Just before Covid made my middle school teaching remote for the past year, I attended a workshop led by mathematician and Math for Love co-founder, Dan Finkel. Math for Love makes visual puzzles and supports parents and teachers with math teaching resources. Little did I know, Dan’s approach to providing intriguing visual puzzles would become a touchstone for learning to teach math from a distance.
Dan’s workshop exemplified the Math for Love approach. He put an image on the screen and told us that we were looking at a stained glass window and that the master stained-glass artist was tired of this design. The artist had a commission to design as many windows as he could that would take up exactly half the square and touch each side of the square once and only once at the numbered points. Dan asked, “Was it possible to come up with any other designs?”
The room sat silent for a few minutes and then people began sketching and wondering aloud. As Dan worked the room he circulated, and listened. He asked questions, waited for our answers and directed us to be curious about each others’ partial solutions. Two or three times he called us together to consider each others’ ideas as a large group. These discussions offered new tools, but no answers. After one and a half hours, participants had convinced each other that the stained glass maker could stay busy for a good long time without repeating a window, but none of us knew exactly how many windows that would be. Dan said good-bye without telling us the answer.
In 2010, Dan and his partner Katherine Cook founded Math for Love with the goal of helping people see how “playful, beautiful and life-changing mathematics can be.” I had long been intrigued by the activities and games I found on their website, and having experienced a workshop, I invited Dan for an interview. We met in a cafe in his Seattle neighborhood. Dan shared his work as a puzzle writer for the New York Times. He told me that making a good puzzle is like poetry. He starts by thinking about something visual, like a cube or overlapping squares and then begins asking himself a question. At best, it is a natural question — that is, a question that could arise for anyone seeing the image.
While distance teaching using Zoom, I start my class by sharing an editable Google slide deck — a set of images and words that anchor an hour of doing mathematics together. My fourteen-year-old students log in from their bedrooms, living rooms and kitchens. At times, students’ wifi is so weak it distorts voices so much they don’t dare talk. With such glitchy connections, the visuals I provide in the slide deck help carry students’ thinking forward. They can add words, and shapes and tables and images of their own.
While not every task rises to the level of poetry in Stained Glass Window, I keep Math for Love principles in mind as I design. In the Seattle cafe, Dan shared that a good puzzle naturally breaks into small doable steps that keep leading you on toward a solution. In the best puzzles, each step feels natural, that is, it doesn’t require sudden insight or extensive formalized knowledge of mathematics or a series of prescribed steps.
As I translate these principles into distance teaching, I find myself leaning heavily on family stories I can tell, like my son’s concern in middle school that his little sister was taller than him or my husband wondering on a dark winter morning about Voyager 2’s power supply. I also take full advantage of the affordances of google slides. In our data unit, most tasks consisted of incomplete graphs that, if examined carefully, could be used to solve a problem or tell the rest of an unfinished story. Students can move the dots on the slides to complete and make sense of the graphs so they can use them to answer questions. I have also adapted ideas from Jo Boalers’ new Mindset Mathematics in a Math for Love-inspired manner. Stairway to Eleven provided a genuine puzzle related to slope. And Find the Fake became an investigation in similarity. You can create your own copy of these lessons with this link.
Even with inspiration from Math for Love, visual Zoom is eerily quiet; however students do share that they are learning, and they often “say in the chat” what they are thinking. One student told me he hasn’t understood math since 5th grade and he finally gets it. Another who said she used to hate math now finds it to be her favorite class. A third shared that she is enjoying and understanding math for the very first time. When I asked for details, all three told me they know what to think about by looking at the slides, even when they can’t hear or understand the words. Their insights remind me of the importance of making math visual. When students miss the words, they can fall back on what they can see with their own eyes. Almost everyone who has been in a math class knows the feeling of having missed the words. If there is any power math can unlock it is a person’s ability to make sense of the world through their own perception. The more math can be a visual puzzle the more it can unlock the power of people’s own perception. Add a teacher who attends to student perception and real change for real people unfolds. As Dan Finkel says, “You have a right to understand the math. As the teacher I have a right to understand you. I will listen to you until I can understand you. That elevates everyone into a realm of relationship, community and kindness.” What better way to get through a pandemic than teaching Math for Love?