One of the goals Andrew Alexander has for himself when he teaches his upper-school mathematics courses is to bring joy into the classroom. In Andrew’s Math 1 course, demonstrating the joy and beauty of math is fundamental to students’ understanding of and appreciation for math.
“Math 1 is the first class in our integrated math curriculum,” Andrew said. “The most important thing we are trying to accomplish is debunking the notion that math is about memorizing formulas and being careful with pedantic little details. It couldn’t be further from the truth. Math is about beauty and joy and wonder in this abstract system.”
To launch the geometry unit in his class, Andrew came up with a creative way to infuse joy and wonder into the learning, even though the class takes place on Zoom (“Even in remote learning, we can experience a lot of joy in math,” he said). Using I-Lab tools, building materials, and a little help from I-Lab shop manager George Jemmott, Andrew constructed a six-foot tall compass and an accompanying 12-foot long straight edge.
“The idea came to me one day as I was making lunch,” Andrew shared. “I thought I should make a giant compass and straightedge because it’s cool and fun. My class has been joking that it’s a socially distanced compass, since it’s six-feet long.”
Andrew began the unit by reading Edna St. Vincent Millay’s sonnet, “Euclid alone has looked on Beauty bare,” which speaks to the beauty of math.
“Many of us know visual beauty; that’s the default type of beauty we think about when we think about beauty,” Andrew said to his class. “But there are other kinds. There’s gustatory beauty, there’s musical beauty, there’s literary beauty, and so forth. This sonnet is another type of beauty: mathematical beauty.”
Following this introduction, Andrew placed his camera on a ladder and proceeded to show students how he uses the compass and straightedge to draw circles and other geometric shapes. Students enthusiastically encouraged him to continue drawing circles. Occasionally, Andrew was interrupted by an oncoming car as he was drawing these circles in the middle of his quiet street.
"The fun aspect of this demonstration was that we were not only dealing with lines and circles, but also with art, beauty, and excitement," said ninth-graders Ellie K. "I loved seeing the happiness in Andrew and my classmates as he ran from the computer to the compass and back again. This activity was
something I had never witnessed before. Even with experience watching teachers at previous schools draw circles on the whiteboard, this demonstration drew me in and kept me engaged.
“The whole thing was just so weird and novel,” Andrew said. “Yes, I could do these same constructions on normal paper with a normal-sized compass, but I wanted students to realize that you only need these two tools—regardless of their size—to build intricate, increasingly complicated shapes.”
It is clear by the students’ laughter and engagement that Andrew met his goal.
"In my first few months at Nueva—and especially reinforced in this demonstration—I have been taught to find beauty and joy in my learning and avoid the conventional, easy path," Ellie shared. "It is more common to use a handheld compass to create constructions rather than a six-foot tall one. However, I do not think I would have seen the delight in geometry or been as inspired to draw shapes of my own if we chose to use the small compass.
“I try to instill in my students a sense of wonder for the natural world, even when that natural world is a world of abstractions,” Andrew added. “I want to instill in them a sense of joy and a sense of playfulness. This class was one of the highlights for me of a strange year.”