Robert Millett's Professional Portfolio
Module 7: Playing
My mom always used to say that I shouldn’t play with my food and now I wonder if she was inadvertently stifling my creativity! Besides allowing for an entertaining way to work with an idea, playing also allows for us to create an environment conducive to creativity where rules don’t have to matter and anything you can imagine is encouraged. Free play allows us to get our feet off the ground and explore the abnormal.
With a bit of direction, my play activity is meant to encourage students to explore graphing in the coordinate plane. Particularly graphing linear inequalities. I would present the students with the challenge of creating a picture. Perhaps we could first start with something simple like a square, rectangle, or triangle. This would be at a time when students have already learned about graphing linear equations and restricting domains of functions so the graphs do not continue forever. This first shape would be to get students engaged in the challenge of graphing a specific shape. From here I would show the students what happens when we replace the equals sign with an inequality sign and observe how we can start to “paint” with our functions. From here the students should challenge themselves to create some sort of picture of their own. This act of playing should start to develop a sense of inquiry within the students. Hopefully I would start to hear the questions, “How can I move the line to the right?” “How can I fill in just one part?” “How can I make a curved line?” and so on. The answers to these questions are filled with opportunities to explore new and important mathematical ideas.
I developed this idea because I have seen how my students react when given freedom to play. They are very creative when given a chance to be and I want to see what setting this creativity loose in the coordinate plane could produce. As I was creating my own painting I started with something I thought would be fairly simple which was the house and I was able to create it, but the more absorbed I became in my picture the more I wanted to continue developing it and seeing what else I could create. The first challenge I came across was painting the roof. I had to think of a way to restrict the “painting” of the inequality with angles and not just a horizontal or vertical edge. I had to creatively think about the restrictions and the method I came up with required three separate sets of restrictions to work. The next challenge was painting the house red without painting the door or windows red. This required me to creatively split up the painting of the house into seven different inequalities with different restrictions. I had considered making a tree and I used sine functions to make the trunk of the tree but when I went to make the leaves I decided it was a challenge I was not willing to undertake at the time so I created the sun and grass instead.
Through my own experience making this picture I had to explore, experiment, and be innovative with how I used the functions to meet my desires. I was engrossed in the mathematics and yet the math wasn’t what I was actually thinking about; I was thinking about the art and pushing myself to make an increasingly complex image. I imagined what I wanted and then searched for ways to make it possible, even learning a few mathematical ideas myself along the way.
If you would like to see the equations I used to create the picture you can follow this link below:
