Learning With Symmetry: Teaching with symmetry
Lilly Vestal teaches at P.S. 202 in the Long Island City section of Queens, New York, a school that ranks in the top percentile in the city on a 100-point scale of school performance based on the National Assessment of Educational Progress, better known as the “Nation’s Report Card.” For her work with students and teachers, she is an award-winning teacher who has served on multiple panels organized by the Association for Supervision and Curriculum Development, or Asch. She writes a weekly online column about education issues for NY School News.
Teaching with symmetry is a way to drive math learning and, she says, “it turns me on. I would have been good with the circle game back in the ’70s when I was a kid, only now I have a lot more things I’m looking at. I like the fact that if a group of three objects have five values in the circle, if they all happen to move in the same direction, each group’s value is never more than one value. Because each group has some value, it allows you to learn mathematical relationships like you would in the example of a nice round circle.
“Here’s the cool thing about mathematical symmetry—I first learned about this with physical dimensions (i.e., symmetries in systems of measurement and movement)—and I never knew about it until I went to this science teacher’s class one day and he taught us about symmetry in the physical world.
“This teacher, I remember, told us that one of the great things about symmetry in symmetrical systems is that it’s not created by tiny changes—if you move the mountains in an apple or apple slice, or if you rearrange blocks in a tower, then the symmetry changes, but there are no really drastic differences in the raw forms. But in your mathematical system, those symmetries don’t change. And it’s often the sort of symmetry that is hard to explain to people.
“The reason that it was really great at my science class was that it took that revelation and turned it into some sort of fun activity. I haven’t heard of students doing it in a math class since.”
The book intro and full chapter is “Take Mathematics from Book to Page: Teaching with Symmetry” by James Ruse, with chapter introductions and appendices by Ray Negron, Helen Mohl, and Aileen Dunne.
For additional information and about learning with symmetry in math classrooms, see the Association for Supervision and Curriculum Development website: www.ascd.org.