The KUA Pentagonal Hexecontahedron!
…and countless opportunities for learning. I met mathematical artist Hans Schepker
12 years ago at the New Hampshire Artisans Fair, and was mesmerized by his booth. It was a perfect summer afternoon and I was strolling through the fairgrounds at Mt. Sunapee absentmindedly thinking about spring skiing and browsing for cool earrings, maybe the perfect salad bowl, when I came upon a zoo of geometric figures hanging in a corner booth. There was a pair of intersecting cubes hanging above the collection, shedding blue and red light over a vast array of colorful polyhedral sculptures, many fashioned into chandeliers. The precision of the work was amazing. A group of fairgoers who had gathered around the proprietor were gazing into a glass cube that appeared to suspend a fourth dimensional hyper-cube inside. When I got close enough, I heard them throwing out ideas about how this illusion was possible. This group of strangers was completely engaged with the mathematical structure of the piece and I knew I was witnessing an amazing learning experience. As I strolled through the fair that day, my thoughts kept returning to Hans’s work and the words of Dr. Dennis Littky from Big Picture Learning who, years earlier, had encouraged me to invite experts into my classroom. “I’ve never met a professional who wasn’t willing to share their passion with kids – all ya’ gotta’ do is ask ‘em!” Littky would proclaim at conferences. I made my way back to the booth with the whimsical banner that read, ‘Mathematically Correct Lighting,’ and asked, “Would you consider an Artist in Residence?” Thus, this classroom partnership
Twice a year for the past 5 years, Hans has loaded up his Mini Cooper with the tools of his trade and the parts for a unique geometric glass sculpture and begun the trip to meet my students. Around the time he leaves his Harrisville, New Hampshire home-studio, I start converting a science lab into his school-studio for the next few days; I cover the school desks with plywood to protect them from the heat of the soldering irons, I replace the new plastic chairs with the old wooden ones, and I set aside the anatomical models to make room for the mathematical ones. On the first day of the workshop, I introduce my students by class, up to 40 per block period, to Hans and their new roles as ‘Geometric Artists.’ Over the years, Hans and I have leveraged the training my students receive in the leadership roles they learn in their team-based math class in order to maximize ownership of the success of the project. Throughout the term, my students have several assessment opportunities that characterize roles specific to a profession or historical context. For example, during Unit 4, Geometry students become naval officers for the team-based scavenger hunt trigonometry assessment called, ‘The Sub-Station Challenge.’ For Unit 11, they become Manor Lords to work through a solids assessment called ‘The Castle Challenge’ and the day before the Glass Geometry Workshop begins, they are Calibration Technicians for a teaching opportunity called the ‘Pull Up a Chair Geometry Fair.’ When they arrive for the Workshop, they start reading their responsibilities as Geometric Artists and they realize that they each now take responsibility over all aspects of the project. The idea is in harmony with the result that understanding is owned by all students at the end of the course.
During the workshop, students focus on accuracy and precision while foiling the glass parts that go into the professional-quality sculpture. They also look for and express repeated reasoning when they solder the congruent polygonal faces, then pyramids of the polyhedron as the work grows. Students analyze errors and amend misconceptions when they must remove upside down faces from completed portions of the sculpture, and in the evenings, they reason both abstractly and quantitatively as they construct viable arguments for the measurements that are held within the structure of the space. Collaboration is high as each group leaves their station ready for the next rotation, and each component of the sculpture is handled by several students on its way to final assembly day.
One of the most important aspects of the Glass Geometry Workshop is that my students work side by side with a passionate mathematics professional who gives them the opportunity to model with mathematics in a beautiful way with a group of their very best friends. I am confident that the experience of the workshop creates an increased ability to hold a mathematical idea in mind… and gives them a reason to want to! We call these learning phenomena, “Going all Paul Lockhart on it!
Sustainability is also highlghted in the workshop. Students practice careful counting processes earlier in the term when they must order paper strips to build one of Heinz Strobl’s Snapology models
accurately. We keep small ziplock waste bag on each station throughout the 3 day workshop so that we can see what is thrown away. Historically, this project has paid itself forward as the sculptures are highly sought after by alumnae artists who want to make sure the opportunity to collaborate with a working mathematician is available to the next class of students.
Sandy Reavill, Director of Innovation and Design at Kimball Union Academy, is an Instructor in the KUA Mathematics Department, a CPM (College Preparatory Mathematics) teacher and a CPM classroom researcher with TRC cohort 3.0. She will be sharing her passion, ‘Making with Students’ in a series of faculty workshops this year.