Collaborative Research: Institutional Mentored Partnerships Advancing Multivariable and Vector Calculus Teaching with CalcPlot3D

About This Grant

The project aims to serve the national interest by helping STEM students to develop a deeper understanding of multivariable calculus concepts through engagement with the three-dimensional (3D) visualization app CalcPlot3D and hands-on learning activities using 3D-printed models. Students can better apply calculus concepts in other STEM settings when equipped with a clear geometric intuition for these concepts (i.e., the ability to clearly visualize the mechanisms and interrelationships involved). This project plans to support faculty who wish to incorporate visualization and 3D models in the classroom through mentored partnerships with faculty teams who are committed to making department level change to multivariable calculus instruction. This project also seeks to expand the capabilities of the CalcPlot3D visualization app to support the visualization of additional topics from vector calculus, multiple integration, and physics. This project at Monroe Community College (Lead) involves collaboration with North Carolina State University and the University of Oklahoma along with several partnering institutions. The partnering institutions include the United States Airforce Academy as lead partner as well as the University of Virginia, Colorado School of Mines, Red Rocks Community College, and Northwestern Michigan College. This Improving Undergraduate STEM Education (IUSE:EDU) collaborative project responds to the NSF Dear Colleague Letter (DCL): Improving Undergraduate STEM Education – Adaptation, Implementation, and Dissemination (IUSE-AID-DCL 24-026). Related to this DCL, the project aims to reach a broad group of faculty members outside of the collaborating and partnering institutions through multifaceted dissemination, sharing instructional materials and findings. The project also seeks to foster an educational research component which could provide insight into how instructors leverage 3D models and a digital platform for 3D visualization to enhance multivariable calculus instruction. In the process, project researchers plan to study the inter- and intra-institutional collaborations to investigate how postsecondary instructors work with and are influenced by other instructors and, in turn, how this impacts the dissemination of educational efforts. The main purposes of this project are (i) to foster institutional implementation of computer visualization and 3D models in multivariable calculus classrooms, helping students develop deeper conceptual understanding, and (ii) to improve the CalcPlot3D visualization tool and produce accompanying learning resources. The project has five major goals. First, the investigators seek to work with the partnering institutions to adopt instructional changes at a departmental level to incorporate visualization with CalcPlot3D and activities from this project using 3D models. In the process, the project team will provide mentoring and equipment to facilitate this implementation. Second, the project team aims to expand the features of CalcPlot3D to include more built-in options to better support advanced topics in vector calculus, multiple integration, and physics applications. Likewise, this team plans to improve the user interface to make it clearer, more attractive, and easier to use. Third, the team seeks to develop and class-test a series of classroom learning activities using a combination of explorations using CalcPlot3D and 3D-printed models. Fourth, the project's investigators intend to conduct and publish educational research on the effectiveness of project learning activities, on the adoption of 3D models and CalcPlot3D by institutional cohorts, and on instructional implementation of particular topics. Project research will include surveys, interviews, and reviews of instructional materials to determine the diffusion of educational innovation at the institutions of the faculty teams. Outcomes are to be based on the instructors' perceptions of the educational resources as well as the institutions' ability to coalesce as a community of practice. The research studies examine resource adoption by considering differences in initial intentions for and actual adoption at individual institutions, differences in adoption by individuals based on their perceptions of ease of use and usefulness of the resources, mechanisms used by the different institutions to encourage adoption, and roles that mentors play in adoption. The determination of best practices will converge through a multi-year, mixed methods research investigation, employing formative and summative feedback and utilizing the development and testing of classroom activities and materials and faculty professional development resources. This dual investigative approach includes correlation analysis of participant activity and performance data and a study of how classroom instructors reflect on and employ use of the 3D-printed models and learning activities based on those models. For a fifth goal, project findings, outcomes, and resources will be disseminated to facilitate the use and adoption of project materials to the broader community of multivariable calculus instructors. Ultimately, the project investigators aim to share a free visualization tool and learning resources for teaching 3D problems and concepts that can extend to other STEM disciplines and courses beyond calculus. The NSF IUSE: EDU Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.