Calculus III explores concepts of Calculus in three dimensions. An inherent part of the course is visualizing surfaces in 3D. This can be a challenging, yet important, part of the course. 3D printing has been a way to encourage such a skill while exploring an emerging technology.
To create a shape to print, students must graph their surface, which
involves creating an equation that will produce the desired shape. Small changes can result in huge graphical differences. For example,
x^2 + y^2 + z^2 = 4
is a sphere. Yet,
2x^2 + 2y^2 + z^2 = 4
is more like an egg but then
x^2 + y^2 – z^2 = 0
is a cone. So, the first question before ever walking to Studio M is:
“What shape do you want and how must you change the equation to create it?”
One this is done, the students are ready to print. But, will it work?
Not everything works on the printer. The assignment emphasized
experimenting and then learning from the outcomes. In our fast-paced world, it is as important, if not more important to make attempts, than to only attempt when guaranteed success. As Thomas J. Watson said, “If you want to increase your success rate, double your failure rate.”
Engaging in this technology enables the entire class to learn and be
inspired by each other. One of my students made this shape:
This and other shapes inspired me to see if I could use mazes from my Math Bytes book to 3D print. Here is what I created:
When I thought of the idea, would it work? I simply didn’t know. Studio M helped me know how to realize the idea, just as they supported my students when they took their work to the space.
In the end, the students had their shapes. One day in class, the students shared their shapes in class. Over and over I heard them asking each other, “How’d you do that?” And they sat and talked about mathematical equations and learned from each other. The conversations broadened and deepened skills necessary for many parts of the course. The best part, I simply became a participant of the class listening, asking questions, sharing and learning.