I presented my Multivariable Calculus students with a lesson using 3D modeling. The base lesson plan was created at Monroe Community College [Source] and presented at the 2024 JMM in San Francisco.

A few weeks earlier, I had approached the Health Sciences School about using their 3D printer. Jonathan Seyfried told me it was mainly for Health Sciences students to do things like create models of organs, but he offered to let me use it and taught me the process. I printed six models (two copies of each), and each one took somewhere between twelve and eighteen hours to print. Take this as a warning to start preparing well in advance.

Students are asked to pick points where the partial derivatives with respect to either variable meet some different combination. Some ask for both positive, some for one negative and one zero, some ask about second derivatives having different signs, etc. Students worked in groups of up to five people sharing a model, and I circulated the room monitoring their behavior. In general, they were engaged in serious conversation about the topic and sharpened their understanding through discussion. Then they did the back half of the worksheet, answering similar questions using only a contour map. I collected the models and the papers at the end of class, giving a quiz grade based on which points they marked and on the answers to the contour map problems.

Unfortunately, one group did not do as well, turning in a model with a number of blurry points that were hard to distinguish from one another. The problem, I believe, was that the group was made up of one student who usually preferred to work alone and two others who spoke English as a second language. I believe there was some communication difficulty and it cause them not to do as well. I will have to discuss with them next time if they want to keep working together or if it would be better to shuffle the members.