Need: This research project aims to serve the national need of STEM students to develop a deeper understanding of 3D concepts in calculus through hands-on, physical 3D explorations using guided learning activities and innovative, pedagogically-designed, 3D-printed models. Students can better apply calculus concepts in other STEM courses when equipped with a clear geometric intuition for these concepts (i.e., the ability to clearly visualize the mechanisms and interrelationships involved). Although visualizing 3D concepts on a screen can provide students with insight, some students still find this process challenging. Additional insight can be gained by students through the use of guided hands-on interactions with physical 3D-printed models. Furthermore, this project aims to lower the bar to entry for faculty who wish to incorporate 3D models in the classroom. To accomplish this goal, the project will provide instructional resources and training that will make it easier for faculty to create 3D models of their design, providing scaffolding for them to begin using 3D models meaningfully in their teaching. This project will expand the usefulness of the CalcPlot3D visualization app and extend its user base. Our research will provide insight into how experienced instructors leverage 3D models to enhance student visualization through coordination of the 3D models with digital renderings in CalcPlot3D.
Guiding Questions: The project will consider two series of related research questions: 1. What, if any, differences are there in how the two professors reflect (both prior to and after instruction) on how they make use of the 3D-printed models and learning activities based on those models in their teaching? Are the pedagogical differences consistent across topics or do they vary with specific topics? What rationales do instructors give for their pedagogical decisions? Are their rationales related to limitations of the medium?2. What, if any, differences are there for each professor in how he or she makes use of the 3D-printed models and the associated learning activities in teaching online vs. in-person multivariable calculus? Outcomes:1. Expand the 3D printing capabilities in CalcPlot3D 2. Develop and class-test a series of classroom learning activities using 3D-printed surfaces and solids. Each activity will include a set of guided exploration questions, the STL files needed to generate a set of corresponding 3D-printed models, and an instructor’s guide to support the educator in effective implementation of the activity.3. Create a series of how-to videos and online tutorials, to support teachers and students4. Conduct educational research to determine how instructors with significant CalcPlot3D experience make use of 3D-printed models in their multivariable calculus instruction.
Broader Impacts: Beyond multivariable calculus, the new 3D printing features for CalcPlot3D proposed for this project can be used for visualizing concepts in single-variable calculus, chemistry, physics, engineering, and topology. This project will provide instructional resources for creating 3D-printed models, training for faculty, and insight into how experienced instructors leverage these models to enhance student learning.
Paul Seeburger, Monroe Community College, Rochester, NY; Deborah Moore-Russo, University of Oklahoma, Norman, OK