arrangements. It’s generally a messy, high-energy class period, with bits of paper and glue being put down with excitement and delight.
Last year it occurred to me to rein in some of this excitement and introduce the students to different kinds of symmetry that would enhance their designs, Things seemed to go pretty well last year, so I tried it out again this year.
While some good things happened, it was clear to me that my own ideas about teaching something new came at a cost: students didn’t do nearly as much decorating as in previous years, and much of the excitement had been sucked out of the project.
Naturally, what I want is the excitement AND to be able to teach something new and valuable.
My experience with the sixth graders was weighing on my mind this past week when I was working with second graders on cut-paper project.
What I think had been my biggest misstep with the sixth graders was that I dampened their paper-punching enthusiasm before they ever got a chance to indulge in the novel activity I was laying out for them. I depend on the use of unusual tools and colorful materials to engage students, but I hadn’t given these kids a chance to experience their excitement before laying out the conditions which seemed to challenge and dampen their spirits.
In hindsight, I think things would have gone much better if I had laid out the materials, let the students create their collections of paper punched bats, balloons, dragongflies etc. and then, only after they had gathered together these personalized treasures, I could then proceed with the references to symmetries.
Now, this week, working with second graders, I tried to learn from what happened during my time with the sixth graders. I had an agenda, which is to use rhombuses to construct plane shapes, such as trapezoids, hexagons, and triangles. This is supposed to be an exciting activity, full of experimentation and discovery. I didn’t want to do anything suck the joy out of playing with the rainbow of colors in search of wisdom.
The students needed to cut out rhombuses from a packet of colorful printed strips. I decided not to tell them exactly what we’d be doing with the rhombuses. Instead, after the rhombuses were cut, I encouraged to students to slide them around on their desk, and organize them into piles or shapes that appealed to them.
This exploration time took only a few minutes, and, as different students finished their cutting at different rates, it kept everyone busy.
I traveled around the room, showing some kids how to use these shapes to make all sorts of arrangements.
It’s worth mentioning that they were notably impressed that three rhombuses could look like a hexagon, or like a cube in perspective, with color choice playing a significant role in creating the illusion that these same shapes were different.
It was only after this time of playing around that we got down to the business. I tried to keep them in discovery mode by asking them to take just a few pieces in their hands (which at this point included some rhombuses that had been cut in half to form two equilateral triangles) and to try to figure out how to make a trapezoid or a triangle or a hexagon, or a scaled up rhombus.
It all worked out.
At no point did I feel like my agenda had sucked the air out of the room. Whew.
My note for next time is to remember to let the kids feel the excitement and let them create their own relationships with the materials before I overlay my lessons into the moment. Whereas I had hijacked their enthusiasm before, I think that this different approach enriches their enjoyment, and hence their learning.
PDF’s for Rhombi: