Wednesday, April 29th, 2015
Preparing students today is preparing for the unknowns of tomorrow. Intellectual flexibility enables someone to adapt knowledge to emerging issues. For me, the college classroom should strive to prepare students for jobs not yet created or envisioned. How do we do this? We have been. The concepts we teach in the classroom introduce concepts, of course, but also ways of thinking. Looking through the mathematical lens brings the world into a unique focus. In math, we solve problems and one need only to open the newspaper or watch the evening news to see our world abounds with questions and unresolved issues. Learning to break down a puzzle, large or small, analyze and solve it is an inherent part of math at all levels.
A year ago, I visited a Digital Studies class, Hacking, Remixing and Design, of Dr. Mark Sample of Davidson College. Dr. Sample crafts an environment that welcomes risk taking by everyone – students and professor – as he responds to the classroom environment. In particular, the class is given assignments that lead to failure. The goal is to successively improve and analyze how and why. In fact, the class wrote flogs, which detail their failures and later analyze their work to better understand their tendencies to fail and innovate. As I watched the students in the class openly share their struggles, I thought about math classes. What better ways could students engage in the unknown and step confidently even if many attempts will most probably be unsuccessful?
In an attempt to move in this direction, I’ve leaned on Davidson’s movement in the realm of digital studies. We have a Maker Space called Studio M offering opportunities in 3D printing, drones to fly and low cost computing devices, many of which do not require programming experience. My first introduction to such technologies came with Makey Makeys. I’m currently working with a student to create a school program using these low-cost computational devices, like playing a piano by touching potatoes rather than keys.
Last semester, I decided to introduce 3D printing into Calculus 3, which inherently requires visualization in 3-space. Adapting a Mathematica workbook from George Hart, I asked my students to create 3D solids to print. A student who worked in Studio M created examples that led to successful and undesirable results. Then the students were tasked with creating an equation that resulted in a solid to print.
The assignment was to create a shape, print it, take a picture of their work, and then write a page sharing their equation, intended result and an evaluation of their work. Did the shape match their intentions? If so, why? If not, why not? If the result matched their intentions, might they push limits more next time? If a shape didn’t print as desired, why not? They needed only to print once and then analyze their result.
I signed the students up for weekly shifts of printing in Studio M to keep a steady stream of students over the 5 week period. I learned from the students and those in Studio M that many students printed multiple times. Early on, I reasserted that student did not need to have 3D models that matched their expectations. One of the students who had completed his assignment laughed, “I knew that. I just really wanted to make it work. It wasn’t about the assignment or the grade.”
Isn’t that truly what we search for in education? We look for students to dig into the material from their own interests and desire to learn. In this case, many students engaged in this way. They applied knowledge from a textbook to a relatively new technology. And some students shared their work. Here is a piece made by a first-year student. She made this 3D solid for her boyfriend.
There are many ways to engage students. Challenging students so they learn to tackle problems and step into the unknown is important part of the mathematical classroom. For me, integrating 3D printing into Calculus created a teachable moment. It was the best kind of moment — one in which the students learned on their own and didn’t need me. I was mainly relevant when they were ready to share their work and, for many, when they wanted to share their excitement.