Rob Dukes, a doctoral student in UNM’s Department of Mathematics & Statistics, approached HSLIC about using the 3D printer to generate models of calculus functions. Dukes wanted to help the students in his Multivariable Calculus course improve their understanding of course concepts by introducing a kinesthetic aspect to his instruction. The first photo here shows Dukes's students using the model printed on HSLIC's 3D printer during a class meeting in February 2024.
The models came from the website Visualizing Mathematics in 2D & 3D produced by Monroe Community College. This site offers several different methods of converting functions into 3D models. Dukes chose to print ready-made STL files from one of the lesson plans, formatted specifically for Cura, the software that matches with HSLIC's Ultimaker S5 printer.
Since so much data gets input into the coding for these prints, the files required a much longer print time than would be expected for a model of this size. When we printed two of the models together, the print time ran to one day, 20 hours and 47 minutes. Our printer performed as we hoped and the mountainous surface models came out great.
In this screenshot from the Cura software, note the print time in the lower right corner and the support material represented in blue. We used water-soluble PVA for the supports, allowing for a smooth underside to the model after some soak time in our water bath.
The lesson using the models went as planned and Dukes featured it in his teaching portfolio: “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.”